Condition-based maintenance for systems with economic dependence and load sharing

Redundancy is often essential for achieving high system availability. An additional benefit of installing redundant components is that the total system load can be shared among components, thus preventing fast deterioration. On the one hand, this provides an incentive to replace failed components as soon as possible, as a component failure increases the load on the remaining components. On the other hand, however, redundancy gives rise to maintenance clustering and postponement opportunities, to reduce the maintenance frequency and thereby lower downtime and maintenance set-up costs. To date, this trade-off has not been investigated under a condition-based maintenance regime. To address this, we consider a parallel system that is subject to both failure dependence through load sharing and economic dependence through maintenance set-up costs. We formulate our system as a Markov Decision Process, and obtain the optimal replacement decisions that minimize the long-run average cost per time unit. Through a numerical investigation and a sensitivity analysis, in which we vary the degree of load sharing, and the maintenance set-up cost, and the degradation process, we obtain key insights into the optimal policy structure. Standard threshold policies, that replace a component as soon as its deterioration exceeds a certain threshold, can be far from optimal, while ignoring or misinterpreting the load sharing effects between components can also lead to a significantly more expensive maintenance policy.