Select Which Component in a System to Improve
Select Which Component in a System to Improve
Select which component to improve for maximal reliability on a three-hour mission.
{Subscript[𝒟, 1], Subscript[𝒟, 2], Subscript[𝒟, 3], Subscript[𝒟, 4]} = {ExponentialDistribution[1], ExponentialDistribution[2], WeibullDistribution[1, 2], ErlangDistribution[1, 2]};
ℛ = ReliabilityDistribution[(x∨y)∧(z∨v), {{x, Subscript[𝒟, 1]}, {y, Subscript[𝒟, 2]}, {z, Subscript[𝒟, 3]}, {v, Subscript[𝒟, 4]}}];
bi = BirnbaumImportance[ℛ, t];
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"]]