Stochastic Processes: Use and Limitations in Reliability Theory

Stochastic processes are powerful tools for the investigation of the reliability and availability of repairable equipment and systems. Because of the involved models and in order to be mathematically tractable, these processes are generally confined to the class of regenerative stochastic processes with a finite state space, to which belong renewal processes, Markov processes, semi-Markov processes, and more general regenerative processes with only few (in the limit case only one) regeneration states. This contribution introduce briefly these processes and uses them to solve some reliability problems encountered in pratical applications. Investigations deal with different kinds of reliabilities and availabilities for one item, series, parallel, and series/ parallel structures. For series/parallel structures useful approximate expressions are developed.