Modelling opportunistic maintenance and its effects on the dependability and performance of k -out-of- n systems

A wide range of production, manufacturing, industrial and general technological systems reveal a k-out-of-n structure. A k-out-of-n system is considered as operational when at least k of the n components are operational. Owing to this, upon a planned or an unplanned stoppage of a component and given that the remaining operating components are equal to or more than k, an opportunity to preventively maintain degraded components arises. Such an action, called Opportunistic Maintenance (OM), aims to improve the condition of the entire k-out-of-n system after the completion of all required restoration actions. In the current work, a new state-based approach is introduced to model OM for k-out-of-n multi-state systems. Based on the proposed model, the effects of OM on k-out-of-n multi-state systems' dependability and performance are extensively studied. The paper provides the appropriate theoretical framework for modelling OM and its effects on transient as well as on asymptotic availability and total expected operational cost. Moreover, through numerical examples, it is obtained that OM manages to provide practically the same availability with the systems without any OM action, but significantly lower operational cost. Thus, this work provides a cost-effective and easy to implement approach for enabling OM on k-out-of-n systems.