Optimal inspection model for a load-sharing redundant system

In this paper we consider a k-out-of-n load sharing system, in which the failure of a component increases the hazard rates of the surviving components. The components failures follow a power law intensity function. The system is periodically inspected to detect failed components if the number of failures is less than n-k+1. However, the system fails when the number of failures equals to n-k+1, which is when all components are opportunistically inspected and repaired if they are in a failed state. Two models of load-sharing are considered: a tampered failure rate model, in which only the scale parameter of the power law is affected due to a change in load, and the cumulative exposure (CE) model, in which both the scale parameter and the ages of the surviving components are affected. We propose a model to find the optimal inspection interval for such systems, and describe the application of the model in several case studies. The results reveal that a system with the CE model requires to be inspected more frequently to avoid a high penalty incurred due to system failure. Moreover, shorter inspection interval is also required for a system with higher load intensity.