Joint maintenance and inspection optimization of a k-out-of-n system

Abstract

Redundantly-configured k-out-of-n systems have wide applications in various industries. Even though the reliability and availability of k-out-of-n systems have been studied in the literature, not many models have been proposed for inspection and maintenance optimization of such systems. In addition, for majority of k-out-of-n systems, it is assumed that a failed component is always rectified by replacement, which is not a realistic assumption for many systems in the real world. In this paper, we consider a k-out-of-n system with components whose failures follow a non-homogeneous Poisson process with power law intensity function. The system is periodically inspected, and if the number of failed components in an inspection interval does not exceed n-k+1, the failed components are detected and rectified only at a periodic inspection. However, if the number of failures reaches n-k+1, the system fails and this is when all the failed components are detected and fixed. When a failure is detected, we should decide whether to minimally repair the component or replace it. Thus, two types of optimal decisions should be made simultaneously: obtaining the optimal maintenance action for a failed component and finding the optimal periodic inspection interval for the entire system. We formulate a model to obtain jointly the optimal maintenance actions and the periodic inspection interval which results in the minimum total expected cost of the system over a finite planning horizon. The optimal maintenance decision is the optimal number of minimal repairs that should be performed before a component is replaced. The total cost includes the cost of periodic inspections, the penalty cost for system failures, minimal repairs and replacements of the components, and the penalty cost for the downtime of the components before they get rectified. We then develop a simulation model to obtain the required model parameters. The application of the proposed model is shown in case studies of a 1-out-of-5 (parallel), 2-out-of-5 and 5-out-of-5 (series) systems. The 1-out-of-5 system incurs the smallest optimal total expected cost of inspection and maintenance, while the 5-out-of-5 system incurs the highest optimal cost. The optimal inspection period is the longest for the 5-out-of-5 system, since the greater number of failures provides a greater number of opportunistic inspections, which reduces the need for frequent periodic inspections.