Reliability analysis and optimal replacement for a k -out-of- n system under a δ -shock model

Abstract

Consider a k-out-of-n system which is subject to shocks that arrive at random times. This study develops $\delta$ -shock model, among the variants of well-known shock models, for such system which consists of independent components. In a $\delta$ -shock model, the system fails when the inter-arrival between two consecutive shocks is less than a critical threshold value of $\delta$ . Depending on the number of components that fail due to the occurrence of the shocks, we introduce two $\delta$ -shock models. The reliability function and mean time to failure of the system are discussed when the time between shocks has an arbitrary distribution. Furthermore, the problem of finding the optimal preventive time concerned with minimizing a mean cost per unit time is investigated. Numerical examples based on a simulation study are also provided to illustrate theoretical achievement.