On a cold standby repairable deteriorating system subject to random shocks and stochastic lead time via phase type quasi-renewal processes

Purpose The objective of this article is to investigate a shock model for a cold standby repairable deteriorating system with non-negligible phase type quasi-renewal process maintenance times and threshold with spare. Design/methodology/approach This paper aims to assess the significance of a property of phase type quasi-renewal processes, it is easy to evaluate the theory concept of a cold standby repairable deteriorating system subject to random shocks and stochastic lead time via phase type quasi-renewal processes. Findings The current research work obtained an optimal replacement policy N * analytically and numerically for a cold standby repairable deteriorating system with spare using a phase type quasi-renewal process. Originality/value The study of a random threshold shock model for a cold standby repairable deteriorating system with spare via-phase type quasi-renewal processes has not been reported anywhere in the literature. In addition, in such a context, an optimal replacement policy N * has not been obtained analytically. The current research paper is to bridge the gap in the literature. The numerical example presented indicates that a maintenance policy suggested in this article aids in generating a significantly.