Use a Gompertz Distribution as a Lifetime Model
Use a Gompertz Distribution as a Lifetime Model
Model the lifetime of a device by a GompertzMakehamDistribution and compare the reliability of systems composed of two such devices put in series or parallel.
r = SurvivalFunction[GompertzMakehamDistribution[λ, ξ], t];
rs = r r;
rp = 1 - (1 - r) (1 - r);Block[{λ = 2, ξ = .3},
Plot[{rs, rp}, {t, 0, 2}, PlotStyle -> Thick, ImageSize -> 400, BaseStyle -> {FontFamily -> "Helvetica"}, 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}]}]]