A sigmoid process for modeling warranty repairs

This paper proposes a sigmoid process to model the warranty data which graphically illustrate S-shape. In the paper, it is shown that the sigmoid process is the non-homogeneous Poisson process super-imposed by warranty dropout process. The nonparametric estimates of warranty repair rate and mean cumulative function (MCF) are presented. The three parameters of the sigmoid model are estimated by maximum likelihood method. The confidence intervals of the estimates of model parameters and MCF are constructed. Likelihood ratio test is developed to test the hypothesis that the historic values of location parameters are statistically equal. An example is presented to illustrate and validate the sigmoid model.