ABSTRACT
In this chapter we make use of the fact that some system reliability problems give rise in a natural way to regenerative stochastic processes.
A stochastic process is said to be regenerative if it has embedded within it a sequence of time points called points of regeneration. A point τ is said to be a point of regeneration of a stochastic process X(t) if the (conditional) distribution of X(t) for t > τ , given X(t) for all t ≤ τ , is identical with the (conditional) distribution of X(t) for t > τ , given X(τ). It is this basic property which is used in setting up the integral equations for the examples in this chapter. For a discussion of regenerative processes, see Kalashnikov [34]. Points of regeneration are conceptually akin to what are called recurrent events (Chapter 13 of Feller [26]).
