Maintenance planning for a deteriorating production process

We consider a system subject to degradation, more precisely a production process with three quality states evolving according to a homogeneous Markov process. The degradation decreases the income generated by the system. To maintain revenue stream and prevent the loss of revenue, the system is inspected according to a Markov-modulated Poisson process. It is assumed that each inspection at time t incurs a time dependent cost. Each inspection improves the system health and therefore the degradation level jumps to a less deteriorated state. In absence of inspections, the system state is prone to shift to a more deteriorated state with a constant rate. The problem is to determine an optimal operating (stopping) time which truly balances some flow of income and increasing costs due to inspections, and so maximizes the expected gain of the proposed policy. To demonstrate the applicability of the explored approach and its effectiveness, some numerical results are provided. - Highlights: • An integrated model based on a quality state-dependent reward structure is explored. • The model allows the revenue stream responds to variation in the quality state. • The production process is inspected according to a Markovmodulated Poisson process. • Assuming a Markovian structure, we predict the quality state behavior. • We determine an optimal production run length based on a stopping decision rule.