An optimal replacement policy for complex multi-component systems

Abstract

Given a reward structure, this paper addresses an optimal replacement problem for complex multi-component systems. To maintain revenue stream resulting from system, the system is inspected according to a homogeneous Poisson process and certain actions are carried out in response to the system state. Decisions are based on a performance measure described by a Squared Bessel process. Given some assumption, we explore the inherent relation between the Squared Bessel process and an extended Gamma (EG) process. Since there are some flow of income and increasing costs due to inspections, the problem is to optimally stop processing the system and carrying out a renewal to maximize the reward functional. To this end, using the local characteristics of the EG process as a stopping criterion and the expected total discounted reward as a measure of policy, this paper aims at determining an optimal operating (stopping) time which truly balances both income and cost and so maximizes the expected discounted reward over a cycle. In support of the model a numerical example is provided to show feasibility of this programme in real application. Attention is restricted to perfect repair and inspection, but the paper provides the structure so that different scenarios can be explored.