Introduction

As the title suggests, the book is devoted to stochastic models for reliability. This very wide topic is naturally ‘censored’ by the current research interests of the authors in the field which are: shock models, burn-in and stochastic modeling in heterogeneous populations. At first sight, it seems that these three areas of research are rather ‘independent’. However, it turns out that they can be naturally combined in the unified framework and some of the results of this kind have been already reported in our recent publications. As most of the real-life populations are heterogeneous, taking this property into account in reliability analysis of various problems is only increasing the adequacy of the corresponding modeling. Furthermore, all objects are operating in a changing environment. One of the ways to model an impact of this environment is via the external shocks occurring in accordance with some point process (e.g., the Poisson process or the renewal process). By a ‘shock’ we understand an ‘instantaneous’, potentially harmful event. Depending on its magnitude, a shock can destroy an operating system (failure), leave it unchanged (as good as old), or, e.g., increase its wear (deterioration) on some increment. Numerous shock models were developed and reported in the reliability-related literature during the past 50 years. However, only a few papers (mostly of the authors) deal with shocks in heterogeneous populations and with shocks as a method of burn-in.