Compare Nonparametric and Parametric Reliability Models
A comparison of NPMLE and MLE estimates of the reliability function for some manufactured ropes using SurvivalDistribution and CensoredDistribution, respectively.
data = {100, 43, 100, 100, 63, 26, 100, 100, 100, 100, 100, 100, 100, 69, 58, 99, 95};pars = FindDistributionParameters[data, CensoredDistribution[{0, 100}, WeibullDistribution[a, b]]];
sf[x_] = SurvivalFunction[CensoredDistribution[{-Infinity, 100}, WeibullDistribution[a, b]], x] /. pars;𝒟 = SurvivalDistribution[EventData[data, Boole[# ≥ 100]& /@ data]];Plot[{SurvivalFunction[𝒟, x], sf[x]}, {x, 0, 120}, PlotPoints -> 100, Exclusions -> None, Filling -> {1 -> {2}}, PlotStyle -> Thick, Frame -> {{True, False}, {True, False}}, FrameLabel -> (Style[#, FontFamily -> "Verdana", Bold, 12]&) /@ {"Force", "Reliability"}, ImageSize -> 500]