As can be seen from the files of the databases of Zentralblatt/Mathematical
Abstracts and Mathematical Reviews, about 1% of all mathematical publications are connected to the keyword reliability. This gives an impression
of the importance of this field and makes it clear that it is impossible to
include all the topics connected to reliability in one book. The existing literature on reliability covers inter alia lifetime analysis, complex systems and
maintenance models, and the books by Barlow and Proschan [33, 34] can
be viewed as first milestones in this area. Since then the models and tools
have been developed further. The aim of Stochastic Models in Reliability
is to give a comprehensive up-to-date presentation of some of the classical
areas of reliability, based on a more advanced probabilistic framework using
the modern theory of stochastic processes. This framework allows the analyst to formulate general failure models, establish formulas for computing
various performance measures, as well as to determine how to identify optimal replacement policies in complex situations. A number of special cases
analyzed previously can be included in this framework. Our book presents
a unifying approach to some of the key research areas of reliability theory,
summarizing and extending results obtained in recent years. Having future
work in this area in mind, it will be useful to have at hand a general setup where the conditions and assumptions are formulated independently of
particular models.