Optimal replacement policies for k-out-of-n systems with minimal repairs and mission durations

Replacement may occur during the mission in accordance with traditional replacement policies. However, this approach may not be feasible for deactivating a mission-oriented system when a mission is initiated to carry out maintenance operations. In this context, we introduce replacement policies for $$k$$ -out-of- $$n$$ systems considering mission durations. In reliability engineering, $$k$$ -out-of- $$n$$ systems are a key class of configurations, consisting of $$n$$ independent components. These systems remain operational as long as at least k components are continuously functional, with overall performance and reliability depending on the condition that a minimum of $$k$$ components are active. Each unit of the system experiences two types of failures. When a type I failure occurs, a failed unit undergoes minimal repair, whereas in the case of a type II failure, the unit remains idle. The system experiences complete failure when $$n - k + 1$$ units are idle, and requires corrective replacement. Initially, a basic replacement policy for mission-critical $$k$$ -out-of- $$n$$ systems is presented, along with a discussion on the determination of the optimal number of units. Next, we incorporate the notations of “replacement first” and “replacement last” separately. “Replacement first” refers to preventive replacement occurring at the scheduled time or when the mission is completed, whichever happens first. “Replacement last” means that preventive replacement takes place when either of the above events occurs, whichever happens last. Subsequently, the optimal policy for each model is analyzed analytically. A numerical example is then provided to illustrate the findings. Finally, the proposed policies are applied to the maintaince of the automated system for the remote monitoring of underwater sections of a gas pipeline to show how to choose a better policy in three scenarios.