Stochastic Processes Used in Modeling Reliability Problems

Abstract

The investigation of the time behaviour of a repairable system, and in particular of its reliability and availability, can theoretically always be performed using stochastic processes. However, in order to be analytically tractable, it is generally necessary to confine the reliability models to a class which can be handled with regenerative stochastic processes. These include renewal and alternating renewal processes, Markov processes with a finite state space, semi-Markov processes, and regenerative stochastic processes with only one (or a few) regeneration state(s). Particular models can also be investigated using some kinds of non-regenerative stochastic processes, like superimposed renewal processes and processes with supplementary variables. This chapter introduces the stochastic processes used in the modeling of reliability problems. Emphasis is given to aspects which are important in practical applications (chapters 4 through 6).