Degradation processes in reliability (Q2812581)

The present book consists of 211 pages organized in four chapters. The first three chapters deal with different degradation models and the last one is devoted to some illustrative studies based on the real data sets described in the previous chapters.NEWLINENEWLINEIn Chapter 1 (Wiener processes), among others, the Wiener process is introduced and its first-passage time distribution is studied. Then, statistical inference is considered for various types of sampling schemes.NEWLINENEWLINEChapter 2 (Gamma processes) is devoted to gamma distribution, Poisson random measures and the construction of gamma processes. Then, time-to-failures problems are investigated from a probabilistic point of view and simulation tools are numerically studied.NEWLINENEWLINEChapter 3 (Doubly stochastic marked Poisson processes) treats a cumulative shock model, where the shocks arrive according to a doubly stochastic Poisson process. Then, different parametric models are analyzed, for which probabilistic results are given (including on the first passage time distribution), and estimation procedures are developed.NEWLINENEWLINEChapter 4 (Model selection and application to real data set) is devoted to the use of the previously described degradation models on real data sets. It highlights some differences between the Wiener and the gamma processes depending on the modeling aims. Some procedures for selecting a model and testing its goodness of fit are also suggested.NEWLINENEWLINEAltogether, this is a carefully written book with a rigorous mathematical treatment that is highly recommended to experts of mathematical reliability theory.