Optimizations of Replacement Policies for Random k-out-of-n Systems

Abstract

In this paper, a random repairable [Formula: see text]-out-of-[Formula: see text] system is studied when random replacement policies are performed, where [Formula: see text] is a stochastic parameter. It is replaced before failure at a planned time [Formula: see text] or at random working cycle [Formula: see text], whichever occurs last or first. Furthermore, optimal replacement policies are obtained for the extended models with working numbers. This paper aims to find the optimal replacement policies when replacement first and last policies are performed. Expected cost rates for the first and last replacement policies are derived, and their optimal replacement policies are derived analytically. Numerical examples are given to illustrate the theoretical results.