Degradation Processes in Reliability

"Degradation process" refers to many types of reliability models, which correspond to various kinds of stochastic processes used for deterioration modeling. This book focuses on the case of a univariate degradation model with a continuous set of possible outcomes. The envisioned univariate models have one single measurable quantity which is assumed to be observed over time.

The first three chapters are each devoted to one degradation model. The last chapter illustrates the use of the previously described degradation models on some real data sets. For each of the degradation models, the authors provide probabilistic results and explore simulation tools for sample paths generation. Various estimation procedures are also developed.

Introduction

1. Wiener Processes

2. Gamma Processes

3. Doubly Stochastic Marked Poisson Processes

4. Model Selection and Application to Real Data Sets

"The main focus of the book is on parametric models. In such a case likelihood maximization is recommended as the main estimation method. The form of the likelihood function is always rigorously derived and the procedure of its maximization is discussed. If the covariance matrix of ML estimates is sufficiently simple, it is also presented. For some models, estimation by the method of moments is described; the corresponding equations are then also rigorously derived. The book also contains very detailed descriptions of various methods for simulation of considered degradation processes." (Mathematical Reviews/MathSciNet April 2017)

Waltraud Kahle is Associate Professor in the Mathematics Department of the Otto-von-Guericke University Magdeburg in Germany.

Sophie Mercier is Full Professor in the Laboratory of Mathematics and their Applications of the University of Pau and Pays de l'Adour in France.

Christian Paroissin is Associate Professor in the Laboratory of Mathematics and their Applications of the University of Pau and Pays de l'Adour in France.