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8: Parametric Probability Distributions
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Core Algorithms
Use a Gompertz Distribution as a Lifetime Model
Model a lifetime of a device by a
GompertzMakehamDistribution
and compare reliability of systems composed of two such devices put in series or in parallel.
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r = SurvivalFunction[GompertzMakehamDistribution[\[Lambda], \[Xi]], t]; rs = r r; rp = 1  (1  r) (1  r);
In[2]:=
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Block[{\[Lambda] = 2, \[Xi] = .3}, Framed[Plot[{rs, rp}, {t, 0, 2}, PlotStyle > Thick, ImageSize > 400, BaseStyle > {FontFamily > "Verdana"}, PlotLabel > "Reliability in series and in parallel", Epilog > {Inset[ Framed[Style["in parallel", 12], Background > LightYellow], {0.7, 0.6}, {Left, Bottom}], Inset[Framed[Style["in series", 12], Background > LightYellow], {0.6, 0.3}, {Right, Top}]}], RoundingRadius > 5, Background > Lighter[Blend[{Yellow, Orange}], 0.8]] ]
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