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Reliability
Which Component to Improve in a System
Select which component to improve for maximal reliability on a three-hour mission.
In[1]:=
X
{Subscript[\[ScriptCapitalD], 1], Subscript[\[ScriptCapitalD], 2], Subscript[\[ScriptCapitalD], 3], Subscript[\[ScriptCapitalD], 4]} = {ExponentialDistribution[1], ExponentialDistribution[2], WeibullDistribution[1, 2], ErlangDistribution[1, 2]};
In[2]:=
X
\[ScriptCapitalR] = ReliabilityDistribution[(x \[Or] y) \[And] (z \[Or] v), {{x, Subscript[\[ScriptCapitalD], 1]}, {y, Subscript[\[ScriptCapitalD], 2]}, {z, Subscript[\[ScriptCapitalD], 3]}, {v, Subscript[\[ScriptCapitalD], 4]}}]; bi = BirnbaumImportance[\[ScriptCapitalR], t];
In[3]:=
X
style = ColorData[1, "ColorList"]; Labeled[Plot[bi, {t, 0, 4}, Filling -> Axis, PlotRange -> {0, 1}, Epilog -> Inset[PieChart[bi /. t -> 3, ChartLabels -> {x, y, z, v}, PlotLabel -> "t=3", SectorSpacing -> {0.1, 0}, Background -> White, ChartStyle -> style, ChartBaseStyle -> FaceForm[Opacity[0.7]], Frame -> True, FrameTicks -> None, FrameStyle -> LightGray], {4, 1}, {Right, Top}, {1.5, 1.5}], Mesh -> {{3}}, MeshShading -> {Automatic, LightGray}, FillingStyle -> Opacity[0.04], PlotStyle -> style, ImageSize -> Medium], Style["Improve x or y for maximum reliability", "Graphics", "Medium"]]
Out[3]=