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Model Standby Systems

Compare mean time to failure (MTTF) between different kinds of standby systems.

Wolfram Language code: marker[c1_, c2_] := Graphics[{c1, Rectangle[], c2, Rectangle[{1, 0}]}];
Wolfram Language code: sfPlot[dist_, c1_, c2_] := Module[{mttf = Mean[dist]}, Legended[Show[Plot[Evaluate@SurvivalFunction[dist, t], {t, 0, 12}, Filling -> Axis, PlotRange -> {0, 1}, Ticks -> None, ImageSize -> 160], ListPlot[{Labeled[{mttf, SurvivalFunction[dist, mttf]}, Row[{"MTTF: ", Round[mttf, 0.01]}]]}, Filling -> Axis]], {Placed[SwatchLegend[{Blue}, {""}, LegendMarkers -> marker[c1, c2], LegendMarkerSize -> {20, 10}], {0.9, 0.9}]}]]
Wolfram Language code: xlabels = {Rotate[SwatchLegend[{Blue}, {"Cold"}], π / 2], Rotate[SwatchLegend[{Red}, {"Warm"}], π / 2], Rotate[SwatchLegend[{Orange}, {"Mixed"}], π / 2]}; ylabels = {"", SwatchLegend[{Green}, {"Perfect Switch"}], SwatchLegend[{Orange}, {"Switch with Probability"}], SwatchLegend[{Lighter@Purple}, {"Switch with Lifetime"}]};
Wolfram Language code: xcolor = {Blue, Red, Orange}; ycolor = {Green, Orange, Lighter@Purple};
Wolfram Language code: 𝒟 = ExponentialDistribution[1 / 2]; Subscript[𝒟, warm] = ExponentialDistribution[1 / 10]; Subscript[𝒟, switch] = ExponentialDistribution[1 / 20]; Subscript[𝒟, cp] = StandbyDistribution[𝒟, {𝒟, 𝒟}]; Subscript[𝒟, ci] = StandbyDistribution[𝒟, {𝒟, 𝒟}, 0.9]; Subscript[𝒟, cil] = StandbyDistribution[𝒟, {𝒟, 𝒟}, Subscript[𝒟, switch]]; Subscript[𝒟, wp] = StandbyDistribution[𝒟, {{Subscript[𝒟, warm], 𝒟}, {Subscript[𝒟, warm], 𝒟}}]; Subscript[𝒟, wi] = StandbyDistribution[𝒟, {{Subscript[𝒟, warm], 𝒟}, {Subscript[𝒟, warm], 𝒟}}, 0.9]; Subscript[𝒟, wil] = StandbyDistribution[𝒟, {{Subscript[𝒟, warm], 𝒟}, {Subscript[𝒟, warm], 𝒟}}, Subscript[𝒟, switch]]; Subscript[𝒟, wcp] = StandbyDistribution[𝒟, {{Subscript[𝒟, warm], 𝒟}, 𝒟}]; Subscript[𝒟, wci] = StandbyDistribution[𝒟, {{Subscript[𝒟, warm], 𝒟}, 𝒟}, 0.9]; Subscript[𝒟, wcil] = StandbyDistribution[𝒟, {{Subscript[𝒟, warm], 𝒟}, 𝒟}, Subscript[𝒟, switch]];
Wolfram Language code: distributions = {{Subscript[𝒟, cp], Subscript[𝒟, ci], Subscript[𝒟, cil]}, {Subscript[𝒟, wp], Subscript[𝒟, wi], Subscript[𝒟, wil]}, {Subscript[𝒟, wcp], Subscript[𝒟, wci], Subscript[𝒟, wcil]}};
Wolfram Language code: table = Table[sfPlot[distributions[[i, j]], xcolor[[i]], ycolor[[j]]], {i, 3}, {j, 3}];
Wolfram Language code: Grid[Prepend[Prepend[table, xlabels], ylabels], Frame -> All, FrameStyle -> Gray, Spacings -> {1.1, 1.1}]