Simple bounds for terminating Poisson and renewal shock processes
A reliabilility system driven by a point process of shocks is considered. The shocks occur in accordance with a renewal or non-homogeneous Poisson process. Each shock independently of the previous history leads to a system failure with probability \(\theta\) and survives with the complimentary probability \(1-\theta\). It is well known that the exact form of the probability of survival is given by an infinite series. In this paper, new simple bounds for the probability of survival are given. In the proofs, stochastic hazard rate processes are used. Thus, the case is treated where the probability of a system failure under the effect of a current shock depends on the time since the previous one.
scientific article; zbMATH DE number 1912373