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Reliability
Compare Reliability of System Configurations
In[1]:=
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\[ScriptCapitalD] = ExponentialDistribution[1/\[Lambda]]; dists = {{x, \[ScriptCapitalD]}, {y, \[ScriptCapitalD]}, {z, \ \[ScriptCapitalD]}}; \[ScriptCapitalR]series = ReliabilityDistribution[x \[And] y \[And] z, dists]; \[ScriptCapitalR]parallel = ReliabilityDistribution[x \[Or] y \[Or] z, dists]; \[ScriptCapitalR]2OutOf3 = ReliabilityDistribution[BooleanCountingFunction[{2, 3}, {x, y, z}], dists]; \[ScriptCapitalR]consecutive = ReliabilityDistribution[BooleanConsecutiveFunction[2, 3][x, y, z], dists]; \[ScriptCapitalR]standby = StandbyDistribution[\[ScriptCapitalD], {\[ScriptCapitalD], \ \[ScriptCapitalD]}]; labels = Map[ Column[#, Center] &, {{"Series:", x \[And] y \[And] z}, {"Parallel:", x \[Or] y \[Or] z}, {"2 out of 3:", BooleanCountingFunction}, {"Consecutive:", BooleanConsecutiveFunction}, {"Standby:", StandbyDistribution}}]; distributions = {\[ScriptCapitalR]series, \[ScriptCapitalR]parallel, \ \[ScriptCapitalR]2OutOf3, \[ScriptCapitalR]consecutive, \ \[ScriptCapitalR]standby};
In[2]:=
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survivals = Map[SurvivalFunction[#, t] &, distributions] // Simplify; data = Table[{labels[[i]], Simplify[survivals[[i]], t > 0], Plot[Evaluate[survivals /. {\[Lambda] -> 15}], {t, 0, 40}, PlotRange -> {0, 1}, Filling -> {i -> Axis}, PlotStyle -> Table[If[i === k, Automatic, Gray], {k, 5}]], Mean[distributions[[i]]]}, {i, 5}]; PrependTo[ data, {"System Configuration", "SurvivalFunction", "Plot (\[Lambda]=10)", "Mean"}];
In[3]:=
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Grid[data, Frame -> All, FrameStyle -> Directive[White, Thick], Background -> {None, {Lighter[Blue, .9], {Hue[.6, .15, .9], GrayLevel[.9]}}}, BaseStyle -> {FontFamily -> "Helvetica", FontSize -> 11}, ItemStyle -> {Automatic, {Directive[Bold, FontSize -> 12]}}, ItemSize -> {Automatic, {2, Automatic}}]
Compare reliability of common system structures.
Out[3]=
