Optimization of Multilevel Inspection Strategy for Nonrepairable Multistate Systems

The reliability function of a specific individual system can be dynamically updated by utilizing inspection data collected over time. However, due to limited inspection resources, such as time, budget, and manpower, it is oftentimes impossible to collect all the inspection data for all the components, subsystems, and the entire system simultaneously. There is an urgent need to optimally allot the limited inspection resources across multiple physical levels of a system, so as to identify the health status of a system and/or its subset of components of interest as accurately as possible to facilitate the ensuing system health management. To address the above research question, a metric is put forth in this paper to quantify the effectiveness of a particular multilevel inspection strategy for multistate systems (MSSs). Based on the proposed metric, an optimization problem is formulated to seek the optimal multilevel inspection strategy which possesses the maximum effectiveness of revealing the true state of a system and/or its subset of components of interest under limited inspection resources. The resulting optimization problem is resolved by a tailored ant colony optimization algorithm. The findings from our illustrative examples are 1) the proposed metric is capable of quantifying the effectiveness of various multilevel inspection strategies; 2) the analytical solution of the proposed metric is exactly the same with the simulation results, but much more computationally efficient; and 3) the optimal inspection strategy varies with respect to the operation time of a specific individual system.