(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.2' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 165002, 3601] NotebookOptionsPosition[ 160383, 3457] NotebookOutlinePosition[ 160792, 3475] CellTagsIndexPosition[ 160749, 3472] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["Exam 1", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.887203586315774*^9, 3.8872035919214087`*^9}, { 3.8965692908918962`*^9, 3.8965692949985943`*^9}}], Cell["Question 1", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.8872035562635403`*^9, 3.887203561802981*^9}}], Cell[CellGroupData[{ Cell["Data Center Reliability", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, 3.896569580567226*^9, {3.896570756364573*^9, 3.8965707665759983`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Show", "[", RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "18"}], ",", "0"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "14"}], ",", "0"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "10"}], ",", "0"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "6"}], ",", "0"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "0"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"2", ",", RowBox[{"-", "2"}]}], "}"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<1\>\"", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "18"}], ",", "0"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<2\>\"", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "14"}], ",", "0"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<3\>\"", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "10"}], ",", "0"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<4\>\"", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "6"}], ",", "0"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<5\>\"", ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "0"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<6\>\"", ",", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\<7\>\"", ",", RowBox[{"{", RowBox[{"2", ",", RowBox[{"-", "2"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "20"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "19"}], ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "17"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "15"}], ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "13"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "11"}], ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "9"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "7"}], ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "5"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"4", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "0"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"4", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "2"}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", RowBox[{"-", "2"}]}], "}"}]}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"3", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", RowBox[{"-", "2"}]}], "}"}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}], "]"}]], "Input", CellChangeTimes->{{3.608196740367448*^9, 3.608196753251458*^9}, { 3.608196789359242*^9, 3.608196914843504*^9}, {3.8866635020392427`*^9, 3.8866638554757957`*^9}, {3.8866639215155153`*^9, 3.886664287744197*^9}, { 3.8965741606635733`*^9, 3.8965742542662153`*^9}}], Cell[BoxData[ GraphicsBox[{CircleBox[{-18, 0}], CircleBox[{-14, 0}], CircleBox[{-10, 0}], CircleBox[{-6, 0}], CircleBox[{-2, 0}], CircleBox[{2, 2}], CircleBox[{2, -2}], InsetBox["\<\"1\"\>", {-18, 0}], InsetBox["\<\"2\"\>", {-14, 0}], InsetBox["\<\"3\"\>", {-10, 0}], InsetBox["\<\"4\"\>", {-6, 0}], InsetBox["\<\"5\"\>", {-2, 0}], InsetBox["\<\"6\"\>", {2, 2}], InsetBox["\<\"7\"\>", {2, -2}], LineBox[{{-20, 0}, {-19, 0}}], LineBox[{{-17, 0}, {-15, 0}}], LineBox[{{-13, 0}, {-11, 0}}], LineBox[{{-9, 0}, {-7, 0}}], LineBox[{{-5, 0}, {-3, 0}}], LineBox[{{-1, 0}, {0, 0}}], LineBox[{{4, 0}, {5, 0}}], LineBox[{{0, -2}, {0, 2}}], LineBox[{{4, -2}, {4, 2}}], LineBox[{{0, 2}, {1, 2}}], LineBox[{{3, 2}, {4, 2}}], LineBox[{{0, -2}, {1, -2}}], LineBox[{{3, -2}, {4, -2}}]}]], "Output", CellChangeTimes->{ 3.886663490143381*^9, {3.886663674020823*^9, 3.886663734603846*^9}, 3.886663792160627*^9, {3.886663844215858*^9, 3.886663857297524*^9}, 3.886663945725881*^9, {3.886663976015362*^9, 3.8866640130167294`*^9}, { 3.8866640475703583`*^9, 3.886664057520357*^9}, {3.886664114756781*^9, 3.886664130285997*^9}, {3.886664171136074*^9, 3.886664192295781*^9}, { 3.8866642338391523`*^9, 3.886664279282569*^9}, 3.896569337421486*^9, 3.896574141647415*^9, {3.896574186086124*^9, 3.896574254825137*^9}, 3.8967820781434383`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearAll", "[", "\"\\"", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dist", "=", RowBox[{"BernoulliDistribution", "[", "p", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[ScriptCapitalR]datacenter", "=", RowBox[{"ReliabilityDistribution", "[", RowBox[{ RowBox[{ "X1", "\[And]", "X2", "\[And]", "X3", "\[And]", "X4", "\[And]", "X5", "\[And]", RowBox[{"(", RowBox[{"X6", "\[Or]", "X7"}], ")"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"X1", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X2", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X3", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X4", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X5", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X6", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X7", ",", "dist"}], "}"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r", "[", "p_", "]"}], "=", RowBox[{"FullSimplify", "[", RowBox[{"Mean", "[", "\[ScriptCapitalR]datacenter", "]"}], "]"}]}]}], "Input", CellChangeTimes->{ 3.728987454155408*^9, {3.8866630499093018`*^9, 3.8866631065763187`*^9}, { 3.8866631474618673`*^9, 3.8866632949709387`*^9}, {3.886666467050343*^9, 3.886666472168633*^9}, {3.8868196813306293`*^9, 3.886819687605598*^9}, { 3.896573300165407*^9, 3.896573350711197*^9}}, CellID->522227289], Cell[BoxData[ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", "p"}], ")"}]}], " ", SuperscriptBox["p", "6"]}]], "Output", CellChangeTimes->{ 3.8866632462219687`*^9, 3.886663327579009*^9, 3.8866664730382547`*^9, 3.886666505051875*^9, 3.886819735317889*^9, 3.88720329573217*^9, { 3.8965733218439837`*^9, 3.8965733559761868`*^9}, 3.896579014690997*^9, 3.896582277287055*^9, 3.896587478379489*^9, 3.896588501065769*^9, 3.8965885635956507`*^9, 3.896782080613895*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox["p", "6"], RowBox[{"(", RowBox[{"2", "-", SuperscriptBox["p", "6"]}], ")"}]}], ",", RowBox[{"r", "[", "p", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"p", ",", "0", ",", "1"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotLegends", "\[Rule]", RowBox[{"Placed", "[", RowBox[{ RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}], ",", "Right"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Blue", ",", "Green"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.886653879874362*^9, 3.886653907183597*^9}, { 3.886654081551045*^9, 3.8866542085694723`*^9}, {3.886654239625498*^9, 3.8866542856528473`*^9}, {3.886654365056555*^9, 3.886654368041767*^9}, { 3.886654545729435*^9, 3.886654650307076*^9}, {3.886654690821553*^9, 3.886654731198338*^9}, {3.886819694772443*^9, 3.886819731475019*^9}, { 3.8872032711328583`*^9, 3.887203292181191*^9}, {3.896573438678541*^9, 3.896573441749414*^9}, {3.8965734994212217`*^9, 3.896573532362856*^9}, { 3.896573763379921*^9, 3.896573794858745*^9}, {3.896782065612709*^9, 3.8967821249006653`*^9}}], Cell[BoxData[ TemplateBox[{GraphicsBox[{{{}, {}, { Directive[ Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 0, 1]], LineBox[CompressedData[" 1:eJwVlnc0l+8fxqVFSamEkmQWoYxIPs9VykwDKb7Zs5CQSBIKkZmVlWwZZWRl 7+wtQnZEfJ4WycjP7/njfp/rvp9z3dfrvM+5z/uw4R01E1oaGhrJ9eX/Vdnk a0fFtAYxyXQut8rE/OTU22uGw2ziCJMNP2xo9+r0vu09/u/YziPn+M7MOtu1 08Kn9ia9ZLsKjljtlUUbPRmaPdPBa4e0oPpKlH1yxVmmY7b0sQGfLjbdFc3J MQyTUTVqKDQIM4DQqRgduVMZMtLtYllBbMYIbEnhCbIpl+GmxKRUR5vC4zHT fq3hNhmGNLpXvw/dwqF4muQXK59lfu+7G8abYAGXnpgLFQEzMp+ffPa7xmcF tqS9426GCzJGiwlV1VetcZJRSi2BhZbSK6xFaIfZgNX4XMyuUwwUFRPGot+9 tuBKeXidRouZUhFVLeHHZoc7riff69ocooh33s/mvXEPam0SA1oxfJRUOmGh smh70FyOrxUYFqFwYPz1tSEHpJq0jk1sO0kJuhfOQx5yBHsjv4X1CoWyJeNi 7FODB9BOuxwYzHKe8mCMlp0zwQlztGG5sQHKFCpr4YvCiYdw4zDx2nBdlWJ0 +fYeVb5HYPmX7HTL8Bqlz4MrYNrMBb8fWgs0hWtT+IYsNldedcW0i+jB5yyG FH1H+XN+866IlM8RD80ypUTuPeymFeaGH5W5xIKUJaU7c7mMV/IxnIs7hfda 2FAYL3xc+dH7GGKDrO/nNO9RFCezpMvuP8Gtkx+oPKuOlCduPvefsbmjgil8 o5yNC6WM3TT/WpE76nScUwu/PqYsFpz5zXXDA7Xk8buKMZ4UUfUDouSyB2af JL2lzDyjWFLn7xRHe+JznEvUnuEASrJ3+5unlKdwoTzRs68PoozwpH9TH3oK zxzdvJ5tYZT9FR5HOV28IPl71tGjKoJy9Ya+2ewhbywfb2rRXnlJ8V+QTiqs 8AbLJdZGdqM4Sv1z5nF3g2eQO7q0/SlLIoVW6DunKq0PZGtc3R24UyiU+kbd gwk+ENhwcDowII1y3ygpevqcL/rMxxOYTd5Scv659OdN+MLw8730P9eyKbMR /7E+9vDDYOUvuRtF7yh8EhLXLvH5I5tmUUHHMJ+i374zZP8Hfxh61pZu0nhP ibKY6Zg0C8Bg5F2xkvASisWTsadamwIhWRH8U2B/BYWuoy25/GogKjpzab1Y qihJHKW1vEmBkBNv8lVRrKHIWqZN+MwH4rSkxMlnWXWU4fcvNv6Ue45OOY0L AVcbKA+3enBphj2H+6tfjNNSzRQ2DduzZZPPsWPkzV5TwzZKfryePo9kEAr4 pdUZLDoo6t9VXJ49DUKa87PIDJUuyneKdMz33iDUqMzcmtDsofj58JdeOxKM vohnw6lBvRSBT3sHS+4Hg/fS5j9sq58oxnYkmzdbCHySm45I2QxTxDYGPcix DoHhXVcpPaNRCm2Q+MDAhxB8XxjQFRUbp7Rz9p7efCgU9+OjQ14KfKG8ynSM FrYPRWoIr6+SyhTFimBfvd4SinOKgtk0UdMUmZYyHTeeMGi/kj2bxTZL6Z/Z eKi7MwysX/xFsz99p7x2THZZPfoCovzx3U7mPykOdEojfG4vYNY77v6R7TdF /sW3M1f6XgCxT+69mJ6n7OXzj3MUCcdlbvOi1IE/lPHc47QJnuEw0xP/suPn X0rOuS7D5s/hkLxxO6FfeIVy2YCV55BvBP72e1hTgmgIju9F7orjETi45dLy n+8biNlHOl9spCPhxM3A4G22kSjeQSMf9TwSDivK9FJ/NhHPouOTa75GwkPk g5ZW3BZCU1BuKxVRKJw3Kb5kRkfwF02ZsbyIwudtF6KeKm8janqPHTWXi8bQ KsPOeitGIti0zTs4Ohrsdj/onLR2EYbzNjMlv6Ih7+wU8p8fE7G2uyB9Z/xL zLUaeM8J7SVa47QYTv19iWqpkJ220cxE9PEVS8MrMXhkyFRkwMlCSF86K5z3 LwY8N9QrXS33E3Sfx/2HNF5h6gFxpPYkO9Fr4UluffMK/dSSY6/2cxBFNSaa b4RicUZB0rSD7TDBxVBAJ6sVC41si95QCS7CW53u/Uf3WBSl3wh21+cmNMfS 2GgGYyFn1rrVYZKXKD+60hCyNQ4THpKtnbL8BJ/NxQdHxeKgbMstSp99hJhf I/vVnsWBg+vIvR+1goS2wlmfqbw48P7aL8NvJUTU+AedfjgaBzE751QIihBB ByWik6TisUwEaWbdPUEsGXuqSBvHgyvS4AqjnShhkNG70hoQD2/XR4zPXcWI 46cf6CxOxqOF6cDP/nIJ4sXjph1+uxOw/kJdDf11kvjXwF52mEiASnLfvhsS UkSLZjnHhdAEmASlh+79Ik2Ix+5qG65IwJTn250sV2WI6CkDF7vZBFB0Mp/I dlEIc/tNIy/PJcI6Z3Tx2OMzBF2IUtz3H4n4sddukPvweWJZanQ5bn8StnrQ XFHaJUdQP9+/pn4uCWut5Rej6eSJLv7X2/NDkmAgFzQ2w6xI1DXD1Kw0Cf7t +r4PBJWIQpveCtbJJNz00f2pd0GZiCneYu8kmQzv0yUvTNNViOf6Me3H9JNh nsf36OjsRcJ980nBIa9kFPIWOXlIXSZuXTYZOdOfDKc9zJ2ZS1cI8fFq5S3O KVjm36qcs+kqwe91I6kgKQUWL0oHNPquEvuFfq3dbE3B98OxVyTeaRBr9lx5 TYdeg+gfZ7F1uU78PFC001nxNS4L0e+RtNEkJipUzYVtXsNsZVxpq4UW0bjN 7dDzqteQthJRSnS4QZRmsj6Q/fYaereXREefaRNZV7O6f+1Jhbqyfjx9ig4R GjPsfc0kFaNWfC70y3qEvijx+wBdGqwOc7MTvoaEem/PpZbjaZDU9VIdkzEi 5B/eTn2klYY77S3Nf34aEYJ10bqjaWmIMHMuWbtjQixoLdcnX0xHSmDhtGn2 TWL6XxC3pn06Aill9+ye3yIGEwQe0b9Kh1ZSiNS+++ZE5ZyWmOX3dMz5Kpjl alkSvm6FL08EZ2Dvpk2C5qesCRe+K4tjxRlo7vT8tlxrTdg2TamFTGQg2C9h 9tE1G+I6MwvdH4k3qImw4X73xJbgSr1nW9L3BtfcXMsMme4Rey/taLm94S0a eU0vbau4R2z9lch/SOAt0qSM/xnctSdmZboH3ZzeQuxbXabXVweioF1UQYEj E08VvHdE7XQi/KdnFY/JZ6LgmBaT0ZgTYUqbosxklYmFo7d0HxY9JPaJH7g0 UJqJ4cf6obucHhHFTW5pBcJZUKDrtLPgdCP4+3QF02Sz0NP0dC4m1o0Injid EX0tCzEmr2Wo3I8Ji9X5N26PsqAlO7CdQ/wJcUDEPPtCaxb0fpzLefTQg/A8 rSBKjGXB/5j9ywssnsRPBZ53xxeyEJr/MjIvz5No1B/KZebIxultQ21Jq0+J B0FqhcO3s0Hdslg7VfyMmIwROdXplo1KH1qK7z0fQi2doagmNBuiE9t5dMV8 CYGauuLU0mykNzEK9xb7Ef3z0uV3d+TA3Orpc263QEKelvWM6eEcSMXMc5eT gUQO43yFpkQOQvsuVVTqPyee8WdWUXRyQFoHNfIpBxHSWtx1W9/kgPE9Y3f8 6RAi2YRGYakiB8J0Zravy0KI3bafP8x250B72ILP6nwoMfPsRUPHSg789ggw 3tIMIyJKtrdEqbzDxUXW0TsJ4cSmhq8X/fXfoShTXbieEkFY99S2utq9w4EZ ul+yAxGEItWl3ST6Hd6qHVzpOhRFLB763SUy+w79X7ojPrW/JDSfDPZX++TC uSJvWJ2MI3aN8B0zi8uFRkw6bbdBPNEgY+O8rSAXvjzMzTkf4wnphc2cqmO5 IGM/2eV+SCAO3BIxGZLKA7Py+KavH5KI7lrHfLdLeZj32nXr4aVkwperZiuv cR4mJA2Wq3qTiZUBzTSLgDzI4e7noJ8pxNClx+Tilzw0LzeaPlBOI8LSm89E L+fhuMwg9+BUGnGZjiUITPl4WOVKveCVTlRUpot7yuQjf+KHmGdnBhEn3uO4 JzgfRyX4WSr9Mgnj/Uc2CZ8pQFpOE4d6Tw7B7mCr0aFRgJvufIa2eEf0dJUk 21kUYOP2EZ7H6e8IeT9VpeKwAszItQkEeucS/DRO/opzBZD04C2S0M0nRrRr h7/RFqJ+5Rc1pS+fCH+/80QAayE27jpcIq9RQNDdTezqOVcIeo+gwqMahcTM lxZWo8hCJFT+OmBmXUTEy7Kab8kqxKhlpOGh1SLiv1eGxam1hTi6rzZZzreY aNL8o/P9eyFKT3o6/8suITKaOBOcFd7j2qBa3j72cuJO9l2h8N/vobo9dcni VBVBlRntaqArwvDhH795AqoIy/pLD5bZi/CiuWz22GQVcXP46AdduSJ0a9YK S4dXE/o7RvR5w4rA/3zBq4yhlrhySyUkR7IY9fMf50VP1xOtv99LT1woxgG5 TWb9KfWEiiv/KLN+MQodxDL27WsgFF/QCjt6FcOh4a23/p8G4kxt4Qd8KgZf 4u7y8pYm4vhh3uXmByVQmst/RdPaRrzNCIr7518Cz00SypyC7cQxKRrF4wkl aG6LbRK1bieOXB4ICW4qASmTdEx6tZ3gdH4u/B97KebZfvIf4u4kmD6tGkyV loJdbMup4thuItDYgo6tsxQ1T9XOqM93E4zf+94qT5ZiuUkzavuFHmLb1tzl N4xlSL8uGDz9t4eglTAPtdMrAxPR/jHbpJf4GfixfsOGcsTUhi7L3u8nSiyz MbGvHIF/91/gme4nnir65tcdK1+fb7kTQ28MEOw0sok+muXw2i9yRFpukJC7 88aFOasc1+TOPaQ7NkQ088lGhYhUoNn/xvQE7yiRHZL50UO6AqGudlrTFqNE GO3B3Q5yFWjM8zQZyBklDIb+eGndqMAZYz7joHNjxELoG3uOpxUw9W2ICrYe Jzg3s6m9HqoAc97UthPLX4jNdz39IqYrcKeWg0tRdZKYGflV/+x3BfYuHnB2 eD1J5JW04va2SuSpHTMW+G+KULZzFxI9WQlmnx0LJ5q+EnbjJF2JXyU43jxK NZz8Rmip6px/E16JKsez/nqXZwmivNElJqESLyVyhhLfzxL0UUkLru/Xz+VZ wpmD5ogYtRsTcl8q8amgP3hGjSTqK+vK22SqMGM1v5Di84NIbl6Z8FOoQoOe 4ZktjT8Ij17RbSpqVQjg3zDITv+TkJ2LuVpvVgXa9Snd0fsnUcLqMF0RVIXf Hf+EuIN/EVl3+PfkfK2CttKb3PKmecL/gY6U9a8qJJhohd3bt0Dc9gjWEf5X BZGLHKY0hguEQNRaStqealzjbjCOXl4gEut6ZRKIauxUzEziPrVIhB/0Mg0J qcZlF1XRI8NLhP2RMh+1V9UwLp4VZJFaJjTEfmftSqtG5eTriaXny8RuJf1l 3/JqxAolrr5WXCF87aQCPWaqYbacaz9QuUq4Nn19b3+mZn3IYRestKXBLUel HVqzNZC+tW9ojmYT0g4w6egu1IA+ZQvbW+lNmC3tyzCiqQWn3oMNf+02wYr2 porV3lq8b6LZJPZtE+x8PH2eyNSCJnlMVmNoM1xeVtO/9a2F+oS/9LmRraiA j9a7sFqUKF4ihLnpQDumlloYW4sMGuq5PFM6uPONKVbn1sJwdtdIFEmHZ5k0 Xn2DtVCe9nvyjW4bQispWzYK1cHatGYx8j8GfDTafI1Osg4lySElHSkMYN3S krTjbB1y/ny5VTDPgEhlbTlWjTr8bNGwCwnegdiuB+5CznV4x/nwYmEvI9K/ FNBqttShQHCjqWHlLlTSi65l3P4Ajc31C9H5e3Dk6vGCZ/c/gHb8D3/h3B4E xgjfufnkA96f3eekzrsX+mKCw9wRH+DfuQrGsL34p81THlnzAZZLvFFvnZkh nbXPxetAPehJmwgbUxbEL+2VNOWrx0XzcMUNySygl9tDnjtRD+eu4FDOSRb0 fdqptyZfj0m10X27b7LCYSM97G3r8eOgn/FnWzbkXlv+Z9RQj+q0Sb61xANg j/ubf7a7HvmMrSKbqQfw5Nsfq0PD9UiUO5KZLskONdffQ/2/6zH06Nv9oWZ2 fE+dK1PlbIDpQKfe0r+DEFodfrT+2KFSz6PS/SwnkhNq/u3nbcSD+cTfBvTc sPa4OgqRRlz/jyXjswQ3TptNVBufakTK4fjhTENutAts8n57sRHeaXXdWqXc +Jt9bo+sfSOc7/1s6bTngUpFFf+tD42o3plQ0LHEi1+DFVcKbjWBYBa5MKN8 FGVlV8QG7zZB445CvdyTo/CKHWHe8KgJ8WzaVfQlR8FuTDOgHNSEc/HbIlqE BSD/DSZDRU1wNd4+pcEmiMi/ZY6bGZpRxWT/6xetEM7sK41Xf9uMJVnHIuuw 49gUynxHrrAZ+nVfrux6fxz1e6xOS1Y1o1PfedvswHFcZjrUvf9jM2IZT0lo cZ2ALoPb5rHVZiieEInZk3MCTrRyN60vtuA0W/9T9c+iyKc2C/nNtkBM21v5 pokEHtzmXXq00IKr1n7h4oESIGad66xpWsG3mMetWCyB2mlhvat7W7HrT7Kl /O6T6J4IDDwg0wr7ht0yadUn8bP/6q9Un1bcafgQZyQuBaEPg4V1Am2Ic5ac uH7lNPZRLeYCJdqwQZC25Zz3adAwLx++caYNmqns5kFVp9FtyOZDarSha9pz QuukDB7+09BhdWuDWwv391guCpol2jaY97Zh/8ncKW9GQKJTP2mLbDuOdn5O H4w6izST1+UWCu2o4kms3lp+Fhx/yU/tKu3Q98fF22NnQcfpwhh1vR32Y06z X4/KYvD2SweR2+2QWgiZTiuWhTt9v5JmeDsitxSrvpo5h+4z6tRUajv2ve5O 8bgvj6VX4y9zfrWjybBqJT9WHofX7l4sXmzHJz+Sh6dBHlalIRnNtB2Imcza /m6/ArZKfzQn93WgU+g8fXqFAqTFtKbE0QEntftK51iVEMurN1Ie0IG3nLvk ORYvoM6dDKgP6cAP+7g4zSMqmBt3QUdEB15/GDnep6kC6fjYmLGEDpxWr+d/ XaSCLo4x7c2FHVD0yRYLcbuILawmn5RHOqCz/ZjXOPtlWG6z6Ow53glpd7/y DjlVJJfuy1c+2YkdjF4aq8aqGLauiig/3YkfR0YKr7urQq2XzSBVvhNCQpL1 EdWqkEqsJx9qd2Jzp4GU1nk1bCL4dvB4dcJ/rMvpzyV1RNuMKtgOd8LEaXhN 5ZkGPvL4CU5NdKLGta2hKlMDO/ukdmrPdEK3TO+DVY8GHhOBH+XmOyGwe+a6 +eFruLkdJmzbu3AxQTx3ofgaxJOiH1ec7IL+fjOp6OXraOq7Xsro34XVW4tZ E8n/4XH/FLN5cBfCH2w0be78D1KDDla14V1IfnRH4fu//5A4/OLQw4QuNNxs CJu7fgMPJ3vdpgu7cDa9P7mWQRtCv6/L14x3Ibr+uhTfYx0E7NRsczzVDTVq 4EDNJX3IM33l7yG6EVSbJF96Ux8ru++7Hj/fDfYoN7a+x/q4uS/8xNSlbngt 7vS6V6CPMwf7gq8adyNAWMNbncsAPwQ0NUUCuhG3qOtW8s8A6vKaoxMT3dBk SjG70GWEoj0n2sanu/HaSYihgTQC1yh96Ri1GxfWCstvMhjjp1Nx+MhiN15Z N/YwyhsjMJvjyiBDD2I9Va78LTJGM/uXsi7xHnQXaOkap5vg/C+b6Cr3HryO Zk5+lGKGjArlZ5XePZifMG9/VG+GPf7c9yv8exCzmCKXNG2GsSM96mXhPet9 CowxOXYTrrpS24syeiAubEYWvLuJ0oZ/jtndPchvqHla1XALJ2N9rsfyfMTW Pl4H672WyKp0cdwu8BET5totRRRLCI7fjbIX+YgZdZFYSTNLcPJpD6tIf8QL FivXhiJLbM84Zvb38kewKFmEqBvfxkhBi72a00ekcQjXH6u0gk/bzrBNnR9R /Zd6PaPDGlt+bCy80/sRPr7v5NOmreG6e/FT/+BHWH7hTa3ZYAN7jZGD2VPr fpM+4pdFbaA/kJWks/oRMs4lWmUhNjg5pZqXf6QX6i91ytj1bDHyL7j7pksv eI0VBqK32YFhtt3Hwb0XRuZ9iu48dpD6tOOcp3cv+P4VPntK2CHw3dPshOBe LI/7z4za2uHMTSf/oZR1v6XBgq+DdojrMFS82t6LD0Zlier592CYeKIEh/uA hdcVyi4O8H9udfcSXx/oVT2/DUQ7oOhRuoCOYB/EJypofIscsFuLN+KBRB+k 7JhVlRYcUL2DzT5PqQ9fT3Fon75zHzwONMcFbftQ9VRxco+ZI74otSXsq+7D xnvOelfuOIHHhz/geX0fVpwefqoKdoJxs8sDhtY+3FcO8NEpdMLYpeOqtJ/6 oCg4ycNA+xBD6s//zVH7EHFtbbvai4fo01HXqt3/CauvFH+9anBGo00vo53t J3joxzw9zO8K+nciS1SHT3gqRXtmg4wrFH8//XLL+RPsrm/S/XPFFR/spUr0 vD4hijjIwu/kihqniFsXYj5B71hDaFi7K0o9btRwNX7C4tqWN3UubsiKGHbs ONyP1V+8v3+Tj2F5lL1flL8f4SZq365vfYIj7zWlQ471QyD3WX8nxxO86utY uibZj4ivs9Rdl57An6XGaVClH1O7XuzOevMEt0NfO0859MM7cumJj407BJ7b uK229OPIx0XdcwyeSPLa6H30wQAy2QKrEeSN3RNej4RdBnBTzHNU5q03XMFo J+Y+gCMPGEzUG73x3wKrHsV/AGTh4y/NtM+w01hYQjV+ANlzgk2/7J7BEVqj 9xsHMODkf+awrg8uLrw9Vb9/EBeUmO2dz/th3ui/GdPiQVz1ufS0ICcQ9nuW 9/RVDKJomTRKrg3EQlUURaluEFW31zan9K3rw58DBTsGYZ3S3vr5XyAWh/Uk v08OwqMpYJxL5TmWbpi4O+7+DNpi2Zx9M89Bc9Waw/fWZxSqxzBuFA/G9vOe atksQ/DQWfVcoA2DTPkdpjr2IXBcdbARYguDlbRWe//hIRzWtRqzFwlD5/Fj lzYdG0LPGyavs9phiDzYqXT9zBCyUuglCvLDcOTPwbOrN4dwRJunTPjOC5xP yxNRKhqC78yW6URqOB7u+sIwqj0ME0N1bluBaAj055wZNBjGHmupb9xy0fiU 4GrXazqMKyeYA2b0onFSkn2wxXoYNa0yL/NDo/FdRz29yH0YrUqMJy/QvoRR eqVSSMa6znjkajP8EsryMZ4KK8OIyjyZz5D2CgxlgjS9F0ew9s1hc1ZlHOZU OHOfXRlBkreYmGRXHFoH9t4k1Eegn1oS2TwRh4C/q21JmiPw0XgrzUUXj90S 7a/sjEbQpcBU4Hg5HqwZdtjtOALL6lP3RkfiwRNZ+uhi4ghy/u6/3sWYCIr9 5dXqpRGoqNRZyUckY8H8q5PS6vr9mfe4Tr5JRpae21Lr2ggmnnsS4pXJ4FJ6 9+fTplHspDdsuzGdDDp2lp8k4yicXeJOaEmnoLtyaPIA9yjuZwTM7RlOgeUO q/a7F0bhef+9daVYKqITfRO4o0dhzRbLV7c9A3rnxGSGY0bRmcPe5c+bAa6x T92RcaNIU5LpMUcGXh/i37I7ZRT1+bmbde5mIDey8iZNzigmX95REBzMQHPg gtDnD6P4vCWx9372G6w+1C8M+zUKWmUHdl6LTOhqiLfQXxjDZl6DsQj/bOgf uBhbeHEMTAv3WJtfZsNg1OSu2ZUxXDkt+ZfuTTaMb79gq9UYg8vhpPb4pmzc 8lgycdUfw0u5Muvr9Dmwy6v4t3BvDDIzNvINnjl4xnzx+ETsGPi3OG9f8H6H vB6T4LKFMRyiUnvf5OThVHMW7WTYOA6dZUppkCkCp5zpfPD5CXBs5k17uVIO CXGJ57mTE7BmvyLHdaAawz/9GhI8vkDri1XX3/A6zIqperCJTmJjIuP6yN8I vm9CMxu6JlGc9FZ44mEbanjudVq7TaFX4tr5bU87EdDdY6TG8xVe25O3zlr2 gFSveE5b8xWyMok9xb59yNFgPnfKZhpCb2+d6MYgElqevBzbPYP7881hf/4O 488HbafdVTMwUjso6sY9hpHn5fO7rL6B8YCENOW/CSx0nGZ7zDiLhPi47/L3 J2EdwlXhWDKLTQ8f+x+t/gqWFq5dE7pz8Hm7+zFT1wzUezJW2P/NoYPTq1Tu 7SwepVgutdFQcXSIu7o1bxavHY8tPt5IRXk7Q6Ba6SxWDmb8+kpHxecQpmvK zbNINk2fyd1DRXdIiuXf6Vks/UntUzlKRbPu0TsqPHOI35+S+/AqFT80Bqfv h8yhedY0R+Q6FWNjef1yUXP4U8aXNaZFxZ3yoOMM8XNQMUpOV9SjYudRzkH3 zDkspCfF7zWnIp/J4wtP4xyUKYmBGS5UBGlQRZnXc//Ui7McTKMig9Ts1NOn Yv7FZgmDN1ScM7ol/tmEisW2W6tfMqnI8Tv1QN2CijWI+pO5VLA6fPQQsKeC gbM6k7Z8nffGXks3Hyp4RyZ+HumiwiWMaKlf/+8Iq1Lxmx4qvMsN5NreU3Hs ypsnon1UbNNvI1vKqBCtuLdX5jMVVfc737yrp4KI3XLy8hQVRe2E76FBKjT1 jzjeW6Yic8jnldUGEjfCfc8urVLx51FX08/NJHTbv9O70JB4Kj5jZbWNhMmZ 95Fe6/ux9jLTF/aQsOVULonaSWL/uWP/xfCQ8B2xWKvkJvGtm/dmmByJANb2 D/J8JJg152V9lUgEXREPbDpCwp47rvX+RRIRFSucPUIkDG6/qJXQIJEc6yf7 VZIEZ/VgI8WYRLl+pgejConEXIOeB64kitosLwxdIvFyeOWrlDuJfEKA6a0q ia0JqdozT0lksCdFX7xOwsbFiI0/gERkX+Q7X8N13+mEvs0vSYQpaDpqm5DQ qQv6rB1L4nk+M47dJMEWy5aenEDCKySwsen2ur/IoNruNBL3rniObnMk4ZGe naeQT8K6/FxKvxOJXZM3RkTfk7AU3nA77RGJNZZoyV0lJAwZHi4qref68eUR e1wliSv1Nju913P8YmMPZGsmoSIp0qMZRELYT+57cCsJheTZyCOh63kHdAfX 2kkQ7mZ89ZEk2gRTtmT0kBA8o0PZmrzut+uCkfoQCb7M/Rt7X5Oouys+fn2E BBdHX31yOonz51OULo6RYF1RuyqfTWLD6y322yZJ7LXYtX9f7nr/uLKZOqdI 7OxvGf6yzrGrRB/PpklsKVS08FjP3b5mu9w0S4KWf8sJjXISqQcWdDWoJFZD qxd4qkjIs5f/ayVJ/L5LPK75QGJlu3d00E8S5NiyQkjjeuXYfmfwF4kZ1fc7 jFvW+3ymh2/fPIlREfGIjV0k/taaUjX/kBiM+aHbtc7FwM3YabBIom9HJk9C HwlVo1LZ//6S6HpoOWM7QGLuzQkB2SUSrd+OZsmuc5u/32PLtkyi8b+pe7tH SbiV/Nk4sq5rGxJPj42TmNfVaQhdIVEhZbghZ537VFpmuvQqiZKUQx/c1jkV l86HtK7rwn2ffVXXOY9TdS1V/5F45xGpdnidq1FT4GD1un77+zrrjx/reU6U B3CvkUgzYh6q+L3O94Tzje26TursTAhc5yAMZXSz1nXs2cBb+us5u7u++Qyu 6+isiyLH1+9JrvvJ8Wddvzi0fX5tvTqu/f8j8T8Eel9b "]]}, { Directive[ Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 1, 0]], LineBox[CompressedData[" 1:eJwVl3c0F/4bxSVFiooUpUQiZGQl+byvUkpG2RQhCYkoKcoqJJRNRspskJmR vUfI5mPvfI18FGnSr99f97zOfc65z3n+uOc8vJeua1nQ09HRfVlDR/d/PWPx X1v5tC5ZEi7NqLS4KjuVrndpmEsar+b6VvfffH50+8auJzlcJ/Dq7MlADfu/ R8WObEt+xqUD9sN3xphsTRTo2KdD//IYgm96r9za764KbXMl980ELsLm57fe a8YRCprmDQVmEWbgcx3qenAoTUG+VSozhOsykmMeb8+2LFPYR4l7WRV7BaMm kce2d7YobHrD9HyJxxqFLU1r2hcGFZa234zYn2iDrQl1C6e8ZhQGHww+1hOw Q8SO6+rL+ssK5j8SK6t07CGwrzPUkpWe0iNmSIwiHPDIOCLzsdAmipoFa+FS zw00mbPK2qlxUMpjqmQeczki2DSzMs6YhyLdfidr/4VbeDeu8uBYoADlNZOY aGmsE5qHhuWT68UpezD+Sm/oNm4Nr5u6+UuGEnLrKT+NxxkxzhnKkxMUyvo0 9RcPzVzw4e8HkbWMJyguY/TcexPvglO0eE/mnTOUec6CyIKJe1A04r5teEqT Yn7Wll1TwA3le8RttNT1KFRvvsBpS3c8W8OlUnjPiCIwZLOuQscDn1i58rjW XaKYOisrPf7mASF9iqXv0yuU6G28noYRnhj+c9B7gesapTPjd+n+w/exKPQl HfoOFFbV7j9feu6j+1pbYANuUU5/ypQvvfMAiyqGUl6DzpQHnv53/Li84Ll8 RKFGxZ1Syn0lT6/QC7bWTX5HWu9TfuQrLvFd8AbTbsehHR4+FEntXZK0397Y 7vLa/niNH+Xa/LfrRbE+EPc/mMaUHUhJedT69iHlIfxOtfwUfRtCGeFPndUe eognDHLUxelwys5yb6G97r5wHpxZxxETRdG5YGo5x/MIUcsNr5Sbn1GeLMsn F5Q/gnL/Lve9p+Ip9cEc415mflCaZrhwZTmRQi+6sFeT3h9B6ps1rf6kUCj1 Hy7uTvQHZQ8ZzDB7Q7ljnhw7rRQAk/aFQnPxdEr2qntf7kQAmA+lPXt5OIsy F3We8773Y2g7rR9fCs+hCMjI6GkIPIHscP8xcbk8imnr5rCddU/QXHeJ6wz/ e0qMzUzbJ8tAbLFhDo02LabYPBh7aMgQBK81H/L6F8soTG0tKWU6QfAblTgT 9bWCkrynpGZ/chB4BqoUufZUU45fezPh/y0Ijftc8+w9ainD7yPXfj0ZDBnZ I/uGdjdQ7jF68xlEBMOtIr9k8FcjhUv3xrHST8FoULWpFuFuoeQlmJjyHw4B d4O+lblSG0V7Qc3d72EINjce2vmTp4OyQJGPW+gJgYTgV4lYgS7KY3/BEr0D oeh3lsyQPd9DEe7dNlB8JxSMtHPPqSW9lMuONK5HXGEQO1hRJsc3TJFaG+KS bR+Gm/TaPV9kRyn0IdL9/XVhiOesyddaM05p3dtzdB1POE5YrSYWfZ2gPM9w jhVzCod4wZ49DSxTFDvCvaLfHA6e6uZgOd1pikJzqbEnfwTeR4Vdmm6cpfTN rOXpbI+AdxKbS9zrBcor5xT3FaFI5DIbMQrJfKXcZlIZEfCMhGx83/u6oUWK cuSs4jlqJMJZNcxPvfpG2SbwJN5Z/CmGtekPPAr9Thl/J0Gf6PMUXx3ubnuQ 8JOSrdRxqWnwKXy8JXIVe35Tzppx8vMEROEca5+EljEd2bNQ6HV6PAqMVacU pvPWkDk340kH+WhwKTQ1zgiuJUUsdMoxwdEQu3jrd0QWA/GLTUip/i8ahdEb veR11xMDkZOM84gBixI3q/g2JiJYOGW5IzIGpTNMPv20DaS656DQ1ZOxuDIQ p6SwlpWEXml5FBobi5anK/1reLaQS98cZooXYyF3xIa9S30r+cuWn7o54RmC 7/ccFxtnJx/jDTcd+fkMRjql2c6qHCRW4s+1S+fi8CPQZLasfjuR1zgmlrsa B/nCY6F71+8kTIPjT4Z0n6NvNpbjeP0u0mPjQ2N8+xzhT55+upa4mxRWWxi8 FX2B1p1yvSmdewnfpnym44YvULKiIyI0y0seaTO97/Z6AZ2LP/+6bdlHDMbe cNENvIAr7cPLA377SZnQn4YwxnjYJRoXfBgWIAIO6i5CUvHQcNr5a0D5APn2 l9an5ReP6Vy6OkE1EWJ06pj/VG48OJ4W51JnD5LqJyFH743GY9U3un3muRgJ 2S0TmyyXgJC5XVES/IfIr8s+avKXE0DX+OWtDI8kMUvr+fMxMAFVtDdGWwWk iMRRF+MfnxIQs3qwiN1QhkTeb2R5zJYI7tu3hvb7yJLVBu5SXpIIaYrn88ny w6TZoGyPangiAinHUqzM5In0iy0tw+WJuG/i//ZQ/VESO2Xm7jiXiPCjzxdz CIVcdWIYeaaUBKP4h0z+YoqEKUwlfuFLElxCVBOK85XIb7nR3/E7kxGlvytY MP4EmR+8o6etlIwC0kTuhZ4kHYKvNuaFJeOE71WTH6GnSG0TrliWJOOdi7Rz esJpUuDQU875KRn7AqVSbYpUSFzReqe7h1MQHnb5qPAmNRJsGtd60DQFCUFe B+pOqBOvdbIiQ74pMEiJ10/w1SDWZy1GFPtS0F1uGJ0edY5Ij1edWe/6EtEq /E/3B2oTQd8LyfnJLxHU06u301iH7BRd/Gv18SVSW+m5Nkvqkr9OfLmNPK9w 2m1zcuEXPfJ1V+Fm19OvoPGxido5oE8myjWvijm8wodve2ZyWwzIB2ZPnuDK V1jUFDePaz5PSjI4XY7PvoKTzHmZrb0XSKZOZuci+2uYSzwq5/1sRMLjhh/p WbzG1qLdmqviJsRUkiztYnqDSnPagi/7JaLd06XRLPEGQaaKw7Oll4jyPdvX boZvcILhiviT6+ZEpDb24uibN3COm/rCPnqZLBv+rk9RT4XvIteuPiYrMr0a ss/AKRXDU2qSM6NWZCBR2G3D81S0NSYrna2wJhWfDaWuLaSCrt/9U3qoDQnw LHh2KDQNByylPNf7XyfuAud+jBWloUOz56Cbuj250TilFTaRBjXR4JzjvfZE n2MH03eZtzgmcuux2x8Hwvf61o1i6luojiyLijs6km0aLM22a9LBqyunNMZ9 izAuJgnyCKeD0yRHYduHW2ROoXPA8246ZPLTPPQkb5P8VslTp/ZkgOFH3lkO igt5Mj13+qByBm4HD9qZMN0lV+hfntlql4FvYR4J5dS7ZLv0Lo3+kgyUmX/n l3jkSooaPd/ki2Vi21AUOzXcgwhSL4q8OZ6JphrJ6xpbPUnoxNG0WL1MdBen kJJAT2Kz8u2tp1sm9lZtdyoNv092iV/NUv2YCc4YV5+vdV7E5+gpSTL2b75j Vv+jkTf5eoo/R2I5E9q+vD7c37zJB9Ohdxx7snDnRcXqOYmHxCVEq2DYNgvv TYV+fW5/RD7FiR9p98xCWcGLOjFvP6KVuqmwOjwLnmeZO6yP+hPh6tqi1yVZ mNUy+rL9XQDp+yZfdpMlG2vEHpbqUAOJMj2n4hXebLzWUXkpqxdEslm/lRvI ZEO9/cFd/8og4ieYUUkxzoZ/cU2nbEIwkTfcV8v4NhsPrHaU5riFkhQLulO/ yrNxbo/gCt+fUMJ2Y7BurjMbfO+osmL3wsiMX2RD259sMIrztJzwCidRxRub Y9RyIOPSHJuRG0kYGv5Tf2KagxYN62Z5lafEvqvmo4djDlL8GhZKhp+S0/Pu rRaxOXAX3ZozwBFNfvAsdYjP5cCQKzed+jKWGDwY6Kvyf4ej1r+sOQ7Hky0j Agct49/BVyfVRjYpnjQoOLgy578Du/NyXyh7ApFfXrdXc+wdTonJagj9TCC7 rMUthuRykf1K5FPDSBLprHHO89TIxeRQxjzVNJkE8FUz7r+ciyLBAJrDeDL5 02/wxiYwF3sf9bVfXUghQxr3aT8mc6FXLBT7TPg1iUhtUoz9nYvzm3zYeMtf k7NMO0KwNQ+XlpTDHhi8IeUVqdI+CnnwYDoWxRaSSuKlu5zZQ/MgSpntjxJK J5d3HmAQU8zHn+jefrNfWYT79g3dNt18KNExSwxfzCZdHcUpjjb5ENUL1BWt ySbKjzVViiLyUdnNUqMXmUME6e4+Of05HyHZonTPtHLJiFHN8Cx9AV51bxA1 qc0lT99vPhTIWQAupv2WQgp5hOlmUkeXUgE8b7jQL4rmk5nJZk7z6AKozv34 KyTyniQc57y6PrMA6S8XKb8z3pPzzy8Vva4pQJVw670thwtJo8F344WFAqQY O9sIqBWRtMa9ia6n3iNWfPOdkZAScj3rpujTpfcQZndgnlGrIPMKox0NTIVo LHwgHPisglyr13D5zV2I7rOXr9vQKojVsFDdxZOF2LaOW40aUUlMWUZM90cU Yr1rh9XnpSpyzlotLPtwEeRrT2668aWWfFx6Lz+hWgTGG0rzhvp1RM1DcJTD tAhNOSdsC0rryOlIejFn3yLc7XfRmwmuJ4o1BXXoLcKPrcEWMWc+EAne/b+b XIrxktaQsHvDR5KeFhK/+qQYF0u2/rzv+5EclKM7LZFYjG4lCdeXG1rIgbP9 YaGN/3xui8oXTK1kr2uw2HnuElwVn/7Du6uNbO1dMZsqKcE50/sPf9t2kKDL Nkxc7SUYSjVd013cQVgXqOlnPpVA7Vii2vtNnYSZ8d3vt6ylkNnEYJyc0Uno Za6GO5qUYk1iW5EZfTf5GtRdv2ZNGbJyO0QWBqmk+FoWJraXodB2I6VLuZc8 PB2QV3uwDBFcAXoHsnoJN93xJH+DMvynKHbrgF8fOXn9rTtHZhlWuzym6DQG SJPA8Zgw8XK0thlTDbaMkKywjG5v+XLIsQzaHtIcIRH0u9lunyzHJzutR2Mh I8Rs6Luv4YVysHByK/dwjpLl8LdOex6W44jiuttnxMfI3nVcWq+GytF80FnO 3HeCrLvp8zhquhx1zyomensmyMzIYr3fUjkmSdi0xoFJklv8EbbMFeBgz9tC mibJGUcvUUnZCphZjl25s3eKOI7TmIofV6B2V4v56z/TxFDT+MTbpxUwynte TjGeIaTsg3tcYgUeZ0XQfpXOkA0xycse7ysQqPOC5bf3LInTujBxcrICWzN2 W13i+0zqK2rLWhQqQZ/VkZKhukBSmv5MPD5VCfcysweDXgvEu0eSWU3rn/9y /GRW6QI5/jlOp96yElWtI/bnpL+QYs7b0+UhlegdXYmMFPxKMq8Lsmf/V4ka duqZRPEl8sTFWM5+sRKZxh6mUzeXiK13qLHYaiUmk1h1ZgqWiHDM35dv2Ktw IGLRVurkN5JU26OQSKpg9+CY5BrLZfJ0t++VsLAqxOkwb2Ru+0GcDpT6az2v wjOzXh9Gvp9EV2opc8ubKnC697sP3/xJ2FRMfweUVUE8RlNSYOcvEuAoF+Q9 U4VSutOyxx1+E4/G/947KVaDjhq844LqKrF2VmExnKsGm2faot1FerzZtdX4 4nI1kgLiL6eF0GOuhJpmTleDJ8+i4y7X0cOO3krNblsNCkdpK6cl18LR38f/ gUIN+D6cfPGLhQHuz6o2pAfU4PuKsWDL4DqUw98wJ6IG2wsZogR2rgf9mNbr ghc1aHrHm8iovx5eAmOnq97VoEj8iOnV9vXwy6DzpQ7UYHU+YLS5hRHhFZT1 a0Vr4XHkj97c5AZ0m6/TYzpci5873h7QEWEG5/rmZJZjtZDVPJOi68CM6DNG Jzl1axHVyUQV+suMFx0uXqKutWB5XVclzbcJqZP59AbNtbiicOtZrQ8rKjZI /k2zrcNc480+6n9bcUBHIt/vTh0cHr/6vGUnG4LixK5bPajD8tee7AJVNphK iQzvi6rDx6dcN89nsmHViL8suroOFwY7xv+4sUM+c7u77656tCbdSHWQ5EDC r22HrwjUg2s4ppjBhgMbTrLTlA7940iO29uSOEDt3WzyV7keuxlczrzdsR23 126A0416PAu5YjDAsAPv9H6vmjfUI/pU9frF75zgjv+Zd6yzHgyXe28UyHHh wex3O57hehR/LwhkcuGClsfSUN9SPQ5eFfVSW+XCwuvPpZp7G/DNgfWQK8su iK4Mu+F2A6bWmu3UObUbKYnVqzv3f4AvT5Vm5w5e2HvrjEL8A1g+TI/TgxdH LSeqLh/5gPfn2kPuXuFFqzDDo3T1D7gLNzr1PF78zFJiP+70AX7+V0/fM+SD WnmloHXdB0jtlHG7nr4PiwPl5/KtG/H32GnB3nABlJaekxq42YgDYl8EhOsE 4PtihGONWyPqNCJ/dPwQAPdluv4zIY2YdFfdIG0sCOVZWAwVNmLqcly5lPAB RP8sdV63qQmBMx1SCV1CUNxekqCd3gS5l1nx/bdEwRDOcf1kQRPCUu7vYc0W RT273dHDlU0I1vrBkDIvirNbeTp3dv9jiRVBJmsxXNzkuW5spQmux7NCki6J 4y79SSt79WYUnfWm738ngbz5JtHHc80oMXh8yn9SEi62+3+5LTfjSObt9feZ pUDmXGvt6T6if0P+hXfiUqiZFjPR2fYRmhtoy00uUuicCArapfARZSNX0M0u ja99Oouv/T8CCZmOAZoyEK0bKKgVbsGJ+KWczJXD2D5v8zlIpgX8Mw1bfcXk QMfxm/eCYgtYy2g6WSZy6LzE5U/TbUFqJ5v870o53FvVNeb0bEGjgtLFO4+P oEmmZc3VnhYcllvRuiN5FDLtpsnrj7f+68csk5QygjcWr8psTrUiWfJWcchv gj0/ab2taq04ERV5dPgwwLTXnTVGvxXz9uZe0VnAgO2z2+K2rTAxnKrr0FGE 14Y+FYOnrXjlFvZeSe8YOhW151/Pt8LMpkT4qocSfj0ff5a92IqJfPdY6wQl 8P69qV70418+k1FHVLUS7ErC0pro27BgbWfzeMMJMMp3X6Vtb8Ofq/+p1oWf gLyU4ZQ02tAS8zwiL/8kXuw3GSkLbENH6Lpytn2nUetFC6wPa0POLgXZp6qn 8XncHW1RbUhYv/G5ruNpyCe8iBtLbIPiBWZ559rT6NgzZrSuoA3dx8blr9qq YD2nRe+ZkTbEvpwWEao9g2vMNu1dEu0IWMMY1Z6kjpSS7XlnZNuRU/JNtpeq jmH7yqiyo+24m906IsyiAa0eLrPXyu14JOL8JtNJA3JJ9bR7Ru2Q10s0P6t+ FgxEgIXftx0brIMuhnidQ6zD6Kkbw+1g6ubraLyohW7+xyJTE+0w0TDX6HTV wmaq3GajmXbQfvX1Mj7Twn0S1H3yWzvCvoz2L/RrwWojLLg2diDvJuVtywVt SCfH3i+X7QDvjQf0M+Y6aKTql7A+6cCNo+c6JiL0cL9viuNqaAeYpW2z/xbq QW7gtl3N0w6MMfp8URnWQ9JwJM+9xA6Iy5to2h7Qx71PPZ7TBR1o9lOcXSrW h+iSvnL1eAd+VrpHStIMELjZoMX5SCeKlfjC65wvQHnrf4JdpBP308JGxZIu 4A/bHQ+JE50gNhLDjR8vwGr700NTGp0YVXOqeMlvBMXd1FCdy52Yvnhsca7d CF+EDQzEA//xrqFNA0cuQlvZYHRiohMfO+tMrkSZopD9UMv4dCeoCku+rpmm 4BvdUDI234la3UamjDpTfL1b9HTkRyeU2XqtzZZNEZS159zApi5cNjl6fL2u GZq4J0s7pLsge/0gvcWOSzix6BBb6dWF1cM7bvBkmSOt/IxfxaMunM8QKMto NAf7k313yp904ahkj7XxJ3OMHejSLn3ahfj2IYWt3JfhcVFuY2FaF4ztxOIG fS+jpGHVOauzC2brSpJ4rCwg+8Jf/wV/Nygjs9GrFEtkVrg7bxTuRmIe0841 JpYQGb8Z4yTejTM5/StCHpbYK2A0rCbfjdASVjdapSU2ph20/Hm2G1Hu2mLq Z6wwkt/spHW3G6oxMmtvmFrDv2VzBEN7NxTXtKZcSLXB+i9rC673dINZZ9ji epsNPNh+9PYNdIOpgLo+/bsNnHRHdmdNdWNVfq1X2olrMO3PTDZe6Ua3s4tP 9sg1yE5p5uYd6MFrc9vWtbx2GFkN7bRy74Ffg2fyhJk9Ns21+t/26kFggwSz mpM95HpZlHwe9WDD/TuH6/3sEZTzMCsxtAeCOyH6N8ceilZ3nwy97AF9Rrim NaMD4tsundZp7UE0hf2XQrYDLiUdKgYvFYXRX330OW/iSbDdTQ0BKhp+hxrc Eb+JQrdUYWMRKhjzNTdnKt8Em+H+KBcZKpLC2G5cvnUTVSxcTrkqVCS+Jj/G Om6C/zadhMgNKn6c4b2vHO6ISZWWxO1VVAhMFqnsF3YCv79gYHA9FegNMLul 7ITLTe4umz5S0fsjnH78khPGNCQ06XupcPsD7Ih1wpB28OrneSquwpB82nwb VGNtw5qdvXjQ1GIotXIbHxx6WB1v9CLa2nJWmuaMDTniv+Zv9yLD336PxWYX nF56OGnt2otXbaqzueIuqHOSKzbx7f33bzIVvLd3QfXdKGvVuF6wtjhPqS25 oMT7QjXfh158HIjkKlhzD5lRw85tvH3YtlP/uoGsG64JcfdJCvYhrDqxcd95 Nxx4byAfdrAPSbUqxVvd3PCc2vZL73AfVjSlK3Rr3fBkR/XdAbU+zHDoC3sa uMM2/JXr1O0+6GvbcZQe84BwsIPnSnMfZuNb/I1dPJHsu/aRkEs/WhwdX/Lv 9wLbhK+bmHs/Co6qRSrKe8EDrI5SXv3475XII7uzXji/zGlCedKPmfg1CXQu Xth8WUxGM6EfB0+LfF1t8YIzDEfvfOjHdyNrOzt3b6gvpx+p3zkAuiur367N +eCb+fmZK0UDkK5Pvxi9xg9O7L/ZqeX//HGW0rrdfliujKGo1A7gpUXeZxb5 f8w7GCTSNoDzDB50kzf88GPY5PDCpwHo3e+vK5v0w68LFl7ObIP4K60ULtvq Dzod+z0B1oNQHf1q96LgMTae8NHK2jGEJOMvSzGfg6BQdn1rLfcQVB9tyZ9a CYKdvGFrH+8QTP7clVJkDUa7xEENhoND6Ntv4bxDPBjRu9tV9BWH4HT7Eoup QzAOfN99bMVqCGbMBasmP4Jx4k2uuErhEGZ2F3w6tyUU97ZMbho1GsbB/Wae GdbhEO7LVhwwG4bji+Tuta7h6E30cOy5Mgzb7Gj1K0HhkD3MPdBsP4xWifYy 3fxwLBhrpxZ6DeNwYU7Q8LoImKdWqISlDaPurmZdcnIEzijH+Zz6Mwy7uxpS 0guR2FQqQtejPgJudaMonpxofFbb+87v3Ah0TcR1JZui8bF/mxXRHsGqkzOX wWQ0An+utCQbjIA9a/7TwI4YsMm0Pnc0H8Fjw7jaJtcYcKY5gs15BLv3bJM4 qx4L/ugSN/WkEbxQs5I6+PsZKE5nV6p+jaB6xpff9MMLxCYFJO6LHYXlPuHL D54l4aKudPMG1TFkx+xM6PJ+jdwui9DS5TGIbp1JiJHNwJGmTPpPEeOIdlU8 Ts3Oxt6TV76FnpjAmM1uzw0ReZCRlgl+92kCUbL+Bck1hRj++rgh0XsSuxO3 H/14swxzUpreXJKfwCrvHjoaVwmBWdGZNR2fcKp2u2R8Rg2q+W+123tOYaNV OmOaQwMCO7vMtfj/A0lySk+yaAZNuzyYvvo/rMm99NB/oBXZuhxKRxymIc5+ cl25SwcSmx88G2ObQVeq7VtryW58rzO6y1Y5g6Enkd9OOfViJLjs2xa7WfjG TfIFrB3EcttRrvuscxDwXyhe+Xdn+zC+cufiOazblOAn6zaGHc18WyYufkaj qFDyRM4EtLvS/nCvfkZ0iKUiA+sUvprEXxt4Mw+a3Rfj7R3TKDPN8GZVo8HK cu+E9fM5FLZcUx3SoOHVI6HX5mlzyCPCW9M1aWA60p9r9n4OadzJser6NKS/ Wf/6asccoqnROQGXaLA9y8mcyfgZt875jDI705B57IL2BofPEFE0pjCm0GA4 M9D7S3keAhk71/a8omHTR905N5158O2h1qek0lCiHGDEeGkenH+0dJSzaHgv NGWw33Ue6wtO23gX07BqTekMz5nHqLh01NoOGgZV6a6p8NIwEPflYkcXDXeX 9qSyi9NAZcngT6TSMOmcrzWmQMPHWaHM40M0+KSsDAYY0FD8kqfOc5qGLcyW 37cH0VCwfTBAc46GjPihAIY4GnK8o7V4aTSoOnAFLf/b6405x1D5Eg3nDzqP TdXRkNzenhj0nYbyis+SU/9yXxwLsjb9RUPuWPXizDgNsZnq4hIrNLh3JO9f /EJDJM/Gb3//0sARd7jh//o/hXf1+w== "]]}}}, { DisplayFunction -> Identity, AspectRatio -> NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, AxesLabel -> {None, None}, AxesOrigin -> {0, 0}, DisplayFunction :> Identity, Frame -> {{False, False}, {False, False}}, FrameLabel -> {{None, None}, {None, None}}, FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, GridLines -> {None, None}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None}, PlotRange -> {{0, 1}, {0., 0.999999999999985}}, PlotRangeClipping -> True, PlotRangePadding -> {{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks -> {Automatic, Automatic}}],FormBox[ FormBox[ TemplateBox[{"\"UpperLim\"", "\"Reliability-iid\""}, "LineLegend", DisplayFunction -> (FormBox[ StyleBox[ StyleBox[ PaneBox[ TagBox[ GridBox[{{ TagBox[ GridBox[{{ GraphicsBox[{{ Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 0, 1]], { LineBox[{{0, 10}, {20, 10}}]}}, { Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 0, 1]], {}}}, AspectRatio -> Full, ImageSize -> {20, 10}, PlotRangePadding -> None, ImagePadding -> Automatic, BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { GraphicsBox[{{ Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 1, 0]], { LineBox[{{0, 10}, {20, 10}}]}}, { Directive[ EdgeForm[ Directive[ Opacity[0.3], GrayLevel[0]]], PointSize[0.5], Opacity[1.], AbsoluteThickness[1.6], RGBColor[0, 1, 0]], {}}}, AspectRatio -> Full, ImageSize -> {20, 10}, PlotRangePadding -> None, ImagePadding -> Automatic, BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}}, GridBoxAlignment -> { "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, AutoDelete -> False, GridBoxDividers -> { "Columns" -> {{False}}, "Rows" -> {{False}}}, GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}}, GridBoxSpacings -> { "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], "Grid"], Alignment -> Left, AppearanceElements -> None, ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> False], TraditionalForm]& ), InterpretationFunction :> (RowBox[{"LineLegend", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Directive", "[", RowBox[{ RowBox[{"Opacity", "[", "1.`", "]"}], ",", RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", InterpretationBox[ ButtonBox[ TooltipBox[ GraphicsBox[{{ GrayLevel[0], RectangleBox[{0, 0}]}, { GrayLevel[0], RectangleBox[{1, -1}]}, { RGBColor[0, 0, 1], RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> True, FrameStyle -> RGBColor[0., 0., 0.6666666666666666], FrameTicks -> None, PlotRangePadding -> None, ImageSize -> Dynamic[{ Automatic, 1.35 CurrentValue["FontCapHeight"]/ AbsoluteCurrentValue[Magnification]}]], "RGBColor[0, 0, 1]"], Appearance -> None, BaseStyle -> {}, BaselinePosition -> Baseline, DefaultBaseStyle -> {}, ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, If[ Not[ AbsoluteCurrentValue["Deployed"]], SelectionMove[Typeset`box$, All, Expression]; FrontEnd`Private`$ColorSelectorInitialAlpha = 1; FrontEnd`Private`$ColorSelectorInitialColor = RGBColor[0, 0, 1]; FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; MathLink`CallFrontEnd[ FrontEnd`AttachCell[Typeset`box$, FrontEndResource["RGBColorValueSelector"], { 0, {Left, Bottom}}, {Left, Top}, "ClosingActions" -> { "SelectionDeparture", "ParentChanged", "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> Automatic, Method -> "Preemptive"], RGBColor[0, 0, 1], Editable -> False, Selectable -> False]}], "]"}], ",", RowBox[{"Directive", "[", RowBox[{ RowBox[{"Opacity", "[", "1.`", "]"}], ",", RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", InterpretationBox[ ButtonBox[ TooltipBox[ GraphicsBox[{{ GrayLevel[0], RectangleBox[{0, 0}]}, { GrayLevel[0], RectangleBox[{1, -1}]}, { RGBColor[0, 1, 0], RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> True, FrameStyle -> RGBColor[0., 0.6666666666666666, 0.], FrameTicks -> None, PlotRangePadding -> None, ImageSize -> Dynamic[{ Automatic, 1.35 CurrentValue["FontCapHeight"]/ AbsoluteCurrentValue[Magnification]}]], "RGBColor[0, 1, 0]"], Appearance -> None, BaseStyle -> {}, BaselinePosition -> Baseline, DefaultBaseStyle -> {}, ButtonFunction :> With[{Typeset`box$ = EvaluationBox[]}, If[ Not[ AbsoluteCurrentValue["Deployed"]], SelectionMove[Typeset`box$, All, Expression]; FrontEnd`Private`$ColorSelectorInitialAlpha = 1; FrontEnd`Private`$ColorSelectorInitialColor = RGBColor[0, 1, 0]; FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; MathLink`CallFrontEnd[ FrontEnd`AttachCell[Typeset`box$, FrontEndResource["RGBColorValueSelector"], { 0, {Left, Bottom}}, {Left, Top}, "ClosingActions" -> { "SelectionDeparture", "ParentChanged", "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> Automatic, Method -> "Preemptive"], RGBColor[0, 1, 0], Editable -> False, Selectable -> False]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{#, ",", #2}], "}"}], ",", RowBox[{"LegendMarkers", "\[Rule]", "None"}], ",", RowBox[{"LabelStyle", "\[Rule]", RowBox[{"{", "}"}]}], ",", RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), Editable -> True], TraditionalForm], TraditionalForm]}, "Legended", DisplayFunction->(GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"], ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> Automatic, BaselinePosition -> {1, 1}]& ), Editable->True, InterpretationFunction->(RowBox[{"Legended", "[", RowBox[{#, ",", RowBox[{"Placed", "[", RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", CellChangeTimes->{ 3.886654209613905*^9, {3.886654286611533*^9, 3.886654304186021*^9}, 3.886654474752037*^9, {3.886654610235767*^9, 3.8866546652038116`*^9}, { 3.88665472586182*^9, 3.886654731992627*^9}, {3.886819732601428*^9, 3.886819736842751*^9}, 3.887203298083955*^9, 3.896573795707345*^9, 3.896579016694997*^9, 3.896582282464028*^9, 3.8965874805612164`*^9, 3.896588502793065*^9, 3.8965885652795687`*^9, {3.8967820681296787`*^9, 3.8967821267992687`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearAll", "[", "\"\\"", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dist", "=", RowBox[{"ExponentialDistribution", "[", "\[Lambda]", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dist4", "=", RowBox[{"ErlangDistribution", "[", RowBox[{"2", ",", "\[Lambda]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[ScriptCapitalR]datacenter", "=", RowBox[{"ReliabilityDistribution", "[", RowBox[{ RowBox[{ "X1", "\[And]", "X2", "\[And]", "X3", "\[And]", "X4", "\[And]", "X5", "\[And]", RowBox[{"(", RowBox[{"X6", "\[Or]", "X7"}], ")"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"X1", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X2", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X3", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X4", ",", "dist4"}], "}"}], ",", RowBox[{"{", RowBox[{"X5", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X6", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X7", ",", "dist"}], "}"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"FullSimplify", "[", RowBox[{"SurvivalFunction", "[", RowBox[{"\[ScriptCapitalR]datacenter", ",", "t"}], "]"}], "]"}], "\[IndentingNewLine]", RowBox[{"FullSimplify", "[", RowBox[{"HazardFunction", "[", RowBox[{"\[ScriptCapitalR]datacenter", ",", "t"}], "]"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"h", "[", "t_", "]"}], "=", RowBox[{"FullSimplify", "[", RowBox[{"HazardFunction", "[", RowBox[{"\[ScriptCapitalR]datacenter", ",", "t"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"FullSimplify", "[", RowBox[{ SubscriptBox["\[PartialD]", "t"], " ", RowBox[{"h", "[", "t", "]"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"Mean", "[", "\[ScriptCapitalR]datacenter", "]"}]}], "Input", CellChangeTimes->{{3.886663255298806*^9, 3.886663265145617*^9}, { 3.8866633003841133`*^9, 3.886663323350614*^9}, {3.886666547619432*^9, 3.886666564208694*^9}, {3.8965779935627527`*^9, 3.896578080757229*^9}, { 3.896578249042924*^9, 3.896578263824471*^9}, {3.896579054660852*^9, 3.896579061862083*^9}, {3.896582287114835*^9, 3.896582324807736*^9}, { 3.896587620413219*^9, 3.896587689929969*^9}, {3.896588478101186*^9, 3.8965885215316257`*^9}, {3.896588576897984*^9, 3.896588585632997*^9}, { 3.896588894372101*^9, 3.896588896203104*^9}, {3.896600252394491*^9, 3.896600253231295*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\[Piecewise]", GridBox[{ {"1", RowBox[{"t", "\[LessEqual]", "0"}]}, { RowBox[{ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "6"}], " ", "t", " ", "\[Lambda]"}]], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"t", " ", "\[Lambda]"}]]}]}], ")"}], " ", RowBox[{"GammaRegularized", "[", RowBox[{"2", ",", RowBox[{"t", " ", "\[Lambda]"}]}], "]"}]}], TagBox["True", "PiecewiseDefault", AutoDelete->True]} }, AllowedDimensions->{2, Automatic}, Editable->True, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.84]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}, Selectable->True]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.35]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "Piecewise", DeleteWithContents->True, Editable->False, SelectWithContents->True, Selectable->False]], "Output", CellChangeTimes->{ 3.8866633296679897`*^9, 3.88666650751689*^9, {3.88666654907437*^9, 3.88666656494932*^9}, 3.887203303425775*^9, 3.896578027437621*^9, { 3.89657806923717*^9, 3.896578081564866*^9}, 3.896578264884604*^9, { 3.896579005369419*^9, 3.89657901926206*^9}, 3.896579062696122*^9, 3.8965822908952627`*^9, 3.896582325589251*^9, 3.896587484025586*^9, { 3.896587650652997*^9, 3.896587690642049*^9}, {3.896588492787896*^9, 3.896588522470093*^9}, 3.89658858643631*^9, 3.896588897089941*^9, 3.89660025435573*^9, 3.8967821324280787`*^9}], Cell[BoxData[ TagBox[GridBox[{ {"\[Piecewise]", GridBox[{ { RowBox[{"\[Lambda]", " ", RowBox[{"(", RowBox[{"6", "+", FractionBox["1", RowBox[{"1", "-", RowBox[{"2", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"t", " ", "\[Lambda]"}]]}]}]], "-", FractionBox["1", RowBox[{"1", "+", RowBox[{"t", " ", "\[Lambda]"}]}]]}], ")"}]}], RowBox[{"t", "\[GreaterEqual]", "0"}]}, {"0", TagBox["True", "PiecewiseDefault", AutoDelete->True]} }, AllowedDimensions->{2, Automatic}, Editable->True, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.84]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}, Selectable->True]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.35]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "Piecewise", DeleteWithContents->True, Editable->False, SelectWithContents->True, Selectable->False]], "Output", CellChangeTimes->{ 3.8866633296679897`*^9, 3.88666650751689*^9, {3.88666654907437*^9, 3.88666656494932*^9}, 3.887203303425775*^9, 3.896578027437621*^9, { 3.89657806923717*^9, 3.896578081564866*^9}, 3.896578264884604*^9, { 3.896579005369419*^9, 3.89657901926206*^9}, 3.896579062696122*^9, 3.8965822908952627`*^9, 3.896582325589251*^9, 3.896587484025586*^9, { 3.896587650652997*^9, 3.896587690642049*^9}, {3.896588492787896*^9, 3.896588522470093*^9}, 3.89658858643631*^9, 3.896588897089941*^9, 3.89660025435573*^9, 3.896782132701907*^9}], Cell[BoxData[ TagBox[GridBox[{ {"\[Piecewise]", GridBox[{ {"Indeterminate", RowBox[{"t", "\[Equal]", "0"}]}, { RowBox[{ SuperscriptBox["\[Lambda]", "2"], " ", RowBox[{"(", RowBox[{ FractionBox["1", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"2", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"t", " ", "\[Lambda]"}]]}]}], ")"}], "2"]], "+", FractionBox["1", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", SuperscriptBox["\[ExponentialE]", RowBox[{"t", " ", "\[Lambda]"}]]}]}]], "+", FractionBox["1", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", RowBox[{"t", " ", "\[Lambda]"}]}], ")"}], "2"]]}], ")"}]}], RowBox[{"t", ">", "0"}]}, {"0", TagBox["True", "PiecewiseDefault", AutoDelete->True]} }, AllowedDimensions->{2, Automatic}, Editable->True, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.84]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}, Selectable->True]} }, GridBoxAlignment->{ "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.35]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "Piecewise", DeleteWithContents->True, Editable->False, SelectWithContents->True, Selectable->False]], "Output", CellChangeTimes->{ 3.8866633296679897`*^9, 3.88666650751689*^9, {3.88666654907437*^9, 3.88666656494932*^9}, 3.887203303425775*^9, 3.896578027437621*^9, { 3.89657806923717*^9, 3.896578081564866*^9}, 3.896578264884604*^9, { 3.896579005369419*^9, 3.89657901926206*^9}, 3.896579062696122*^9, 3.8965822908952627`*^9, 3.896582325589251*^9, 3.896587484025586*^9, { 3.896587650652997*^9, 3.896587690642049*^9}, {3.896588492787896*^9, 3.896588522470093*^9}, 3.89658858643631*^9, 3.896588897089941*^9, 3.89660025435573*^9, 3.8967821331294203`*^9}], Cell[BoxData[ FractionBox["199", RowBox[{"882", " ", "\[Lambda]"}]]], "Output", CellChangeTimes->{ 3.8866633296679897`*^9, 3.88666650751689*^9, {3.88666654907437*^9, 3.88666656494932*^9}, 3.887203303425775*^9, 3.896578027437621*^9, { 3.89657806923717*^9, 3.896578081564866*^9}, 3.896578264884604*^9, { 3.896579005369419*^9, 3.89657901926206*^9}, 3.896579062696122*^9, 3.8965822908952627`*^9, 3.896582325589251*^9, 3.896587484025586*^9, { 3.896587650652997*^9, 3.896587690642049*^9}, {3.896588492787896*^9, 3.896588522470093*^9}, 3.89658858643631*^9, 3.896588897089941*^9, 3.89660025435573*^9, 3.896782133972681*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearAll", "[", "\"\\"", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Lambda]", "=", "1."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"R", "[", "t_", "]"}], "=", RowBox[{ RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "6"}], " ", "\[Lambda]", " ", "t"}], "]"}], "*", RowBox[{"(", RowBox[{"1", "+", RowBox[{"\[Lambda]", " ", "t"}]}], ")"}], " ", "*", " ", RowBox[{"(", RowBox[{"2", "-", RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "\[Lambda]"}], " ", "t"}], "]"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"f", "[", "t_", "]"}], "=", RowBox[{"-", RowBox[{ SubscriptBox["\[PartialD]", "t"], " ", RowBox[{"R", "[", "t", "]"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"h", "[", "t_", "]"}], "=", RowBox[{ RowBox[{"f", "[", "t", "]"}], "/", RowBox[{"R", "[", "t", "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"h", "[", "t", "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0.001", ",", "10."}], "}"}], ",", RowBox[{"AxesOrigin", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.886663255298806*^9, 3.886663265145617*^9}, { 3.8866633003841133`*^9, 3.886663323350614*^9}, {3.886666547619432*^9, 3.886666564208694*^9}, {3.88907604087598*^9, 3.889076053392647*^9}, { 3.889076442467484*^9, 3.889076493440548*^9}, {3.889076608342888*^9, 3.889076613765264*^9}, {3.88907874297992*^9, 3.889078803584547*^9}, { 3.889080123564246*^9, 3.8890803338583*^9}, {3.889176655926646*^9, 3.8891768279544764`*^9}, {3.889230890351398*^9, 3.889230983275075*^9}, { 3.889231612811893*^9, 3.889231659540691*^9}, 3.8892326676627083`*^9, { 3.8892327651608143`*^9, 3.88923286672547*^9}, {3.8892330665876083`*^9, 3.8892330725229692`*^9}, {3.889233481153637*^9, 3.889233483431973*^9}, { 3.8892339073828707`*^9, 3.8892339082127943`*^9}, {3.8965784726702957`*^9, 3.8965785269397573`*^9}, {3.8965785703328667`*^9, 3.896578639006274*^9}, { 3.8965787449066887`*^9, 3.8965790389491987`*^9}, {3.896579073612748*^9, 3.896579159203478*^9}, {3.8965882886565313`*^9, 3.8965882893503857`*^9}, { 3.8965885409103813`*^9, 3.896588541238549*^9}, {3.896588582356346*^9, 3.896588583129958*^9}, 3.8965887922929497`*^9}], Cell[BoxData[ GraphicsBox[{{}, {}, {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ 1.], LineBox[CompressedData[" 1:eJwV1Hk8VVsbB/BTOubpnLPP3hHCVii6lEzJeqQyK6TrVjcZK643KYlLKm6S OZHQjZPqiNKVvJGhpEjGDF1jMg+HjswU737/WJ/n8/3jt571WWt9HiXXM/Ye a2k0Goda/69mld2Tam4HUXVTcBRDQBr8iIKSP7i+qOLIS4aPuDR8Kn22W0o/ BOnLK2q9YEuDBb114+OtUaj9SJOKuJo00NWH4wM2pSL/EgfTTitp6Df0tTjO yUb+tx+JbYun8m8LHjSdKEJdQZFJi+IM0I+trPuoXozchHmrVhgD/nZqmX33 vRhhx4u/x29ggNfE9L7i8BJUUZ4hMK3OgLXEjiEOtxyd7+14vmE/A2ReOLEM FypQ3dJwmVwwAyyEPzuIwQfkcocrmf+FAcmiaXt+5H5AVSGtBYwhBvSJO2tP yNQgf9nWEQ8eA4IZw5IN0zWosPaoH2+BAU9l5z/cfFSLXM/Td/szmBCZLKYY I9SITsQfmY8BJkxytyZjZ5qRg+H93qjbTMAex0jEPGhGaw5XnXuWzgTDnG/h 9K5mJCKyNbs2kwkRT56fmzNvQYbe/ha8HCYo5u+y+1e5FdFVlgJrypng8MpK PL2tDXUkXctmDjHhZZ33VdK4A00ehHdmmixw87AdWvXtQFUaPGyXNgskf2pZ dt3vQKdjTg6o7WSBu8YcI0mkE92Teb1txogFjKjLmYKtnSh9Cf1tac0CL/Ok 16Pe3SjoGGN+9TQLYl2cVz9b96ITGQrFDZlU/slB7f2evaiie5f95gcsMFg0 cSsI7UVZn0xSLnJZMBCvUhWf34vuZXXaSOexYNfr0ViL9V/RYP8nA4kSFowo nFd41f8VCXz9lmPaygKTruu7/w7qR/MNPOWWdRisy9d5FZ3Yj0RFDU0zhDCo jujV/zO3H53liTFOi2JwcIe+jlNPP1oO+esjXwqDEzeGtzD3DKAvNMyxXRaD y/r7118TGUQlcrm/s7QweH1LYNonZQj5k8qYrRMG4V55vsf+GULmKRptRUcw MIejk5Y1Q6hxNqNP+XcMGsfzR1V/DKHdpu/HeS4Y9O5x7f3qPIyKaqR0XLwx oE29rnNUHUGJbpvV60MwAJtL3N2Fo+jXpkTPlgwMLLe0y1k0jaKL0/INCvcx cBTSSTjEG0VtPu1Jng8w8HozGuitPIb2K720nczGIHGno9Wd2DH0roD/tScf gyF5jckZz3HEaNZmmFdiEDPZviOXmECfZv5DdxzEIOWjDve/2ydQ5fPwMvth DDjcOLm3NhOor4NhYzuKQaHrPnpH2ASK7UyeN56gzt/2rE2IP4GqzOhdgrMY 6JRHBLpVT6Jm58m0HevYMFGV6hxjxEd3HXYksJXYgB0bwTQs+CjPQVKuUJkN hvydNTWOfCRQUoo5qrDh2vomHeEzfNQxxvs1VpUNiqeFRMMy+ehwrYjzpCYb DomeL7goOIUKu/O0PA3ZUGxtI+LeOIX0mfJ6e+ypfNNqvqH7NIo+8z5L/BIb Do5m9Q+fnUYcKyOOXygbZNZYYkmh0+iXynqzz5fZkKt1y/9b6jTSTrS8mR7G huY4Nf2spmk0JEBzJCKp/rZ2pRJoBkXoiIs1JFL9ajhVvTKziPRrCrDnsmHy 7b6uaw1zqDeuXG25jg15itXbZ7rm0AG6igqzgQ2+IZaRLmNzyKFCQlOtkQ1T ugd0jejzSK6kx9vuExtmsp3ipwznUVu5TElKGxuW47z3Hns4jxaNXycv97BB +FhCrnbIAqroUXCV+cYGcqYruGvLEqrjVeNj4jhcuxBa76pHuZsnUSqBw8iC kuKo6RIKYQ54xEnikPvT8+3ssSX0JqHecLs0DjpCUyJScUtIlZyP9GXhsFeW fttkeglt9pDf3yiDgzto/vPw1TL6Q8vWXnEzDlnRIYO+1j/RH0qDdkq7cci+ GZBPP/ITbUkbe/uF8tOUs6GpJ3+iZ7LB9+8a41CU5SFTefUn2puT9oQAHOpL bGyIop/ohrfkyjpTHBZ48i9KN60gnqGL1DtzHKxtysJFV1fQ43aPjz0OOCxd W2V8cqJBmscho6RTONSli8+pOdNA5a/tlWqnccjIl+kI9aDBy8GYkVeUzXp2 cDT9aCDioCz81QuHWztPbY+MosG8p3/uZh8ctg002kMZDX4pVmi7dxYHFxNO 4lNyDWwX/PzDKgiH6uW97KjJNeCikTSZfgOHEKkdLebBAqBrzizFHuGQcpux 0rqVDueCrkRHvsGho3km6mqZIAydfKvU3IZDWHh1+IqfMLgvX1TtHsOB2bLX IHSjKNwqMTm5ukzt//md3cY8MSjMbOrARQkYOKDXGntCAo5z47UfEASoBj8p kZ+VBG+fy9E8ZQJOSd4QKnOUhsSDc5t6NQnQepoQ+02DAb/rbRC7rkeAGDet 6tksAzLuNnzLRwTIdMkX/tbAhB/17vZvzQjY5cU5fDOVBX99cNR5YEtAo9ny oTpqzhyy0SjrOkRAinOtMN+ATc1lbg77KAHnmu79hyOAQ57XywP+Jwi4GjIe adSDQ61JnVO3BwHrAsUE2guo+njT3EcvAu7Ua26jh6wHmaNrZtefIcD1eLWk zGEZMGM5DgWcI8DY3COzRFEWovSdm60DCIi50pbgOiwLfMd2n3+DCJCeLdfj l22Aq2ENxkGXCHhYkRMncV0Ouj0KMp5eIeBMjdRdpqs8GJlm0xbDCbDSuHDs kaYCDBe1rO+PICCt+1mg8awCFKgEpqfdIEDhg5t1ad1G2OLTvOQVQ8DRiOiR QStFGHnY8H0sjgAwu093KVIEzzTuq8s3CfiyLcuuW0UJ8lQG7vNuEXDd9OEF pUglWDsYpoDfJsDS3/1C+6wS1DhdF3S8Q/3gFvLAb0eV4Zf7yom/phGQfqTu cEeZMtjt23DV6C513yvbDRq2kNAc3S6ve4963/o7M1FxJLQqjFcvZxCwdV1u pU0CCbqpgdECmQT4GZTdkkokITy/3FaMMi2rTycxmQRFkfMNspTlArf6p94l ofbstTcGlB3I0lluDgnEeOqpAMoVAb1z76pI+GBaUTlFWeTJ9/cRH0g4Ej7g vEj5YN+62xYfSejhVC/SOAT0WKvr1dWTYFH8WV2a8qKSX0BLKwl+0rJ/bqOs VSuw0NdPQsr4+T4vygFr8OqsQRKqXTpO+1Eu01VL8RwmwSdHkB9I2TrTWn9s jATu94KF65RPXUi6ODVFwvdu3+WHlPNyHpk/nyYhMYQd+JTyXG/Rev9ZEoRc wmZfUA636nm5sEBCsnrJWCXlj5f514uXSLiSHeFWS5lZuPa34B8k9HHkO5sp O41j6sYrJHS6XrLrpHxPUXVxdZWEP3Ufv++j/D+VgY4i "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{0., 0.}, DisplayFunction->Identity, Frame->{{False, False}, {False, False}}, FrameLabel->{{None, None}, {None, None}}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None}, PlotRange->{{0., 10.}, {0., 5.909068206919637}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.889176730914851*^9, {3.8891768167960587`*^9, 3.889176828555921*^9}, 3.889230909149411*^9, 3.889230945140864*^9, 3.889231660372856*^9, 3.889232782631487*^9, 3.889232867523501*^9, 3.889233073194221*^9, 3.889233517067259*^9, 3.8892339088243647`*^9, 3.896578527615899*^9, { 3.896578621491197*^9, 3.896578639755615*^9}, 3.896578754169569*^9, { 3.896578804528798*^9, 3.896578809399897*^9}, {3.896578851633987*^9, 3.896578883276846*^9}, {3.896578918234569*^9, 3.896578986621378*^9}, 3.8965790211757507`*^9, {3.8965790838255043`*^9, 3.896579112197215*^9}, { 3.896579150741479*^9, 3.89657915980765*^9}, 3.896588290282835*^9, 3.8965885424963903`*^9, 3.896588793412013*^9, 3.896600259311976*^9, 3.896782135537678*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearAll", "[", "\"\\"", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Lambda]", "=", "1."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dist", "=", RowBox[{"ExponentialDistribution", "[", "\[Lambda]", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dist4", "=", RowBox[{"ErlangDistribution", "[", RowBox[{"2", ",", "\[Lambda]"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[ScriptCapitalR]datacenter", "=", RowBox[{"ReliabilityDistribution", "[", RowBox[{ RowBox[{ "X1", "\[And]", "X2", "\[And]", "X3", "\[And]", "X4", "\[And]", "X5", "\[And]", RowBox[{"(", RowBox[{"X6", "\[Or]", "X7"}], ")"}]}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"X1", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X2", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X3", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X4", ",", "dist4"}], "}"}], ",", RowBox[{"{", RowBox[{"X5", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X6", ",", "dist"}], "}"}], ",", RowBox[{"{", RowBox[{"X7", ",", "dist"}], "}"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"p", "=", "0.5"}], ";"}], "\[IndentingNewLine]", RowBox[{"\[Xi]", "=", RowBox[{"Quantile", "[", RowBox[{"\[ScriptCapitalR]datacenter", ",", "p"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{"0.5", "\[LessEqual]", RowBox[{"1", "-", RowBox[{"Exp", "[", RowBox[{"-", "1."}], "]"}]}]}], ",", RowBox[{"Print", "[", RowBox[{"{", RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"p", "*", "\[Xi]"}], RowBox[{"Log", "[", RowBox[{"1", "-", "p"}], "]"}]]}], ",", RowBox[{"-", FractionBox["\[Xi]", RowBox[{"Log", "[", RowBox[{"1", "-", "p"}], "]"}]]}]}], "}"}], "]"}], ",", RowBox[{"Print", "[", RowBox[{"{", RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"p", "*", "\[Xi]"}], RowBox[{"Log", "[", RowBox[{"1", "-", "p"}], "]"}]]}], ",", "\[Xi]"}], "}"}], "]"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"Mean", "[", "\[ScriptCapitalR]datacenter", "]"}], "\[IndentingNewLine]", FractionBox["2", RowBox[{"11", " ", "\[Lambda]"}]]}], "Input", CellChangeTimes->{{3.896588642109021*^9, 3.896588659373969*^9}, { 3.896588721413899*^9, 3.896588724515895*^9}, {3.896588775114819*^9, 3.8965888637025414`*^9}, {3.8965889138337*^9, 3.89658904112381*^9}}], Cell[BoxData["0.16442341735103014`"], "Output", CellChangeTimes->{{3.8965886477687902`*^9, 3.896588670074689*^9}, 3.896588711559341*^9, 3.896588865054153*^9, {3.89658893742447*^9, 3.896588940575057*^9}, {3.896589027753283*^9, 3.896589042007699*^9}, 3.8966002630978117`*^9, 3.89678213785366*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"0.11860642440917375`", ",", "0.2372128488183475`"}], "}"}]], "Print", CellChangeTimes->{{3.8965890277635317`*^9, 3.896589042017283*^9}, 3.896600263106243*^9, 3.896782137856061*^9}], Cell[BoxData["0.22562358276636932`"], "Output", CellChangeTimes->{{3.8965886477687902`*^9, 3.896588670074689*^9}, 3.896588711559341*^9, 3.896588865054153*^9, {3.89658893742447*^9, 3.896588940575057*^9}, {3.896589027753283*^9, 3.896589042007699*^9}, 3.8966002630978117`*^9, 3.896782137957707*^9}], Cell[BoxData["0.18181818181818182`"], "Output", CellChangeTimes->{{3.8965886477687902`*^9, 3.896588670074689*^9}, 3.896588711559341*^9, 3.896588865054153*^9, {3.89658893742447*^9, 3.896588940575057*^9}, {3.896589027753283*^9, 3.896589042007699*^9}, 3.8966002630978117`*^9, 3.8967821379596653`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Question 2 \[LongDash]\[NonBreakingSpace]Type II/item censoring without \ replacement", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.8872035562635403`*^9, 3.887203571506999*^9}, { 3.889075948658783*^9, 3.889075948905105*^9}, {3.889233499580864*^9, 3.889233499742189*^9}, {3.896685606598037*^9, 3.896685616824679*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearAll", "[", "\"\\"", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"data", "=", RowBox[{"{", RowBox[{ "10.2", ",", "89.6", ",", "54.0", ",", "96.0", ",", "23.3", ",", "30.4", ",", "41.2", ",", "0.8", ",", "73.2", ",", "3.6", ",", "28.0", ",", "31.6"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"data", "=", RowBox[{"Sort", "[", "data", "]"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"n", "=", "20."}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"r", "=", "12"}], ";"}], "\[IndentingNewLine]", RowBox[{"tau", "=", RowBox[{ RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "1"}], "r"], RowBox[{"data", "[", RowBox[{"[", "i", "]"}], "]"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{"n", "-", "r"}], ")"}], "*", RowBox[{"data", "[", RowBox[{"[", "r", "]"}], "]"}]}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"tau", "/", "r"}], ")"}]}], "*", RowBox[{"Log", "[", RowBox[{"1", "-", "0.75"}], "]"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"2", "*", "tau"}], "\[IndentingNewLine]", RowBox[{"Quantile", "[", RowBox[{ RowBox[{"ChiSquareDistribution", "[", RowBox[{"2", "*", "r"}], "]"}], ",", "0.025"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Quantile", "[", RowBox[{ RowBox[{"ChiSquareDistribution", "[", RowBox[{"2", "*", "r"}], "]"}], ",", "0.975"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ SubscriptBox["\[Lambda]", "L"], "=", RowBox[{ RowBox[{"Quantile", "[", RowBox[{ RowBox[{"ChiSquareDistribution", "[", RowBox[{"2", "*", "r"}], "]"}], ",", "0.025"}], "]"}], "/", RowBox[{"(", RowBox[{"2", "*", "tau"}], ")"}]}]}], "\[IndentingNewLine]", RowBox[{ SubscriptBox["\[Lambda]", "U"], "=", RowBox[{ RowBox[{"Quantile", "[", RowBox[{ RowBox[{"ChiSquareDistribution", "[", RowBox[{"2", "*", "r"}], "]"}], ",", "0.975"}], "]"}], "/", RowBox[{"(", RowBox[{"2", "*", "tau"}], ")"}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", SubscriptBox["\[Lambda]", "U"]}], "*", RowBox[{"Log", "[", RowBox[{"1", "-", "0.75"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", SubscriptBox["\[Lambda]", "L"]}], "*", RowBox[{"Log", "[", RowBox[{"1", "-", "0.75"}], "]"}]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ SubscriptBox["\[Lambda]", "L"], "=", RowBox[{"12.40", "/", "2499.8"}]}], "\[IndentingNewLine]", RowBox[{ SubscriptBox["\[Lambda]", "U"], "=", RowBox[{"39.36", "/", "2499.8"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", SubscriptBox["\[Lambda]", "U"]}], "*", RowBox[{"Log", "[", RowBox[{"1", "-", "0.75"}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "/", SubscriptBox["\[Lambda]", "L"]}], "*", RowBox[{"Log", "[", RowBox[{"1", "-", "0.75"}], "]"}]}], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.896680160353107*^9, 3.896680273356593*^9}, { 3.896684846080412*^9, 3.896684857080522*^9}, {3.8966848875284643`*^9, 3.8966849314046373`*^9}, {3.896685301146098*^9, 3.896685338595141*^9}, { 3.8966854791749773`*^9, 3.8966855440449457`*^9}, {3.896685579206609*^9, 3.8966855842342577`*^9}, {3.896685886008314*^9, 3.896685992782037*^9}, { 3.89668618954557*^9, 3.896686200190599*^9}, {3.896687370482834*^9, 3.896687394487364*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.8`", ",", "3.6`", ",", "10.2`", ",", "23.3`", ",", "28.`", ",", "30.4`", ",", "31.6`", ",", "41.2`", ",", "54.`", ",", "73.2`", ",", "89.6`", ",", "96.`"}], "}"}]], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.896782144649453*^9}], Cell[BoxData["1249.9`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.896782144652081*^9}], Cell[BoxData["144.39411016364593`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.89678214465403*^9}], Cell[BoxData["2499.8`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.8967821446559772`*^9}], Cell[BoxData["12.401150217444433`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.896782144680193*^9}], Cell[BoxData["39.36407702660391`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.89678214468223*^9}], Cell[BoxData["0.004960856955534216`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.8967821446841917`*^9}], Cell[BoxData["0.015746890561886513`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.896782144686154*^9}], Cell[BoxData["88.03607008454432`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.896782144688121*^9}], Cell[BoxData["279.44654997023713`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.896782144690098*^9}], Cell[BoxData["0.004960396831746539`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.8967821446920643`*^9}], Cell[BoxData["0.01574525962076966`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.896782144694037*^9}], Cell[BoxData["88.04518912417437`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.89678214469602*^9}], Cell[BoxData["279.47247128447606`"], "Output", CellChangeTimes->{{3.896601885840949*^9, 3.896601899732293*^9}, { 3.8966019317590523`*^9, 3.8966019453568373`*^9}, {3.896680253909157*^9, 3.896680274773491*^9}, 3.896685364268423*^9, 3.8966855051672487`*^9, { 3.89668553548955*^9, 3.896685544843717*^9}, 3.8966855851069393`*^9, { 3.896685911157158*^9, 3.896685921122596*^9}, 3.896685983651566*^9, 3.896686192146106*^9, 3.89668650404677*^9, 3.896687395236752*^9, 3.896782144697997*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Question 3", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.8872035562635403`*^9, 3.887203571506999*^9}, { 3.889075948658783*^9, 3.889075948905105*^9}, {3.889233499580864*^9, 3.889233499742189*^9}, {3.893051552889963*^9, 3.893051553359744*^9}, { 3.893068465963595*^9, 3.893068480337051*^9}, {3.893068535343358*^9, 3.893068536877803*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"ClearAll", "[", "\"\\"", "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"data", "=", RowBox[{"{", RowBox[{ "2", ",", "3", ",", "8", ",", "1", ",", "1", ",", "4", ",", "1", ",", "4", ",", "5", ",", "1"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ SubscriptBox["\[Lambda]", "0"], "=", RowBox[{"Mean", "[", "data", "]"}]}], "\[IndentingNewLine]", RowBox[{"LCL", "=", RowBox[{"Ceiling", "[", RowBox[{"Max", "[", RowBox[{"0", ",", " ", RowBox[{ SubscriptBox["\[Lambda]", "0"], "-", RowBox[{"3", "\[Times]", SqrtBox[ SubscriptBox["\[Lambda]", "0"]]}]}]}], "]"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"UCL", "=", RowBox[{"Floor", "[", RowBox[{ SubscriptBox["\[Lambda]", "0"], "+", RowBox[{"3", "\[Times]", SqrtBox[ SubscriptBox["\[Lambda]", "0"]]}]}], "]"}]}]}], "Input", CellChangeTimes->{{3.57951102764242*^9, 3.579511196986095*^9}, { 3.6105601066100607`*^9, 3.610560118453377*^9}, {3.610560161503229*^9, 3.610560175996048*^9}, {3.610560515453166*^9, 3.610560627635491*^9}, { 3.610560668811268*^9, 3.610560679858243*^9}, {3.610561022965145*^9, 3.610561061909997*^9}, {3.610561107153459*^9, 3.6105611536145153`*^9}, { 3.610561210183519*^9, 3.610561213637278*^9}, {3.610561268462509*^9, 3.6105613561059093`*^9}, 3.610561396169139*^9, {3.610561550030942*^9, 3.6105615548368397`*^9}, {3.610561589225767*^9, 3.610561716964278*^9}, { 3.610561781717751*^9, 3.6105617839827957`*^9}, {3.610561837584435*^9, 3.610561842161105*^9}, 3.6105619699199753`*^9, {3.610563629476055*^9, 3.610563634207102*^9}, {3.610565822327497*^9, 3.610565835237051*^9}, 3.629018471886993*^9, {3.62920045304277*^9, 3.6292006007139387`*^9}, { 3.629200667521793*^9, 3.629200688197505*^9}, {3.62920103532907*^9, 3.6292010354714537`*^9}, {3.691250450936693*^9, 3.6912504516234426`*^9}, { 3.691250482962205*^9, 3.691250530686264*^9}, {3.691500334377445*^9, 3.691500335664619*^9}, {3.8967126625993567`*^9, 3.896712709464292*^9}}], Cell[BoxData["3"], "Output", CellChangeTimes->{3.896712713788753*^9, 3.8967821597710648`*^9, 3.8971517007081213`*^9}], Cell[BoxData["0"], "Output", CellChangeTimes->{3.896712713788753*^9, 3.8967821597710648`*^9, 3.89715170071089*^9}], Cell[BoxData["8"], "Output", CellChangeTimes->{3.896712713788753*^9, 3.8967821597710648`*^9, 3.897151700712743*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"L", "=", "0"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"U", "=", "10"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"gammaL", "=", "0.038733"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"gammaU", "=", "0.591561"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Xi]", "[", "\[Theta]_", "]"}], "=", RowBox[{"1", "-", RowBox[{"(", RowBox[{ RowBox[{"CDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", RowBox[{ SubscriptBox["\[Lambda]", "0"], "+", "\[Theta]"}], "]"}], ",", "U"}], "]"}], "-", RowBox[{"CDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", RowBox[{ SubscriptBox["\[Lambda]", "0"], "+", "\[Theta]"}], "]"}], ",", RowBox[{"L", "-", "1"}]}], "]"}]}], ")"}], "+", " ", RowBox[{"gammaL", "*", RowBox[{"PDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", RowBox[{ SubscriptBox["\[Lambda]", "0"], "+", "\[Theta]"}], "]"}], ",", "L"}], "]"}]}], "+", " ", RowBox[{"gammaU", "*", RowBox[{"PDF", "[", RowBox[{ RowBox[{"PoissonDistribution", "[", RowBox[{ SubscriptBox["\[Lambda]", "0"], "+", "\[Theta]"}], "]"}], ",", "U"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ RowBox[{ RowBox[{"\[Xi]star", "[", "0", "]"}], "\[IndentingNewLine]", "1"}], "-", RowBox[{"(", RowBox[{"0.9997", "-", "0"}], ")"}], "+", RowBox[{"0.038733", "*", " ", RowBox[{"(", RowBox[{"0.0498", "-", "0"}], ")"}]}], "+", RowBox[{"0.591561", "*", " ", RowBox[{"(", RowBox[{"0.9997", "-", "0.9989"}], ")"}]}]}], "*)"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"\[Xi]", "[", RowBox[{"-", "1"}], "]"}], "\[IndentingNewLine]", RowBox[{"1", "-", RowBox[{"(", RowBox[{"1.0000", "-", "0"}], ")"}], "+", RowBox[{"0.038733", "*", RowBox[{"(", RowBox[{"0.1353", "-", "0"}], ")"}]}], "+", RowBox[{"0.591561", "*", " ", RowBox[{"(", RowBox[{"1.0000", "-", "0.9998"}], ")"}]}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ARL", "[", "\[Theta]_", "]"}], "=", RowBox[{"1", "/", RowBox[{"\[Xi]", "[", "\[Theta]", "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"ARL", "[", "0", "]"}], "\[IndentingNewLine]", RowBox[{"ARL", "[", RowBox[{"-", "1"}], "]"}], "\[IndentingNewLine]", RowBox[{"1", "/", "0.00535889"}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ARL", "[", "\[Theta]", "]"}], ",", RowBox[{"ARL", "[", "\[Theta]", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", RowBox[{"-", "3"}], ",", "3"}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.57951102764242*^9, 3.579511196986095*^9}, { 3.6105601066100607`*^9, 3.610560118453377*^9}, {3.610560161503229*^9, 3.610560175996048*^9}, {3.610560515453166*^9, 3.610560627635491*^9}, { 3.610560668811268*^9, 3.610560679858243*^9}, {3.610561022965145*^9, 3.610561061909997*^9}, {3.610561107153459*^9, 3.6105611536145153`*^9}, { 3.610561210183519*^9, 3.610561213637278*^9}, {3.610561268462509*^9, 3.6105613561059093`*^9}, 3.610561396169139*^9, {3.610561550030942*^9, 3.6105615548368397`*^9}, {3.610561589225767*^9, 3.610561716964278*^9}, { 3.610561781717751*^9, 3.6105617839827957`*^9}, {3.610561837584435*^9, 3.610561842161105*^9}, 3.6105619699199753`*^9, {3.610563629476055*^9, 3.610563634207102*^9}, {3.610565822327497*^9, 3.610565835237051*^9}, 3.629018471886993*^9, {3.62920045304277*^9, 3.6292006007139387`*^9}, { 3.629200667521793*^9, 3.629200688197505*^9}, {3.62920103532907*^9, 3.6292010354714537`*^9}, {3.691500342401845*^9, 3.691500477764662*^9}, { 3.691500513765565*^9, 3.69150052352726*^9}, {3.691500661453508*^9, 3.691500720591703*^9}, {3.691500899880618*^9, 3.691500905981058*^9}, 3.6915012316452637`*^9, 3.691667047188452*^9, {3.691675403131289*^9, 3.691675565001405*^9}, 3.6916760642110786`*^9, {3.691676172380252*^9, 3.691676178937262*^9}, {3.896713068706211*^9, 3.8967130695123777`*^9}, { 3.8967132104635077`*^9, 3.896713257045137*^9}, {3.896713665900667*^9, 3.8967136747072153`*^9}, {3.896714115688006*^9, 3.8967142201045303`*^9}, { 3.8967143523363113`*^9, 3.896714357836465*^9}, {3.8967144743968267`*^9, 3.896714480059052*^9}, {3.897151692551014*^9, 3.897151708884482*^9}}], Cell[BoxData["0.005272841376211979`"], "Output", CellChangeTimes->{ 3.896713258854409*^9, 3.896713676521207*^9, {3.89671421255935*^9, 3.896714220734174*^9}, 3.8967143594898987`*^9, 3.896714484059466*^9, 3.896782162109133*^9, {3.8971516972429037`*^9, 3.8971517111330147`*^9}}], Cell[BoxData["0.005358887099999986`"], "Output", CellChangeTimes->{ 3.896713258854409*^9, 3.896713676521207*^9, {3.89671421255935*^9, 3.896714220734174*^9}, 3.8967143594898987`*^9, 3.896714484059466*^9, 3.896782162109133*^9, {3.8971516972429037`*^9, 3.897151711135837*^9}}], Cell[BoxData["370.37128784627987`"], "Output", CellChangeTimes->{ 3.896713258854409*^9, 3.896713676521207*^9, {3.89671421255935*^9, 3.896714220734174*^9}, 3.8967143594898987`*^9, 3.896714484059466*^9, 3.896782162109133*^9, {3.8971516972429037`*^9, 3.897151711137815*^9}}], Cell[BoxData["189.65106830473295`"], "Output", CellChangeTimes->{ 3.896713258854409*^9, 3.896713676521207*^9, {3.89671421255935*^9, 3.896714220734174*^9}, 3.8967143594898987`*^9, 3.896714484059466*^9, 3.896782162109133*^9, {3.8971516972429037`*^9, 3.897151711139771*^9}}], Cell[BoxData["186.60580829238893`"], "Output", CellChangeTimes->{ 3.896713258854409*^9, 3.896713676521207*^9, {3.89671421255935*^9, 3.896714220734174*^9}, 3.8967143594898987`*^9, 3.896714484059466*^9, 3.896782162109133*^9, {3.8971516972429037`*^9, 3.897151711141716*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[ 1.], LineBox[CompressedData[" 1:eJwt2Hc4V+//B3Arb6OojORjZqWBjJByv7JCRhmFzAaSmfdQqIQUhRDZe4aW UZL7LSMVWUUikZDK1psQ3/O7rt9f53pczz/u67zO8z73uY7kaR+LcyxMTEyb mJmY/u965mHs9Po6ic7poiVq16kJ9BhRWa1VEn3Z/L/YG180QcS3xJ66RKL/ HfanP5vQhB6lxje/Z0j0gfozZxVYDoDhk8XcvmESPbrt5AYnlQOgUOlo87SB RKeYJGz+lHgAlmr21LtGkOiWq43PDp7WgtvNLXFtPCS6ttuxLb7ch0BCeNj3 OCc73TTXzIX9GoDvQcvj8gIb6GxtmLcvUQecCxkG72TY6H8Ef+/88l0Pas0u 06R2sNLDN28M+1Z9BLobT5a0K7LQtfO60mOfGIM1TUBIWZ6Zvit+ujjL1gwC LrKlOsox0XUCepZX1I5DeUAK1HmtYeHHLo6zdpagE/6bvvvsKvYP7B0oXbEG M8U5/cPBy/iz6c30B/U2kOph9+dn5hJW1y2s3NhxCrBYqDBzCgO/36B5X/mO E9j5OunhqgUcxUmXyX7pAu8OrI5MlMxhLaHvzC93nIUriStlRUUzmL5tqiy9 2RWOizv8FYubxCojkxbhIefBklXvelPIBN5D2pG/je4Jejvi+GurRjHnD2Xh JCZfGFZ2iYtKGcb6LM2m0OMHrK0/37BL9WPVO7UT/un+QC58yzHB1o8rxs9P D+b6w/frJUfejX3GLuOOcUdK/KFJ06MppuQzLh+uj9xS7Q8RhRN0IeXPOOVw zKGIDn/gDv1RvetwH36oEWw8y0IGvgNj+WZOvfjZovnU5XNkCBNo/q50uBcv vahsuHGBDAsz+VJ8Ur1Yr8V9KdqPDB8Lz2X3jvXg5IcR1gnBZEgSGE1z9u7B QbsjK/3ukeG/2ZH4i8EfsYuJXLFXIxmkioZDElO7sU9ywAtRcQpIRInenL7c jVXrm7i2yVBAzNs22tCuG0c69NO4dlNAWLUzZVmoGx/jAr+v+ymwlU5/6pjY hYuvFhiCGQWYP2WOyt7txKsbGis6AimAeWvjvDe14yXxMkZjJwVqPqpkSrS+ x2ep3pdGeyhQlfrgQVfke5x+twbW+ilQLpfauJ/jPeatsncRGqNABrrMWGNp wx5hnMaTfykQ5KNhF7P0Foc+zHyxUYIKGu0Vko9GmrFUhuOOF+eoMMLRoFBd 0IxD0g7uDD1PhWidTq268804g92wT8eLyCsnrVunm/CW23M8xWQiT5ON/LHS iJtlR27yhhL5+ftzEvwNWGAX1+cDGUSeW7Au1/sK/9LdqReQTaz3pWKjYsor 3FWtUFCaR+THOmUPSbzCWXJPZJdLqKCpznXKdk89NuPPmpStpoIo59INqVt1 WHGzjktdGxUuBvFn7+Otw2yFMVauHVRomVZ6ge69xJOp4sls3UTec376VHYt 9qNfnpL6ROS5/ScTntfgE4a8z38PU0Fs25JfDqrBgr8mpQ2+U8E/kv/2o6bn 2CCuLuHeGJH7mdJbO59h1mvjdoK/qEDWxjs3/KzCUz7u1zLmqfD2cb8On28V vuToylX4hwriMkv2koxKvGJUaZ6/SOTc++4eYqnErU6UiesrRN6X85ci/BSL cXl71LPQgGyC+cKynuCdPyy/Utlo8Bb3742TfYIPeAm1SrITeQH/6XLlx3iC S37yJCcNEsY33mu7V46NOH/66fHSYEiQNvi0oAzPaI4spW+mwW6DYbmU6lIs pHNSZnILDV7lVda49pXgbg9k6clPA54P4mymP4uxSrnqkTQBGtixRpqqrBTh Uc/CpnpBGsy6OA6tixRiPjEOw0khGhy82yI/trcAn2tSRvPbaXCTruzfqp2P 75ZYFU4J00BCnMSe7JyLZ18yPWkSoYGnmZ/5Vb8crOp+yzBblAbVwf33z13P xral7BoXxWiQ/szp5FnDTKzsO8m1IE4D1W2qP5U80vGOQ6IjeRI0aKVwBP+L SsV6ye//GUvS4MyHAd63Zcl4KCbPeozwsvLjnMT2JBy7wX6UuoMGcXfD1c7M 3sMif94VrhKWn7FtUeRLwBeiRpNoUjSgmymcWlWNw1N2FY/GCduUsUy1nIjF I1cdJ02kaTC4rZx59+xtnN0lbVRIeNPHE3KNqrfwT54zmEH4YNy6iUNAOL61 FHNUS4YGHuZFFxkvQnBNxKEJMuF923OUxNcDcT3v9oRcwtHx84HHb5Dxsuuv I68J9/wXGU36zwOrciczDRGWkLQz/mRxAn8w31EzSbj041XJy4e10dGLub4z hFc23Cl7+/w0CuqykvhBOIuDwv30oy/S3hTV9IGwbrQU/ZpZAAoSrbavIjzG 10U2e30VMUJcv90m3GhC5+fJCkXuZ3UtbQgnxmybJttHII8n/KVChN26vN/0 C0UhU726iTbi/jQEmnN1Pkaj5wzgDCC8oZQHfzC8iy721pC2EfY2PbCHQy4e Sai4fSsh5tczdS5Za8M9lIMzElUIo9i77D4jiWj8aa/kY2L+Rfte+ufU30ce 4/khUoQvkfnNOK+kodjdY5VjxPP9JgAvDtpnoOR//DfUCef3q/FriGYhzSaL HcFEH3iCXUIurGSjtUhcPUb055Xponr4zxwk6JJWxkWYKnZnKqMvF2lv/O4u RfTtK352qqs6H5W6Ou5SIfqYEGu29XdBAQr4oaywi+irocv3lg2JhUiTpWpO gOjzI5bN+zXJxegtm2PNO6L/1/XdNmcplSFFaX6VR8T+ae0Tuc2qWo4OSaeF KxD7S8C7i+Sm/hBp8kglZW6igdW7jHXBzEfIymRo0ZaLmP885+KX/CcoBYLr FFlpwFX3vSJG7ilSFVYW1GOmgeJNfPFw8VPU8qxK+eg6FQJEKFN5pRXIuc6K vo94H3DpD41eeFqFIuWDTjvPUUGB90WuqFo1Kj4twM89QwXLvnsu7VXViJNd K7VokgppXke/KNc8Q9xGb9Rqf1BBMbHqw196DVrO7mDoD1LBavx2Q8T7OmQ9 4csz3kys99gtRPMYRqzrN9vpDVRID9RBvzoxatE/VXSHToV5UpBDoQcd0eWy qplqqHAwbV8fl3c9onrxz5uUUqG9Ma2jk9yA1Jq3p4ZGU+GbfOTDksoGdEPq RsfdSCosRNOiQxkNqPBKYGT8DSoI2VqYqAU0oja1nlK/K1Q4PUlquR/YhFSX B5KTifNiQcAfO11/jcZuF3FlGVHBhvQ2faTuNTpk8ylJS58KL5YkgtxWXqNt 3X6vW4EK1/vfa/iQW5Bkq4VShzoVeLN3Pbni+gY9uz4qbi9DhV17vuWlG79D TmwiEbFrFHDWOR7Zv7UdffO8o/64mAKNKkXuTubtKOHmrnK+PArIyawbjES1 o0siTtxeGRRYDO0JobB0oKw7YkVs8RSocw3TDg7sQHksxpUtxHl7dM9Q9W2v TnTqI8uj8qMUcK1OKnlwvBs9NLM3NR4lQ+ROty7qxW6k3Waut3WQDOXJ+5cP x3cjt9/G5zt7yLAY+NHo04duJDo3cF2thQw3gW+CzeYDmsq+MJhYQoYHb6Ll HB0/ogSNjoo2LzLM9Ifnbb7Qiwbf1IlETvnDJSZyBiWsHwUd/vdb98tF0GE5 Q6a1DKNWiSVp/RRfsH0jvfnsrVEkno+c5Kc9oTHjHJ2WOoHSFbgOK8S7A2gi Ny33SfRr9zwH39RZSPtUbP8rdgadHJ+sP9XhAkXr1GGm5BlUF2ui1dvgApWy eq6C2TPon5i70qlqF3hPHvQ5/HgGcemthQVluADzFr7QpM4ZdDY3MEnaywVc jYKKdbfOIu6eh4hjowso1pgxUuNnUS7Ns4TrmDO8Sp2PMUmcQ+Opar33hhzA dqGM3Js+h2pLx2XY2hxgxsTd9nT+HHpfFNdz9bkDiK4N7AiomEO9n4z1MuMc IMC5uTK3aw5pRpmkB+s7gIJMcv8yzzyq8rqU8KTMHpLLteWKI+aRXLOlcHvE KfCtv1W34dIC+nopU97SxRakhbxmlUMWkDbjHinM3BZ6vY9JO99aQOFcBWmv DtmCtsi2yJrkBeRQt/DaXdgWuGl51j41C6i60EnW5oMNFOzBvz+tLKAlR7Lw C2MbGEhaEC698get/Oh8ZHH4JBh6O9EswhjIUtmMu9vSGm4wFLn+RDGQmJ6n qJSBNTRcYUpPimcgpTA31WANa9COyX41kMNAFpHfrcxFrUH10cgmt3oGqtmy Oc1j3Aok5tzyAtcYyEo4dA8t2AqWKL6deQGL6PS1kn3PHllCcXDI7kXPJfTr RviN08oWkBNY5OVPXkL0+Mve6nIWkHKp/eF04BISJ1s58otYQCRFVPVH5BLi 6lXWHttgAZ5ezw/2FS0hzpxKu4m+46DkMGv64vsSim/ymXMLPQ7PDrr4XrX/ i2qnjQvFBo5BywpUkkyWkYVs7cJlA3P4shirL2u1jFp+CskfVDaHufmhj3r2 y8i/Qotrk5g5iPy+xgjxXEa9PGcyv/wxA78Buvrq7WUUs6L0UKPADIRfQs1M 2zI607HZ8h2nGXheAdxnvoIq7jJYNw6YwBZmePPAchV9/qyBz5QYwyOF4Ofo 1CrK19RzaksxhmP2NcXdp1dRbEeckE6UMURXq0au+K2iA7zUChNPY9joLX/0 aOwqWmSVzR5VMAb2/q1tP1tX0df2jmGxKiNYrhjtkDf4h34FC/0itxrCN/eo T4Uaa+j+ndKmOcEjkJEwKzgIa8hR1NnmHccRsKOftOY3WkM6/cG55csG0LVN uuua7Rq6o/1G+96gAbxqrn1ne3kN6SGu6OECA8iWnqrjrl1DEqGP33lrGoDz 0LF8H7SOAkVJKuKu+jC9m/v5f1JMoDZbxMk9oAslQRMPpeSYYD6WvTO8Qxdc 214X7N7NBGn7hhkcTbow4B2WoKXCBCEZoTo7y3WJ781/Pqd0mUBskk347TVd KFCfkU09wwTCC6HDCXK64Kj7MUE4jwk2J6a+FArUgVa7TN/tMsxg9+6zWqDG YZis6ZNpEGCBPZI+AdeOakPuoEpWlTArBOaeib965QCkq6gKneBhg7PLKdXS QerAQKyBu/+xwagdi8TBBVX4zjuXY8zEDts9nKcuJCuD4JaIFoE5dpiyou1K qlSCGHUpP1MGO8hcF0jCZUrA4Yi3hy+zQw4r88LvfCVYKVn0WGAhAWvmjM+J RCUY0nPf1M1HgojV/ZxnaUpQHGBkEatGgv0xON71gBIcHOIe4LpEAp+vBrSh CEWoZC8K0wkmgXrXkatOlxRBYa/e3sshJFjQv3Nj3EMRJC8HXZm4RYJPE7oB W80UgZ1/UqIlhQSH3u9V7OZXhI4j78+F15LAxiVOZTlXAYy8PXhe0knwqM5d hD1RAV4lsFcvNJKAed+VNOGbClA5rM1xto0E6MsOIwdPBUgJfFiiM0iCAo/c PEM1BeDLOWp5+Rth/vSk+3IKcLtlfOXxGAlGJnqnZ7YrwBUBCVPJaRJMGVOq a9b2wqJW7R+beRJIdiUK75ndC76nbTJiF0nQ4Ud7mz+yF37eXDBoWSHBoD9r vVzPXvj//xcQrL5n6XHLXvgfoHcE9g== "]]}, {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[ 1.], LineBox[CompressedData[" 1:eJwt2Hc4V+//B3Arb6OojORjZqWBjJByv7JCRhmFzAaSmfdQqIQUhRDZe4aW UZL7LSMVWUUikZDK1psQ3/O7rt9f53pczz/u67zO8z73uY7kaR+LcyxMTEyb mJmY/u965mHs9Po6ic7poiVq16kJ9BhRWa1VEn3Z/L/YG180QcS3xJ66RKL/ HfanP5vQhB6lxje/Z0j0gfozZxVYDoDhk8XcvmESPbrt5AYnlQOgUOlo87SB RKeYJGz+lHgAlmr21LtGkOiWq43PDp7WgtvNLXFtPCS6ttuxLb7ch0BCeNj3 OCc73TTXzIX9GoDvQcvj8gIb6GxtmLcvUQecCxkG72TY6H8Ef+/88l0Pas0u 06R2sNLDN28M+1Z9BLobT5a0K7LQtfO60mOfGIM1TUBIWZ6Zvit+ujjL1gwC LrKlOsox0XUCepZX1I5DeUAK1HmtYeHHLo6zdpagE/6bvvvsKvYP7B0oXbEG M8U5/cPBy/iz6c30B/U2kOph9+dn5hJW1y2s3NhxCrBYqDBzCgO/36B5X/mO E9j5OunhqgUcxUmXyX7pAu8OrI5MlMxhLaHvzC93nIUriStlRUUzmL5tqiy9 2RWOizv8FYubxCojkxbhIefBklXvelPIBN5D2pG/je4Jejvi+GurRjHnD2Xh JCZfGFZ2iYtKGcb6LM2m0OMHrK0/37BL9WPVO7UT/un+QC58yzHB1o8rxs9P D+b6w/frJUfejX3GLuOOcUdK/KFJ06MppuQzLh+uj9xS7Q8RhRN0IeXPOOVw zKGIDn/gDv1RvetwH36oEWw8y0IGvgNj+WZOvfjZovnU5XNkCBNo/q50uBcv vahsuHGBDAsz+VJ8Ur1Yr8V9KdqPDB8Lz2X3jvXg5IcR1gnBZEgSGE1z9u7B QbsjK/3ukeG/2ZH4i8EfsYuJXLFXIxmkioZDElO7sU9ywAtRcQpIRInenL7c jVXrm7i2yVBAzNs22tCuG0c69NO4dlNAWLUzZVmoGx/jAr+v+ymwlU5/6pjY hYuvFhiCGQWYP2WOyt7txKsbGis6AimAeWvjvDe14yXxMkZjJwVqPqpkSrS+ x2ep3pdGeyhQlfrgQVfke5x+twbW+ilQLpfauJ/jPeatsncRGqNABrrMWGNp wx5hnMaTfykQ5KNhF7P0Foc+zHyxUYIKGu0Vko9GmrFUhuOOF+eoMMLRoFBd 0IxD0g7uDD1PhWidTq268804g92wT8eLyCsnrVunm/CW23M8xWQiT5ON/LHS iJtlR27yhhL5+ftzEvwNWGAX1+cDGUSeW7Au1/sK/9LdqReQTaz3pWKjYsor 3FWtUFCaR+THOmUPSbzCWXJPZJdLqKCpznXKdk89NuPPmpStpoIo59INqVt1 WHGzjktdGxUuBvFn7+Otw2yFMVauHVRomVZ6ge69xJOp4sls3UTec376VHYt 9qNfnpL6ROS5/ScTntfgE4a8z38PU0Fs25JfDqrBgr8mpQ2+U8E/kv/2o6bn 2CCuLuHeGJH7mdJbO59h1mvjdoK/qEDWxjs3/KzCUz7u1zLmqfD2cb8On28V vuToylX4hwriMkv2koxKvGJUaZ6/SOTc++4eYqnErU6UiesrRN6X85ci/BSL cXl71LPQgGyC+cKynuCdPyy/Utlo8Bb3742TfYIPeAm1SrITeQH/6XLlx3iC S37yJCcNEsY33mu7V46NOH/66fHSYEiQNvi0oAzPaI4spW+mwW6DYbmU6lIs pHNSZnILDV7lVda49pXgbg9k6clPA54P4mymP4uxSrnqkTQBGtixRpqqrBTh Uc/CpnpBGsy6OA6tixRiPjEOw0khGhy82yI/trcAn2tSRvPbaXCTruzfqp2P 75ZYFU4J00BCnMSe7JyLZ18yPWkSoYGnmZ/5Vb8crOp+yzBblAbVwf33z13P xral7BoXxWiQ/szp5FnDTKzsO8m1IE4D1W2qP5U80vGOQ6IjeRI0aKVwBP+L SsV6ye//GUvS4MyHAd63Zcl4KCbPeozwsvLjnMT2JBy7wX6UuoMGcXfD1c7M 3sMif94VrhKWn7FtUeRLwBeiRpNoUjSgmymcWlWNw1N2FY/GCduUsUy1nIjF I1cdJ02kaTC4rZx59+xtnN0lbVRIeNPHE3KNqrfwT54zmEH4YNy6iUNAOL61 FHNUS4YGHuZFFxkvQnBNxKEJMuF923OUxNcDcT3v9oRcwtHx84HHb5Dxsuuv I68J9/wXGU36zwOrciczDRGWkLQz/mRxAn8w31EzSbj041XJy4e10dGLub4z hFc23Cl7+/w0CuqykvhBOIuDwv30oy/S3hTV9IGwbrQU/ZpZAAoSrbavIjzG 10U2e30VMUJcv90m3GhC5+fJCkXuZ3UtbQgnxmybJttHII8n/KVChN26vN/0 C0UhU726iTbi/jQEmnN1Pkaj5wzgDCC8oZQHfzC8iy721pC2EfY2PbCHQy4e Sai4fSsh5tczdS5Za8M9lIMzElUIo9i77D4jiWj8aa/kY2L+Rfte+ufU30ce 4/khUoQvkfnNOK+kodjdY5VjxPP9JgAvDtpnoOR//DfUCef3q/FriGYhzSaL HcFEH3iCXUIurGSjtUhcPUb055Xponr4zxwk6JJWxkWYKnZnKqMvF2lv/O4u RfTtK352qqs6H5W6Ou5SIfqYEGu29XdBAQr4oaywi+irocv3lg2JhUiTpWpO gOjzI5bN+zXJxegtm2PNO6L/1/XdNmcplSFFaX6VR8T+ae0Tuc2qWo4OSaeF KxD7S8C7i+Sm/hBp8kglZW6igdW7jHXBzEfIymRo0ZaLmP885+KX/CcoBYLr FFlpwFX3vSJG7ilSFVYW1GOmgeJNfPFw8VPU8qxK+eg6FQJEKFN5pRXIuc6K vo94H3DpD41eeFqFIuWDTjvPUUGB90WuqFo1Kj4twM89QwXLvnsu7VXViJNd K7VokgppXke/KNc8Q9xGb9Rqf1BBMbHqw196DVrO7mDoD1LBavx2Q8T7OmQ9 4csz3kys99gtRPMYRqzrN9vpDVRID9RBvzoxatE/VXSHToV5UpBDoQcd0eWy qplqqHAwbV8fl3c9onrxz5uUUqG9Ma2jk9yA1Jq3p4ZGU+GbfOTDksoGdEPq RsfdSCosRNOiQxkNqPBKYGT8DSoI2VqYqAU0oja1nlK/K1Q4PUlquR/YhFSX B5KTifNiQcAfO11/jcZuF3FlGVHBhvQ2faTuNTpk8ylJS58KL5YkgtxWXqNt 3X6vW4EK1/vfa/iQW5Bkq4VShzoVeLN3Pbni+gY9uz4qbi9DhV17vuWlG79D TmwiEbFrFHDWOR7Zv7UdffO8o/64mAKNKkXuTubtKOHmrnK+PArIyawbjES1 o0siTtxeGRRYDO0JobB0oKw7YkVs8RSocw3TDg7sQHksxpUtxHl7dM9Q9W2v TnTqI8uj8qMUcK1OKnlwvBs9NLM3NR4lQ+ROty7qxW6k3Waut3WQDOXJ+5cP x3cjt9/G5zt7yLAY+NHo04duJDo3cF2thQw3gW+CzeYDmsq+MJhYQoYHb6Ll HB0/ogSNjoo2LzLM9Ifnbb7Qiwbf1IlETvnDJSZyBiWsHwUd/vdb98tF0GE5 Q6a1DKNWiSVp/RRfsH0jvfnsrVEkno+c5Kc9oTHjHJ2WOoHSFbgOK8S7A2gi Ny33SfRr9zwH39RZSPtUbP8rdgadHJ+sP9XhAkXr1GGm5BlUF2ui1dvgApWy eq6C2TPon5i70qlqF3hPHvQ5/HgGcemthQVluADzFr7QpM4ZdDY3MEnaywVc jYKKdbfOIu6eh4hjowso1pgxUuNnUS7Ns4TrmDO8Sp2PMUmcQ+Opar33hhzA dqGM3Js+h2pLx2XY2hxgxsTd9nT+HHpfFNdz9bkDiK4N7AiomEO9n4z1MuMc IMC5uTK3aw5pRpmkB+s7gIJMcv8yzzyq8rqU8KTMHpLLteWKI+aRXLOlcHvE KfCtv1W34dIC+nopU97SxRakhbxmlUMWkDbjHinM3BZ6vY9JO99aQOFcBWmv DtmCtsi2yJrkBeRQt/DaXdgWuGl51j41C6i60EnW5oMNFOzBvz+tLKAlR7Lw C2MbGEhaEC698get/Oh8ZHH4JBh6O9EswhjIUtmMu9vSGm4wFLn+RDGQmJ6n qJSBNTRcYUpPimcgpTA31WANa9COyX41kMNAFpHfrcxFrUH10cgmt3oGqtmy Oc1j3Aok5tzyAtcYyEo4dA8t2AqWKL6deQGL6PS1kn3PHllCcXDI7kXPJfTr RviN08oWkBNY5OVPXkL0+Mve6nIWkHKp/eF04BISJ1s58otYQCRFVPVH5BLi 6lXWHttgAZ5ezw/2FS0hzpxKu4m+46DkMGv64vsSim/ymXMLPQ7PDrr4XrX/ i2qnjQvFBo5BywpUkkyWkYVs7cJlA3P4shirL2u1jFp+CskfVDaHufmhj3r2 y8i/Qotrk5g5iPy+xgjxXEa9PGcyv/wxA78Buvrq7WUUs6L0UKPADIRfQs1M 2zI607HZ8h2nGXheAdxnvoIq7jJYNw6YwBZmePPAchV9/qyBz5QYwyOF4Ofo 1CrK19RzaksxhmP2NcXdp1dRbEeckE6UMURXq0au+K2iA7zUChNPY9joLX/0 aOwqWmSVzR5VMAb2/q1tP1tX0df2jmGxKiNYrhjtkDf4h34FC/0itxrCN/eo T4Uaa+j+ndKmOcEjkJEwKzgIa8hR1NnmHccRsKOftOY3WkM6/cG55csG0LVN uuua7Rq6o/1G+96gAbxqrn1ne3kN6SGu6OECA8iWnqrjrl1DEqGP33lrGoDz 0LF8H7SOAkVJKuKu+jC9m/v5f1JMoDZbxMk9oAslQRMPpeSYYD6WvTO8Qxdc 214X7N7NBGn7hhkcTbow4B2WoKXCBCEZoTo7y3WJ781/Pqd0mUBskk347TVd KFCfkU09wwTCC6HDCXK64Kj7MUE4jwk2J6a+FArUgVa7TN/tMsxg9+6zWqDG YZis6ZNpEGCBPZI+AdeOakPuoEpWlTArBOaeib965QCkq6gKneBhg7PLKdXS QerAQKyBu/+xwagdi8TBBVX4zjuXY8zEDts9nKcuJCuD4JaIFoE5dpiyou1K qlSCGHUpP1MGO8hcF0jCZUrA4Yi3hy+zQw4r88LvfCVYKVn0WGAhAWvmjM+J RCUY0nPf1M1HgojV/ZxnaUpQHGBkEatGgv0xON71gBIcHOIe4LpEAp+vBrSh CEWoZC8K0wkmgXrXkatOlxRBYa/e3sshJFjQv3Nj3EMRJC8HXZm4RYJPE7oB W80UgZ1/UqIlhQSH3u9V7OZXhI4j78+F15LAxiVOZTlXAYy8PXhe0knwqM5d hD1RAV4lsFcvNJKAed+VNOGbClA5rM1xto0E6MsOIwdPBUgJfFiiM0iCAo/c PEM1BeDLOWp5+Rth/vSk+3IKcLtlfOXxGAlGJnqnZ7YrwBUBCVPJaRJMGVOq a9b2wqJW7R+beRJIdiUK75ndC76nbTJiF0nQ4Ud7mz+yF37eXDBoWSHBoD9r vVzPXvj//xcQrL5n6XHLXvgfoHcE9g== "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->{True, True}, AxesLabel->{None, None}, AxesOrigin->{0, 0}, DisplayFunction->Identity, Frame->{{False, False}, {False, False}}, FrameLabel->{{None, None}, {None, None}}, FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}}, GridLines->{None, None}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> None}, PlotRange->{{-3, 3}, {0., 370.37120117040894`}}, PlotRangeClipping->True, PlotRangePadding->{{ Scaled[0.02], Scaled[0.02]}, { Scaled[0.05], Scaled[0.05]}}, Ticks->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.896713258854409*^9, 3.896713676521207*^9, {3.89671421255935*^9, 3.896714220734174*^9}, 3.8967143594898987`*^9, 3.896714484059466*^9, 3.896782162109133*^9, {3.8971516972429037`*^9, 3.897151711174015*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Question 4 \[LongDash] (X-bar,", Cell[BoxData[ FormBox[ SuperscriptBox["S", "2"], TraditionalForm]]], ")\[NonBreakingSpace]joint scheme for \[Mu] and ", Cell[BoxData[ FormBox[ SuperscriptBox["\[Sigma]", "2"], TraditionalForm]]] }], "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.8872035562635403`*^9, 3.887203571506999*^9}, { 3.889075948658783*^9, 3.889075948905105*^9}, {3.893068488938219*^9, 3.893068489604116*^9}, 3.894353121097001*^9, {3.894355313323731*^9, 3.894355315510623*^9}, {3.89436020311318*^9, 3.894360216677417*^9}, { 3.89453939123385*^9, 3.894539436008844*^9}, {3.89678693169916*^9, 3.896786931885768*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"n", "=", "4"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[Mu]", "0"], "=", "0"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["\[Sigma]", "0"], "=", "1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"incontrolARLindiv", "=", "500."}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"distmu", "=", RowBox[{"NormalDistribution", "[", RowBox[{"0", ",", "1"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"\[Gamma]mu", "=", RowBox[{"Quantile", "[", RowBox[{"distmu", ",", RowBox[{"1", "-", RowBox[{"1", "/", RowBox[{"(", RowBox[{"2", "*", "incontrolARLindiv"}], ")"}]}]}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Xi]mu", "[", RowBox[{"\[Delta]_", ",", "\[Theta]_"}], "]"}], "=", RowBox[{"1", "-", RowBox[{"(", RowBox[{ RowBox[{"CDF", "[", RowBox[{"distmu", ",", FractionBox[ RowBox[{"\[Gamma]mu", "-", "\[Delta]"}], "\[Theta]"]}], "]"}], "-", RowBox[{"CDF", "[", RowBox[{"distmu", ",", FractionBox[ RowBox[{ RowBox[{"-", "\[Gamma]mu"}], "-", "\[Delta]"}], "\[Theta]"]}], "]"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ARLmu", "[", RowBox[{"\[Delta]_", ",", "\[Theta]_"}], "]"}], "=", RowBox[{"1", "/", RowBox[{"\[Xi]mu", "[", RowBox[{"\[Delta]", ",", "\[Theta]"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ARLmu", "[", RowBox[{"0", ",", "1"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"distsigma", "=", RowBox[{"ChiSquareDistribution", "[", RowBox[{"n", "-", "1"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"\[Gamma]sigma", " ", "=", RowBox[{"Quantile", "[", RowBox[{"distsigma", ",", RowBox[{"1", "-", RowBox[{"1", "/", "incontrolARLindiv"}]}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Xi]sigma", "[", "\[Theta]_", "]"}], "=", RowBox[{"1", "-", RowBox[{"CDF", "[", RowBox[{"distsigma", ",", FractionBox["\[Gamma]sigma", SuperscriptBox["\[Theta]", "2"]]}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ARLsigma", "[", "\[Theta]_", "]"}], "=", RowBox[{"1", "/", RowBox[{"\[Xi]sigma", "[", "\[Theta]", "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ARLsigma", "[", "1", "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Xi]musigma", "[", RowBox[{"\[Delta]_", ",", "\[Theta]_"}], "]"}], "=", RowBox[{ RowBox[{"\[Xi]mu", "[", RowBox[{"\[Delta]", ",", "\[Theta]"}], "]"}], "+", RowBox[{"\[Xi]sigma", "[", "\[Theta]", "]"}], "-", RowBox[{ RowBox[{"\[Xi]mu", "[", RowBox[{"\[Delta]", ",", "\[Theta]"}], "]"}], "\[Times]", RowBox[{"\[Xi]sigma", "[", "\[Theta]", "]"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ARLmusigma", "[", RowBox[{"\[Delta]_", ",", "\[Theta]_"}], "]"}], "=", RowBox[{"1", "/", RowBox[{"\[Xi]musigma", "[", RowBox[{"\[Delta]", ",", "\[Theta]"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"ARLmusigma", "[", RowBox[{"0", ",", "1"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ARLmusigma", "[", RowBox[{"\[Delta]_", ",", "\[Theta]_"}], "]"}], "=", FractionBox[ RowBox[{ RowBox[{"ARLmu", "[", RowBox[{"\[Delta]", ",", "\[Theta]"}], "]"}], "*", RowBox[{"ARLsigma", "[", "\[Theta]", "]"}]}], RowBox[{ RowBox[{"ARLmu", "[", RowBox[{"\[Delta]", ",", "\[Theta]"}], "]"}], "+", RowBox[{"ARLsigma", "[", "\[Theta]", "]"}], "-", "1"}]]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"shiftmu", "=", "0.1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ARLmusigma", "[", RowBox[{"shiftmu", ",", "1"}], "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"ARLmu", "[", RowBox[{"shiftmu", ",", "1"}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ARLsigma", "[", "1", "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "-", RowBox[{"\[Xi]mu", "[", RowBox[{"shiftmu", ",", "1"}], "]"}]}], ")"}], "\[Times]", RowBox[{"\[Xi]sigma", "[", "1", "]"}]}], RowBox[{"\[Xi]musigma", "[", RowBox[{"shiftmu", ",", "1"}], "]"}]], "\[IndentingNewLine]", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "-", RowBox[{"1", "/", RowBox[{"ARLmu", "[", RowBox[{"shiftmu", ",", "1"}], "]"}]}]}], ")"}], "\[Times]", RowBox[{"1", "/", RowBox[{"ARLsigma", "[", "1", "]"}]}]}], RowBox[{"1", "/", RowBox[{"ARLmusigma", "[", RowBox[{"shiftmu", ",", "1"}], "]"}]}]], "\[IndentingNewLine]", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "-", FractionBox["1", "475.1454"]}], " ", ")"}], "*", FractionBox["1", "500"]}], RowBox[{ FractionBox["1", "475.1454"], "+", FractionBox["1", "500"], "-", RowBox[{ FractionBox["1", "475.1454"], "\[Times]", FractionBox["1", "500"]}]}]], "\[IndentingNewLine]"}], "Input", CellChangeTimes->{{3.610566851562529*^9, 3.610567236912198*^9}, { 3.6105676861101637`*^9, 3.610567688877533*^9}, {3.610600911285817*^9, 3.610600960216777*^9}, {3.610600991170627*^9, 3.6106010412172527`*^9}, { 3.610704762320983*^9, 3.610704762583201*^9}, {3.629216315522439*^9, 3.629216452138616*^9}, {3.629217432516494*^9, 3.62921745745497*^9}, { 3.6292177033925047`*^9, 3.629217735654768*^9}, 3.629217773089197*^9, { 3.6292643556015053`*^9, 3.6292643705074463`*^9}, {3.629269564739069*^9, 3.629269577276051*^9}, {3.6293408145163107`*^9, 3.62934081809447*^9}, { 3.629340849614993*^9, 3.629340899714168*^9}, {3.6293410738113337`*^9, 3.6293411054385777`*^9}, 3.6293418132986794`*^9, {3.629344670455871*^9, 3.6293446963241377`*^9}, {3.69181686049205*^9, 3.691817269191139*^9}, { 3.6918173152889547`*^9, 3.6918173772397957`*^9}, {3.691817756229415*^9, 3.6918177609950523`*^9}, {3.691818934978718*^9, 3.6918189662325373`*^9}, { 3.691819857216969*^9, 3.6918199536372137`*^9}, {3.693992738340912*^9, 3.693992739970517*^9}, {3.693992830553602*^9, 3.6939929888834543`*^9}, { 3.693993074971363*^9, 3.693993106567788*^9}, {3.694072436145273*^9, 3.694072464901731*^9}, {3.694072502280669*^9, 3.694072568903949*^9}, { 3.694072701672122*^9, 3.694072733828229*^9}, {3.694073518272686*^9, 3.694073544691671*^9}, {3.694073788461231*^9, 3.694073794569219*^9}, { 3.8943553547623367`*^9, 3.894355372038225*^9}, {3.894355500615923*^9, 3.8943556423704643`*^9}, {3.894356084544202*^9, 3.894356114818677*^9}, { 3.894356193045001*^9, 3.894356399386421*^9}, 3.894357064791*^9, { 3.894357305220826*^9, 3.894357437561091*^9}, {3.894357955574892*^9, 3.894357961498468*^9}, {3.894358022575542*^9, 3.894358041725114*^9}, { 3.89435809196469*^9, 3.894358118815227*^9}, {3.8943581730796013`*^9, 3.894358174053856*^9}, {3.894358278781322*^9, 3.894358330658637*^9}, { 3.894359301655196*^9, 3.894359418995804*^9}, {3.8967870714409723`*^9, 3.896787090439411*^9}, {3.896787128091507*^9, 3.8967871576042223`*^9}, { 3.896787427072158*^9, 3.8967875364748096`*^9}, {3.896787571888487*^9, 3.896787668765843*^9}, {3.896788612309732*^9, 3.8967886209209146`*^9}}], Cell[BoxData["3.090232306167813`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.896788622319502*^9}}], Cell[BoxData["499.9999999999718`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.896788622322082*^9}}], Cell[BoxData["14.795517054552388`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.896788622323935*^9}}], Cell[BoxData["499.99999999999955`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.896788622325823*^9}}], Cell[BoxData["250.25025025026417`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.8967886223276777`*^9}}], Cell[BoxData["243.87805836678993`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.896788622329523*^9}}], Cell[BoxData["475.14535595434`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.8967886223314133`*^9}}], Cell[BoxData["499.99999999999955`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.896788622333746*^9}}], Cell[BoxData["0.4867295758853451`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.896788622336067*^9}}], Cell[BoxData["0.486729575885351`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.896788622338393*^9}}], Cell[BoxData["0.48672959909270225`"], "Output", CellChangeTimes->{ 3.610567239133748*^9, 3.610567693644808*^9, {3.610601012543502*^9, 3.610601042368022*^9}, 3.6106011187313128`*^9, 3.610642047987028*^9, 3.6107047630913057`*^9, {3.6292163882729607`*^9, 3.629216409185521*^9}, 3.629216452678238*^9, {3.629217433093609*^9, 3.629217458022676*^9}, 3.6292177371686296`*^9, {3.629264356877611*^9, 3.629264371044162*^9}, 3.62926957830231*^9, {3.629341088458417*^9, 3.629341106626956*^9}, 3.629341813942048*^9, 3.629341935060129*^9, 3.6293447157382317`*^9, 3.629377688741724*^9, 3.629464182463147*^9, {3.691817219408803*^9, 3.6918172410763893`*^9}, 3.69181727251726*^9, {3.691817365268092*^9, 3.69181737793106*^9}, 3.691817761849625*^9, 3.6918189669984217`*^9, 3.691819011906039*^9, {3.691819910362315*^9, 3.691819954670439*^9}, 3.693992948138544*^9, 3.693992989450602*^9, {3.6939930792386293`*^9, 3.69399310920816*^9}, 3.694072399384956*^9, 3.694072466563129*^9, { 3.694072528922606*^9, 3.69407257334441*^9}, 3.694072734883706*^9, 3.694073545550599*^9, 3.6940737980672493`*^9, {3.8943553583915653`*^9, 3.894355379550091*^9}, {3.894355596923451*^9, 3.894355600577169*^9}, 3.89435565814253*^9, {3.8943561057526407`*^9, 3.894356120155342*^9}, { 3.894356278183148*^9, 3.8943563037824583`*^9}, 3.894356400011545*^9, 3.894357065951386*^9, {3.894357354932864*^9, 3.894357401056988*^9}, { 3.894357431872126*^9, 3.894357438153936*^9}, 3.894357964946764*^9, 3.894358175615156*^9, 3.894358347109344*^9, 3.894359407883816*^9, 3.89436046677752*^9, 3.896787098249817*^9, 3.896787542236806*^9, { 3.896787602602728*^9, 3.896787632388706*^9}, 3.896787669394834*^9, { 3.896788613505958*^9, 3.896788622340732*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Question 5 \[LongDash]\[NonBreakingSpace]Single sampling plan for attributes \ with RECTIFYING INSPECTION\ \>", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.8872035562635403`*^9, 3.887203571506999*^9}, { 3.889075948658783*^9, 3.889075948905105*^9}, {3.893068488938219*^9, 3.893068489604116*^9}, 3.894353121097001*^9, {3.894355313323731*^9, 3.894355315510623*^9}, {3.89436020311318*^9, 3.894360270691959*^9}, { 3.89678817818736*^9, 3.896788178311158*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"Clear", "[", RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"Context", "[", "]"}], "<>", "\"\<*\>\""}], "]"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["p", "1"], "=", "0.005"}], ";"}], " ", StyleBox[ RowBox[{"(*", " ", "AQL", " ", "*)"}], FontSize->9]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Alpha]", "=", RowBox[{"1", "-", "0.95"}]}], ";"}], " ", StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{"producer", "'"}], "s", " ", "risk"}], " ", "*)"}], FontSize->9]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["p", "2"], "=", "0.175"}], ";"}], " ", StyleBox[ RowBox[{"(*", " ", "LTPD", " ", "*)"}], FontSize->9]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Beta]", "=", "0.15"}], ";"}], " ", StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{"consumer", "'"}], "s", " ", "risk"}], " ", "*)"}], FontSize->9], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Q", "[", RowBox[{"c_", ",", "x_"}], "]"}], "=", RowBox[{"Quantile", "[", RowBox[{ RowBox[{"ChiSquareDistribution", "[", RowBox[{"2", "\[Times]", RowBox[{"(", RowBox[{"c", "+", "1"}], ")"}]}], "]"}], ",", "x"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"r", "[", "c_", "]"}], "=", FractionBox[ RowBox[{"N", "[", RowBox[{ RowBox[{"Q", "[", RowBox[{"c", ",", RowBox[{"1", "-", "\[Beta]"}]}], "]"}], ",", "5"}], "]"}], RowBox[{"N", "[", RowBox[{ RowBox[{"Q", "[", RowBox[{"c", ",", "\[Alpha]"}], "]"}], ",", "5"}], "]"}]]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"i", "=", "0"}], ";"}], "\[IndentingNewLine]", RowBox[{"While", "[", RowBox[{ RowBox[{ RowBox[{"r", "[", "i", "]"}], ">", FractionBox[ SubscriptBox["p", "2"], SubscriptBox["p", "1"]]}], ",", RowBox[{ RowBox[{"Print", "[", RowBox[{ "\"\\"", ",", "i", ",", "\"\< because r(c)=\>\"", ",", RowBox[{"N", "[", RowBox[{ RowBox[{"Q", "[", RowBox[{"i", ",", RowBox[{"1", "-", "\[Beta]"}]}], "]"}], ",", "5"}], "]"}], ",", "\"\\"", ",", RowBox[{"N", "[", RowBox[{ RowBox[{"Q", "[", RowBox[{"i", ",", "\[Alpha]"}], "]"}], ",", "5"}], "]"}], " ", ",", "\"\<=\>\"", ",", RowBox[{"r", "[", "i", "]"}], ",", "\"\<>\!\(\*FractionBox[SubscriptBox[\(p\), \(2\)], SubscriptBox[\(p\), \ \(1\)]]\)=\>\"", ",", FractionBox[ SubscriptBox["p", "2"], SubscriptBox["p", "1"]]}], "]"}], ";", RowBox[{"i", "++"}]}]}], "]"}], "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{ "\"\\"", ",", "i", ",", "\"\< because r(c)=\>\"", ",", RowBox[{"N", "[", RowBox[{ RowBox[{"Q", "[", RowBox[{"i", ",", RowBox[{"1", "-", "\[Beta]"}]}], "]"}], ",", "5"}], "]"}], ",", "\"\\"", ",", RowBox[{"N", "[", RowBox[{ RowBox[{"Q", "[", RowBox[{"i", ",", "\[Alpha]"}], "]"}], ",", "5"}], "]"}], " ", ",", "\"\<=\>\"", ",", RowBox[{"r", "[", "i", "]"}], ",", "\"\<\[LessEqual]\!\(\*FractionBox[SubscriptBox[\(p\), \(2\)], \ SubscriptBox[\(p\), \(1\)]]\)=\>\"", ",", FractionBox[ SubscriptBox["p", "2"], SubscriptBox["p", "1"]]}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"samplesize", "[", "c_", "]"}], "=", RowBox[{"Ceiling", "[", FractionBox[ RowBox[{"Q", "[", RowBox[{"i", ",", RowBox[{"1", "-", "\[Beta]"}]}], "]"}], RowBox[{"2", "\[Times]", SubscriptBox["p", "2"]}]], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Ceiling", "[", FractionBox[ RowBox[{"Q", "[", RowBox[{"i", ",", RowBox[{"1", "-", "\[Beta]"}]}], "]"}], RowBox[{"2", "\[Times]", SubscriptBox["p", "2"]}]], "]"}], "\[LessEqual]", RowBox[{"Floor", "[", FractionBox[ RowBox[{"Q", "[", RowBox[{"i", ",", "\[Alpha]"}], "]"}], RowBox[{"2", "\[Times]", SubscriptBox["p", "1"]}]], "]"}]}], ",", RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{"samplesize", "[", "i", "]"}], ",", "\"\<.\>\""}], "]"}], ",", RowBox[{"Print", "[", "\"\\"", "]"}]}], "]"}]}], "Input", CellChangeTimes->{ 3.532605428673882*^9, {3.581247455648386*^9, 3.581247466526042*^9}, { 3.58124756210353*^9, 3.5812475670958023`*^9}, {3.581247736672215*^9, 3.581247748140965*^9}, {3.58124785896005*^9, 3.58124785934206*^9}, { 3.5816718651212883`*^9, 3.581671990019285*^9}, {3.581672309336495*^9, 3.581672338433188*^9}, {3.581672452757107*^9, 3.581672453754414*^9}, { 3.62935306064037*^9, 3.629353083908741*^9}, {3.629353119733007*^9, 3.629353179657146*^9}, {3.6293532283641233`*^9, 3.629353297438581*^9}, { 3.629353334092362*^9, 3.629353359557012*^9}, {3.629354115348728*^9, 3.62935417080341*^9}, {3.629354256253642*^9, 3.629354256353353*^9}, { 3.6940819598965*^9, 3.6940819682609453`*^9}, {3.694082011272462*^9, 3.694082032908976*^9}, {3.89436033052048*^9, 3.894360344420833*^9}, { 3.894360386849416*^9, 3.8943603890973*^9}, 3.8943604595757113`*^9, { 3.894360573839727*^9, 3.894360581588643*^9}, {3.89436063457828*^9, 3.8943607093545713`*^9}, {3.894360740880534*^9, 3.894360769643279*^9}, { 3.894361775450355*^9, 3.894361805124662*^9}, {3.894361837317771*^9, 3.8943618682637978`*^9}, {3.894361959492255*^9, 3.894362038117751*^9}, { 3.894362315188889*^9, 3.894362343937152*^9}, {3.894362381989642*^9, 3.8943623844881372`*^9}, {3.8943629797527437`*^9, 3.8943631903567657`*^9}, {3.8943632557464867`*^9, 3.894363304921726*^9}}], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"Do not use acceptance number c=\"\>", "\[InvisibleSpace]", "0", "\[InvisibleSpace]", "\<\" because r(c)=\"\>", "\[InvisibleSpace]", "3.794239969771762`", "\[InvisibleSpace]", "\<\"/\"\>", "\[InvisibleSpace]", "0.10258658877510116`", "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", "36.98573093301514`", "\[InvisibleSpace]", "\<\">\\!\\(\\*FractionBox[SubscriptBox[\\(p\\), \\(2\ \\)], SubscriptBox[\\(p\\), \\(1\\)]]\\)=\"\>", "\[InvisibleSpace]", "35.`"}], SequenceForm[ "Do not use acceptance number c=", 0, " because r(c)=", 3.794239969771762, "/", 0.10258658877510116`, "=", 36.98573093301514, ">\!\(\*FractionBox[SubscriptBox[\(p\), \(2\)], SubscriptBox[\(p\), \ \(1\)]]\)=", 35.], Editable->False]], "Print", CellChangeTimes->{ 3.5812474917380743`*^9, 3.58124756819413*^9, {3.581247738136841*^9, 3.5812477489157333`*^9}, 3.58124786471029*^9, 3.581247907080031*^9, { 3.581671949196847*^9, 3.581671963653523*^9}, 3.5816722763239*^9, { 3.5816723099601927`*^9, 3.581672339553278*^9}, {3.581672454501172*^9, 3.581672478471991*^9}, 3.6293530890671186`*^9, {3.6293531215316467`*^9, 3.629353183019148*^9}, {3.629353239100585*^9, 3.629353301142063*^9}, { 3.62935333890705*^9, 3.62935336003929*^9}, 3.6293536945624866`*^9, { 3.629354124092083*^9, 3.629354171309757*^9}, 3.629354258541307*^9, 3.629354404114555*^9, 3.6294708095682697`*^9, 3.629470839978318*^9, 3.629471941234346*^9, 3.629472102060915*^9, 3.6940819702560453`*^9, { 3.694082018098744*^9, 3.694082033410187*^9}, 3.694149959984191*^9, 3.694150969448477*^9, 3.694157752011487*^9, {3.694157838927938*^9, 3.6941578549263906`*^9}, 3.894360345274507*^9, {3.894360460935989*^9, 3.894360470697587*^9}, 3.894360582791684*^9, 3.894360710349966*^9, { 3.894360759040967*^9, 3.894360770673149*^9}, {3.894361776134691*^9, 3.894361806249374*^9}, {3.894361863074456*^9, 3.894361868973769*^9}, { 3.8943619663217707`*^9, 3.894362002302685*^9}, 3.894362039161701*^9, 3.894362084515448*^9, {3.894362335635091*^9, 3.894362344573263*^9}, 3.894362385711423*^9, {3.894362992001525*^9, 3.894363190868415*^9}, { 3.894363259649087*^9, 3.894363305403614*^9}, 3.894539308725625*^9, 3.896878375126075*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"Use the acceptance number c=\"\>", "\[InvisibleSpace]", "1", "\[InvisibleSpace]", "\<\" because r(c)=\"\>", "\[InvisibleSpace]", "6.74488308721242`", "\[InvisibleSpace]", "\<\"/\"\>", "\[InvisibleSpace]", "0.7107230213973244`", "\[InvisibleSpace]", "\<\"=\"\>", "\[InvisibleSpace]", "9.49017111328626`", "\[InvisibleSpace]", \ "\<\"\[LessEqual]\\!\\(\\*FractionBox[SubscriptBox[\\(p\\), \\(2\\)], \ SubscriptBox[\\(p\\), \\(1\\)]]\\)=\"\>", "\[InvisibleSpace]", "35.`"}], SequenceForm[ "Use the acceptance number c=", 1, " because r(c)=", 6.74488308721242, "/", 0.7107230213973244, "=", 9.49017111328626, "\[LessEqual]\!\(\*FractionBox[SubscriptBox[\(p\), \(2\)], \ SubscriptBox[\(p\), \(1\)]]\)=", 35.], Editable->False]], "Print", CellChangeTimes->{ 3.5812474917380743`*^9, 3.58124756819413*^9, {3.581247738136841*^9, 3.5812477489157333`*^9}, 3.58124786471029*^9, 3.581247907080031*^9, { 3.581671949196847*^9, 3.581671963653523*^9}, 3.5816722763239*^9, { 3.5816723099601927`*^9, 3.581672339553278*^9}, {3.581672454501172*^9, 3.581672478471991*^9}, 3.6293530890671186`*^9, {3.6293531215316467`*^9, 3.629353183019148*^9}, {3.629353239100585*^9, 3.629353301142063*^9}, { 3.62935333890705*^9, 3.62935336003929*^9}, 3.6293536945624866`*^9, { 3.629354124092083*^9, 3.629354171309757*^9}, 3.629354258541307*^9, 3.629354404114555*^9, 3.6294708095682697`*^9, 3.629470839978318*^9, 3.629471941234346*^9, 3.629472102060915*^9, 3.6940819702560453`*^9, { 3.694082018098744*^9, 3.694082033410187*^9}, 3.694149959984191*^9, 3.694150969448477*^9, 3.694157752011487*^9, {3.694157838927938*^9, 3.6941578549263906`*^9}, 3.894360345274507*^9, {3.894360460935989*^9, 3.894360470697587*^9}, 3.894360582791684*^9, 3.894360710349966*^9, { 3.894360759040967*^9, 3.894360770673149*^9}, {3.894361776134691*^9, 3.894361806249374*^9}, {3.894361863074456*^9, 3.894361868973769*^9}, { 3.8943619663217707`*^9, 3.894362002302685*^9}, 3.894362039161701*^9, 3.894362084515448*^9, {3.894362335635091*^9, 3.894362344573263*^9}, 3.894362385711423*^9, {3.894362992001525*^9, 3.894363190868415*^9}, { 3.894363259649087*^9, 3.894363305403614*^9}, 3.894539308725625*^9, 3.8968783751397133`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"Use the sample size n=\"\>", "\[InvisibleSpace]", "20", "\[InvisibleSpace]", "\<\".\"\>"}], SequenceForm["Use the sample size n=", 20, "."], Editable->False]], "Print", CellChangeTimes->{ 3.5812474917380743`*^9, 3.58124756819413*^9, {3.581247738136841*^9, 3.5812477489157333`*^9}, 3.58124786471029*^9, 3.581247907080031*^9, { 3.581671949196847*^9, 3.581671963653523*^9}, 3.5816722763239*^9, { 3.5816723099601927`*^9, 3.581672339553278*^9}, {3.581672454501172*^9, 3.581672478471991*^9}, 3.6293530890671186`*^9, {3.6293531215316467`*^9, 3.629353183019148*^9}, {3.629353239100585*^9, 3.629353301142063*^9}, { 3.62935333890705*^9, 3.62935336003929*^9}, 3.6293536945624866`*^9, { 3.629354124092083*^9, 3.629354171309757*^9}, 3.629354258541307*^9, 3.629354404114555*^9, 3.6294708095682697`*^9, 3.629470839978318*^9, 3.629471941234346*^9, 3.629472102060915*^9, 3.6940819702560453`*^9, { 3.694082018098744*^9, 3.694082033410187*^9}, 3.694149959984191*^9, 3.694150969448477*^9, 3.694157752011487*^9, {3.694157838927938*^9, 3.6941578549263906`*^9}, 3.894360345274507*^9, {3.894360460935989*^9, 3.894360470697587*^9}, 3.894360582791684*^9, 3.894360710349966*^9, { 3.894360759040967*^9, 3.894360770673149*^9}, {3.894361776134691*^9, 3.894361806249374*^9}, {3.894361863074456*^9, 3.894361868973769*^9}, { 3.8943619663217707`*^9, 3.894362002302685*^9}, 3.894362039161701*^9, 3.894362084515448*^9, {3.894362335635091*^9, 3.894362344573263*^9}, 3.894362385711423*^9, {3.894362992001525*^9, 3.894363190868415*^9}, { 3.894363259649087*^9, 3.894363305403614*^9}, 3.894539308725625*^9, 3.896878375142173*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{"Unnecessary", " ", "verification"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["n", "tot"], "=", "1000"}], ";"}], " ", StyleBox[ RowBox[{"(*", " ", RowBox[{"lot", " ", "size"}], " ", "*)"}], FontSize->10], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"exactdist", "[", "p_", "]"}], "=", RowBox[{"HypergeometricDistribution", "[", RowBox[{ RowBox[{"samplesize", "[", "i", "]"}], ",", RowBox[{"Round", "[", RowBox[{ SubscriptBox["n", "tot"], "\[Times]", "p"}], "]"}], ",", SubscriptBox["n", "tot"]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"CDF", "[", RowBox[{ RowBox[{"exactdist", "[", SubscriptBox["p", "1"], "]"}], ",", "i"}], "]"}], "\[GreaterEqual]", RowBox[{"1", "-", "\[Alpha]"}]}], " ", "&&", RowBox[{ RowBox[{"CDF", "[", RowBox[{ RowBox[{"exactdist", "[", SubscriptBox["p", "2"], "]"}], ",", "i"}], "]"}], "\[LessEqual]", "\[Beta]"}]}], ",", RowBox[{ "Print", "[", "\"\\"", "]"}], ",", RowBox[{ "Print", "[", "\"\\"", "]"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.894361927577982*^9, 3.894361950564671*^9}, { 3.894362059804772*^9, 3.8943622902601147`*^9}, 3.8943624731538677`*^9, { 3.8943625226798477`*^9, 3.8943625472363377`*^9}, {3.894362582079486*^9, 3.894362605293244*^9}, {3.89436263636924*^9, 3.894362641443512*^9}, { 3.894362674982443*^9, 3.8943628235601187`*^9}, 3.89436452325114*^9, { 3.8945393276454763`*^9, 3.894539340194544*^9}}], Cell[BoxData["\<\"The single sampling plan for attributes complies with the \ producer's and consumer's risk points.\"\>"], "Print", CellChangeTimes->{3.894362825447496*^9, 3.8943629950403347`*^9, 3.894363202045453*^9, 3.8943633233327923`*^9, 3.8943645394988127`*^9, 3.894539314306116*^9, 3.8945393470142603`*^9, 3.896878382490243*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"(*", " ", RowBox[{"Average", " ", "Outgoing", " ", "Quality", " ", RowBox[{"(", "AOQ", ")"}], " ", "or", " ", "percentage", " ", "of", " ", "defective", " ", "due", " ", "to", " ", "rectifying", " ", "inspection", " ", "in", " ", "a", " ", "single", " ", "sampling", " ", "plan", " ", "and", " ", "using", " ", "the", " ", "binomial", " ", "approximation", " ", "to", " ", "the", " ", "acceptance", " ", "probability"}], " ", "*)"}], FontSize->10], RowBox[{ RowBox[{ RowBox[{ RowBox[{"ATI", "[", RowBox[{"n_", ",", "c_", ",", "p_"}], "]"}], "=", RowBox[{ RowBox[{"n", "*", RowBox[{"CDF", "[", RowBox[{ RowBox[{"BinomialDistribution", "[", RowBox[{"n", ",", "p"}], "]"}], ",", "c"}], "]"}]}], "+", RowBox[{ SubscriptBox["n", "tot"], "*", RowBox[{"(", RowBox[{"1", "-", RowBox[{"CDF", "[", RowBox[{ RowBox[{"BinomialDistribution", "[", RowBox[{"n", ",", "p"}], "]"}], ",", "c"}], "]"}]}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"midp", "=", "0.1"}], ";"}], "\[IndentingNewLine]", RowBox[{"ATI", "[", RowBox[{ RowBox[{"samplesize", "[", "i", "]"}], ",", "i", ",", "midp"}], "]"}], "\[IndentingNewLine]", RowBox[{"(*", " ", RowBox[{"Results", " ", "using", " ", "the", " ", "tables"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"20", "*", "0.3917"}], "+", RowBox[{"1000", "*", RowBox[{"(", RowBox[{"1", "-", "0.3917"}], ")"}]}]}]}]}]], "Input", CellChangeTimes->{ 3.532605853537725*^9, {3.532606065511526*^9, 3.5326060793540163`*^9}, { 3.532606243987359*^9, 3.532606275994974*^9}, {3.532606485306294*^9, 3.532606486099886*^9}, {3.894362471892501*^9, 3.894362517292061*^9}, { 3.8943625700675383`*^9, 3.8943625727294893`*^9}, {3.894362850861459*^9, 3.894362936638308*^9}, {3.894363217519985*^9, 3.894363232369625*^9}, { 3.8943633425349407`*^9, 3.894363381048128*^9}, {3.894363429939167*^9, 3.894363463074844*^9}, {3.8943634987514057`*^9, 3.894363533951611*^9}, { 3.894364520652769*^9, 3.8943645462001047`*^9}, 3.894364609352087*^9, { 3.894365928145643*^9, 3.8943659492837048`*^9}, 3.8945393031321383`*^9, 3.896878267215274*^9, {3.8968783169550133`*^9, 3.896878413717278*^9}}], Cell[BoxData["616.0879418373355`"], "Output", CellChangeTimes->{{3.8968784086580133`*^9, 3.896878414280624*^9}}], Cell[BoxData["616.134`"], "Output", CellChangeTimes->{{3.8968784086580133`*^9, 3.896878414282411*^9}}] }, Open ]] }, Open ]], Cell["\<\ Question 5 \[LongDash]\[NonBreakingSpace]Single sampling plan for variables \ with UNKNOWN STANDARD DEVIATION\ \>", "Subsubsection", CellChangeTimes->{{3.728978072142015*^9, 3.728978078436468*^9}, { 3.7289787758916683`*^9, 3.728978777915042*^9}, {3.728979117073182*^9, 3.728979124168069*^9}, {3.72897937739428*^9, 3.7289793834544497`*^9}, { 3.728980621199177*^9, 3.728980659270624*^9}, {3.72898742841497*^9, 3.728987435586033*^9}, {3.8872035562635403`*^9, 3.887203571506999*^9}, { 3.889075948658783*^9, 3.889075948905105*^9}, {3.893068488938219*^9, 3.893068489604116*^9}, 3.894353121097001*^9, {3.894355313323731*^9, 3.894355315510623*^9}, {3.89436020311318*^9, 3.894360270691959*^9}, { 3.894539364307907*^9, 3.8945393803073893`*^9}, {3.89687861519657*^9, 3.896878618083435*^9}}], Cell[CellGroupData[{ Cell["Exerc\[IAcute]cio 7(b)", "Subsection", CellChangeTimes->{{3.528544419253316*^9, 3.528544422002598*^9}, { 3.5285533563574753`*^9, 3.528553367972056*^9}, {3.528553593741721*^9, 3.5285535972847424`*^9}, {3.5293340763983088`*^9, 3.529334084946261*^9}, { 3.579441979545072*^9, 3.579442000295053*^9}, {3.579510984491907*^9, 3.5795110142633*^9}, {3.57952948304319*^9, 3.579529483120823*^9}, { 3.579531044451522*^9, 3.579531084474572*^9}, {3.5795313963611383`*^9, 3.579531396465128*^9}, {3.5795314666830273`*^9, 3.579531466792997*^9}, { 3.579532076610524*^9, 3.579532076689464*^9}, {3.579532140706715*^9, 3.579532156179016*^9}, {3.579533925595467*^9, 3.579533931105175*^9}, { 3.610569049269457*^9, 3.6105690500433617`*^9}, {3.709532014865305*^9, 3.7095320218955393`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"Clear", "[", RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"Context", "[", "]"}], "<>", "\"\<*\>\""}], "]"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["p", "1"], "=", "0.01"}], ";", " ", StyleBox[ RowBox[{"(*", " ", "AQL", " ", "*)"}], FontSize->9], "\[IndentingNewLine]", RowBox[{"\[Alpha]", "=", RowBox[{"1", "-", "0.95"}]}], ";"}], " ", StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{"producer", "'"}], "s", " ", "risk"}], " ", "*)"}], FontSize->9]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["p", "2"], "=", "0.05"}], ";"}], " ", StyleBox[ RowBox[{"(*", " ", "LTPD", " ", "*)"}], FontSize->9]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[Beta]", "=", "0.1"}], ";"}], " ", StyleBox[ RowBox[{"(*", " ", RowBox[{ RowBox[{"consumer", "'"}], "s", " ", "risk"}], " ", "*)"}], FontSize->9], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ SubscriptBox["n", "s"], "=", "59"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ SubscriptBox["k", "s"], "=", "1.937713"}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"gdist", "=", RowBox[{"NormalDistribution", "[", RowBox[{"0", ",", "1"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"\[CapitalOmega]", "[", "x_", "]"}], ":=", RowBox[{"Quantile", "[", RowBox[{"gdist", ",", "x"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Round", "[", RowBox[{ FractionBox[ RowBox[{ RowBox[{"\[CapitalOmega]", "[", RowBox[{"1", "-", SubscriptBox["p", "1"]}], "]"}], "-", RowBox[{ SubscriptBox["k", "s"], "\[Times]", SqrtBox[ FractionBox[ RowBox[{ RowBox[{"3", "\[Times]", SubscriptBox["n", "s"]}], "-", "4"}], RowBox[{ RowBox[{"3", "\[Times]", SubscriptBox["n", "s"]}], "-", "3"}]]]}]}], SqrtBox[ FractionBox[ RowBox[{"1", "+", FractionBox[ RowBox[{"3", "\[Times]", SubscriptBox["n", "s"], "\[Times]", SuperscriptBox[ SubscriptBox["k", "s"], "2"]}], RowBox[{ RowBox[{"6", "\[Times]", SubscriptBox["n", "s"]}], "-", "8"}]]}], SubscriptBox["n", "s"]]]], ",", "0.01"}], "]"}], "\[IndentingNewLine]", RowBox[{"CDF", "[", RowBox[{ RowBox[{"NormalDistribution", "[", RowBox[{"0", ",", "1"}], "]"}], ",", "%"}], "]"}], "\[IndentingNewLine]", RowBox[{"Round", "[", RowBox[{ FractionBox[ RowBox[{ RowBox[{"\[CapitalOmega]", "[", RowBox[{"1", "-", SubscriptBox["p", "2"]}], "]"}], "-", RowBox[{ SubscriptBox["k", "s"], "\[Times]", SqrtBox[ FractionBox[ RowBox[{ RowBox[{"3", "\[Times]", SubscriptBox["n", "s"]}], "-", "4"}], RowBox[{ RowBox[{"3", "\[Times]", SubscriptBox["n", "s"]}], "-", "3"}]]]}]}], SqrtBox[ FractionBox[ RowBox[{"1", "+", FractionBox[ RowBox[{"3", "\[Times]", SubscriptBox["n", "s"], "\[Times]", SuperscriptBox[ SubscriptBox["k", "s"], "2"]}], RowBox[{ RowBox[{"6", "\[Times]", SubscriptBox["n", "s"]}], "-", "8"}]]}], SubscriptBox["n", "s"]]]], ",", "0.01"}], "]"}], "\[IndentingNewLine]", RowBox[{"CDF", "[", RowBox[{ RowBox[{"NormalDistribution", "[", RowBox[{"0", ",", "1"}], "]"}], ",", "%"}], "]"}]}], "Input", CellChangeTimes->{{3.610712670086217*^9, 3.610712761239393*^9}, { 3.63162399794171*^9, 3.631624012526164*^9}, {3.709533753686307*^9, 3.7095337679732933`*^9}, {3.70953380274963*^9, 3.70953381891016*^9}, { 3.709534798744567*^9, 3.709534811048921*^9}, {3.709534904137961*^9, 3.7095349180014668`*^9}, {3.709536163487693*^9, 3.709536172195784*^9}, 3.709536370856907*^9, {3.896879698168229*^9, 3.896879716969473*^9}, { 3.896879760570779*^9, 3.8968797799943933`*^9}}], Cell[BoxData["1.77`"], "Output", CellChangeTimes->{ 3.61071276223855*^9, 3.63162401493174*^9, 3.709533769543936*^9, 3.709533827087884*^9, 3.7095348117170973`*^9, 3.709534918395637*^9, { 3.709536167590341*^9, 3.709536173063541*^9}, 3.709536371255932*^9, 3.8968796682413607`*^9, {3.8968797085278473`*^9, 3.8968797483803043`*^9}, 3.896879780631671*^9, {3.896879951605439*^9, 3.896879968065864*^9}, 3.896880192583536*^9}], Cell[BoxData["0.9616364296371287`"], "Output", CellChangeTimes->{ 3.61071276223855*^9, 3.63162401493174*^9, 3.709533769543936*^9, 3.709533827087884*^9, 3.7095348117170973`*^9, 3.709534918395637*^9, { 3.709536167590341*^9, 3.709536173063541*^9}, 3.709536371255932*^9, 3.8968796682413607`*^9, {3.8968797085278473`*^9, 3.8968797483803043`*^9}, 3.896879780631671*^9, {3.896879951605439*^9, 3.896879968065864*^9}, 3.896880192586133*^9}], Cell[BoxData[ RowBox[{"-", "1.29`"}]], "Output", CellChangeTimes->{ 3.61071276223855*^9, 3.63162401493174*^9, 3.709533769543936*^9, 3.709533827087884*^9, 3.7095348117170973`*^9, 3.709534918395637*^9, { 3.709536167590341*^9, 3.709536173063541*^9}, 3.709536371255932*^9, 3.8968796682413607`*^9, {3.8968797085278473`*^9, 3.8968797483803043`*^9}, 3.896879780631671*^9, {3.896879951605439*^9, 3.896879968065864*^9}, 3.896880192588138*^9}], Cell[BoxData["0.09852532904974787`"], "Output", CellChangeTimes->{ 3.61071276223855*^9, 3.63162401493174*^9, 3.709533769543936*^9, 3.709533827087884*^9, 3.7095348117170973`*^9, 3.709534918395637*^9, { 3.709536167590341*^9, 3.709536173063541*^9}, 3.709536371255932*^9, 3.8968796682413607`*^9, {3.8968797085278473`*^9, 3.8968797483803043`*^9}, 3.896879780631671*^9, {3.896879951605439*^9, 3.896879968065864*^9}, 3.896880192590138*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"U", "=", "3"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"sigma", "=", "0.1"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"dist", "=", RowBox[{"NormalDistribution", "[", RowBox[{ RowBox[{"U", "+", RowBox[{"2", "*", "sigma"}]}], ",", "sigma"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"data", "=", RowBox[{"RandomVariate", "[", RowBox[{"dist", ",", RowBox[{ SubscriptBox["n", "s"], "+", "1"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"xbar", "=", RowBox[{"Round", "[", RowBox[{ RowBox[{"Mean", "[", "data", "]"}], ",", "0.001"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"sx", "=", RowBox[{"Round", "[", RowBox[{ SqrtBox[ RowBox[{"Variance", "[", "data", "]"}]], ",", "0.001"}], "]"}]}], "\[IndentingNewLine]", FractionBox[ RowBox[{"U", "-", "xbar"}], "sx"], "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ FractionBox[ RowBox[{"U", "-", "xbar"}], "sx"], "\[GreaterEqual]", SubscriptBox["k", "s"]}], ",", RowBox[{"Print", "[", "\"\\"", "]"}], ",", RowBox[{"Print", "[", "\"\\"", "]"}]}], "]"}]}], "Input", CellChangeTimes->{{3.610569661612401*^9, 3.610569666512258*^9}, { 3.6105697503413897`*^9, 3.6105698651763563`*^9}, {3.610569919995222*^9, 3.610569928844089*^9}, {3.610570570499569*^9, 3.6105705708373337`*^9}, { 3.6105964731854*^9, 3.610596473612959*^9}, {3.894540978219243*^9, 3.8945409785184298`*^9}, {3.8945410186197863`*^9, 3.894541047909112*^9}, { 3.8945410848090773`*^9, 3.894541142284721*^9}, {3.894541194536516*^9, 3.894541307101515*^9}, {3.894543120780569*^9, 3.89454315841819*^9}, { 3.896879907497072*^9, 3.8968799972621193`*^9}, {3.896880118564131*^9, 3.896880200266685*^9}}], Cell[BoxData["3.207`"], "Output", CellChangeTimes->{ 3.610569788694401*^9, 3.6105698245098743`*^9, 3.610569934585927*^9, { 3.6105705446881523`*^9, 3.610570599048304*^9}, 3.610596476057232*^9, { 3.8945411996354837`*^9, 3.894541207369759*^9}, {3.8945412451070957`*^9, 3.8945413102693443`*^9}, {3.894543123534935*^9, 3.894543158864936*^9}, { 3.896879937592246*^9, 3.896879998122654*^9}, {3.896880127946143*^9, 3.896880150210474*^9}, 3.896880204560849*^9}], Cell[BoxData["0.12`"], "Output", CellChangeTimes->{ 3.610569788694401*^9, 3.6105698245098743`*^9, 3.610569934585927*^9, { 3.6105705446881523`*^9, 3.610570599048304*^9}, 3.610596476057232*^9, { 3.8945411996354837`*^9, 3.894541207369759*^9}, {3.8945412451070957`*^9, 3.8945413102693443`*^9}, {3.894543123534935*^9, 3.894543158864936*^9}, { 3.896879937592246*^9, 3.896879998122654*^9}, {3.896880127946143*^9, 3.896880150210474*^9}, 3.896880204562624*^9}], Cell[BoxData[ RowBox[{"-", "1.724999999999999`"}]], "Output", CellChangeTimes->{ 3.610569788694401*^9, 3.6105698245098743`*^9, 3.610569934585927*^9, { 3.6105705446881523`*^9, 3.610570599048304*^9}, 3.610596476057232*^9, { 3.8945411996354837`*^9, 3.894541207369759*^9}, {3.8945412451070957`*^9, 3.8945413102693443`*^9}, {3.894543123534935*^9, 3.894543158864936*^9}, { 3.896879937592246*^9, 3.896879998122654*^9}, {3.896880127946143*^9, 3.896880150210474*^9}, 3.896880204563773*^9}], Cell[BoxData["\<\"We should reject the lot.\"\>"], "Print", CellChangeTimes->{{3.896879982450095*^9, 3.8968799981267157`*^9}, { 3.896880127950138*^9, 3.896880150214514*^9}, 3.896880204565073*^9}] }, Open ]] }, Open ]] }, WindowSize->{649, 1278}, WindowMargins->{{805, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, FrontEndVersion->"10.2 for Mac OS X x86 (32-bit, 64-bit Kernel) (July 29, \ 2015)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[558, 20, 442, 6, 35, "Subsubsection"], Cell[1003, 28, 393, 5, 29, "Subsubsection"], Cell[CellGroupData[{ Cell[1421, 37, 436, 6, 29, "Subsubsection"], Cell[CellGroupData[{ Cell[1882, 47, 6718, 210, 573, "Input"], Cell[8603, 259, 1389, 22, 112, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10029, 286, 1571, 42, 131, "Input", CellID->522227289], Cell[11603, 330, 520, 12, 32, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12160, 347, 1325, 30, 74, "Input"], Cell[13488, 379, 32656, 585, 239, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[46181, 969, 2631, 64, 216, "Input"], Cell[48815, 1035, 2560, 66, 53, "Output"], Cell[51378, 1103, 2474, 64, 59, "Output"], Cell[53855, 1169, 2928, 77, 89, "Output"], Cell[56786, 1248, 647, 11, 48, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[57470, 1264, 2485, 57, 131, "Input"], Cell[59958, 1323, 5084, 94, 242, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[65079, 1422, 2756, 78, 337, "Input"], Cell[67838, 1502, 307, 4, 28, "Output"], Cell[68148, 1508, 228, 5, 21, "Print"], Cell[68379, 1515, 308, 4, 28, "Output"], Cell[68690, 1521, 310, 4, 28, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[69049, 1531, 612, 8, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[69686, 1543, 3677, 105, 453, "Input"], Cell[73366, 1650, 683, 12, 28, "Output"], Cell[74052, 1664, 490, 7, 28, "Output"], Cell[74545, 1673, 501, 7, 28, "Output"], Cell[75049, 1682, 492, 7, 28, "Output"], Cell[75544, 1691, 502, 7, 28, "Output"], Cell[76049, 1700, 500, 7, 28, "Output"], Cell[76552, 1709, 506, 7, 28, "Output"], Cell[77061, 1718, 504, 7, 28, "Output"], Cell[77568, 1727, 501, 7, 28, "Output"], Cell[78072, 1736, 502, 7, 28, "Output"], Cell[78577, 1745, 506, 7, 28, "Output"], Cell[79086, 1754, 503, 7, 28, "Output"], Cell[79592, 1763, 500, 7, 28, "Output"], Cell[80095, 1772, 502, 7, 28, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[80646, 1785, 635, 9, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[81306, 1798, 2097, 43, 125, "Input"], Cell[83406, 1843, 121, 2, 28, "Output"], Cell[83530, 1847, 118, 2, 28, "Output"], Cell[83651, 1851, 119, 2, 28, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[83807, 1858, 4841, 111, 403, "Input"], Cell[88651, 1971, 286, 4, 28, "Output"], Cell[88940, 1977, 284, 4, 28, "Output"], Cell[89227, 1983, 282, 4, 28, "Output"], Cell[89512, 1989, 282, 4, 28, "Output"], Cell[89797, 1995, 282, 4, 28, "Output"], Cell[90082, 2001, 12565, 219, 243, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[102696, 2226, 956, 19, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[103677, 2249, 7570, 192, 703, "Input"], Cell[111250, 2443, 1775, 25, 28, "Output"], Cell[113028, 2470, 1775, 25, 28, "Output"], Cell[114806, 2497, 1776, 25, 28, "Output"], Cell[116585, 2524, 1776, 25, 28, "Output"], Cell[118364, 2551, 1778, 25, 28, "Output"], Cell[120145, 2578, 1776, 25, 28, "Output"], Cell[121924, 2605, 1775, 25, 28, "Output"], Cell[123702, 2632, 1776, 25, 28, "Output"], Cell[125481, 2659, 1776, 25, 28, "Output"], Cell[127260, 2686, 1775, 25, 28, "Output"], Cell[129038, 2713, 1777, 25, 28, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[130864, 2744, 766, 12, 59, "Subsubsection"], Cell[CellGroupData[{ Cell[131655, 2760, 6021, 166, 476, "Input"], Cell[CellGroupData[{ Cell[137701, 2930, 2306, 38, 57, "Print"], Cell[140010, 2970, 2312, 37, 57, "Print"], Cell[142325, 3009, 1720, 27, 22, "Print"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[144094, 3042, 1986, 51, 199, "Input"], Cell[146083, 3095, 342, 4, 38, "Print"] }, Open ]], Cell[CellGroupData[{ Cell[146462, 3104, 2443, 56, 165, "Input"], Cell[148908, 3162, 113, 1, 28, "Output"], Cell[149024, 3165, 103, 1, 28, "Output"] }, Open ]] }, Open ]], Cell[149154, 3170, 822, 13, 59, "Subsubsection"], Cell[CellGroupData[{ Cell[150001, 3187, 795, 11, 36, "Subsection"], Cell[CellGroupData[{ Cell[150821, 3202, 4142, 128, 479, "Input"], Cell[154966, 3332, 439, 7, 28, "Output"], Cell[155408, 3341, 453, 7, 28, "Output"], Cell[155864, 3350, 456, 8, 28, "Output"], Cell[156323, 3360, 454, 7, 28, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[156814, 3372, 1886, 49, 230, "Input"], Cell[158703, 3423, 472, 7, 28, "Output"], Cell[159178, 3432, 471, 7, 28, "Output"], Cell[159652, 3441, 501, 8, 28, "Output"], Cell[160156, 3451, 199, 2, 22, "Print"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)