Stochastic modeling for reliability. Shocks, burn-in and heterogeneous populations
In the framework of \textit{stochastic modeling for reliability} a combination of the three areas \textit{shock models}, \textit{burn-in} and \textit{stochastic modeling in heterogeneous populations} is presented. Here, by a ``shock'' an instantaneous, potentially harmful event is meant, ``burn-in'' is a method, of elimination of initial failures in field usage. Hence, during a fixed time period, the system is under a simulated use prior to the actual operation. Moreover, due to the instability of production processes, environmental and other factors, most populations of manufactured items are heterogeneous in practice. The book -- written for researchers as well as practitioners in reliability engineering -- contains the following chapters: After a description of the aims and scope in the first chapter, in Chapter 2 ``Basic Stochastics for Reliability Analysis'' an introduction to reliability and the corresponding notations is given. Basic shock models and simple applications are treated in Chapter 3 ``Shocks and Degradation''. Extended and generalized shock models are considered in Chapter 4 ``Advanced Theory for Poisson Shock Models''. Stochastic analyses of heterogeneous populations are presented in Chapter 5 ``Heterogeneous Populations''. Here, mixtures of distributions represent a mathematical tool for modeling heterogeneity. The concept of ``burn-in'' is introduced and then applied to repairable items in Chapter 6 ``The Basics of Burn-in'' and Chapter 7 ``Burn-in for Repairable Systems''. While in Chapters 6 and 7 burn-in procedures for homogeneous populations have been considered, Chapter 8 ``Burn-in for Heterogeneous Populations'' is devoted to burn-in for heterogeneous populations of items. The stochastic theory of shocks described in previous parts of the book is applied in Chapter 9 ``Shocks as Burn-in'' to burn-in modeling. In the last Chapter 10 ``Stochastic Models for Environmental Stress Screening'' another method for eliminating weak items is discussed. An Index concludes the book, while references are given to each chapter. The book can be recommended for reliability engineers, statisticians working in reliability engineering, as well as for courses in advanced methods of reliability models and methods.
scientific article; zbMATH DE number 6154489