Reliability systems in random environment

Abstract

A parallel reliability system is subject to shocks which are generated by a renewal point process. The shocks cause the components to fail with certain probabilities. First we study the case when the components fail independently of each other with the same probability. For this case simple closed expressions for the Laplace-Stieltjes transform and expectation of time to system failure are derived. Then a case of dependent components is studied: the probability of failure of a component depends on the number of functioning components. Some extensions are mentioned.