Modified block-replacement for multiple-component systems

Abstract

This paper extends the modified block-replacement policy (MBRP) of Berg and Epstein (1976) in two ways; we consider: a discrete time framework which allows the use of any discrete lifetime distribution, and multi-component systems. Both of these extensions increase the practical value of the MBRP. In MBRP, components are replaced immediately on failure, and preventive maintenance (PM) is performed at regular intervals. During PM every component whose age is greater than a fixed threshold age is replaced. Unlike many models for multicomponent systems, this policy is structured. In both the standard block-replacement policy (SBRP) and MBRP, PM is performed at regular intervals and so can be planned in advance. However MBRP results in a lower average cost-rate by replacing components selectively during PM. Our results show how successful the MBRP is in this respect by comparing its cost with the costs of good, but difficult to compute and implement, age-based PM policies. This paper shows that MBRP is appreciably better than SBRP and only slightly poorer than the age replacement policy (ARP) for multi-component systems with a variety of lifetime distributions and a range of cost parameters. In most of our examples the MBRP bridges more than 2/3 of the gap between the minimum average cost of the ARP and SBRP. Compared to the ARP, the MBRP is more convenient because PM can be planned in advance, tracking the ages of components is unnecessary and, for multi-component systems, the optimal MBRP is easier to compute and characterize.