OPTIMIZATION PROBLEM IN K-OUT-OF-N SYSTEM WITH NUMBER-DEPENDENT MINIMAL REPAIR

摘要

A k-out-of-n system with number-dependent minimal repair is a system subject to shocks that arrive according to a non-homogeneous Poisson process with n independent identity components such that the system operates if and only if at least k of these n components operate successfully. Such a system is an important complex system and is used for mass transit, safety systems and computer systems. The long-run expected cost rate is obtained. The aim of the paper is to find the optimal number n~* of elements and the optimal age replacement time T~* which minimize the long-run expected cost per unit time of the policy. Various special cases are considered. Numerical examples are given to illustrate the method.