Importance Measure for Multilevel Inspections of Multistate Systems: A Value of Information Perspective

Inspection is a crucial activity for an engineered system as its results can reduce the uncertainty of identifying the true states of the system and its components, so as to facilitate subsequent proactive maintenance. The preliminary work to conduct an inspection activity is to evaluate its effectiveness. In many real-world scenarios, engineered systems oftentimes possess both multistate and hierarchical characteristics, and inspection can be performed across multiple physical levels of a system. We, therefore, need a measure to assess the effectiveness of a multilevel inspection activity of multistate systems. Inspired by the concept of importance measure, in this article, we define a new measure, namely, inspection importance measure (InsIM), to assess the contribution of a multilevel inspection strategy to the efficiency improvement of the subsequent preventive maintenance from a value of information perspective. The proposed measure evaluates the increased efficiency of preventive maintenance after conducting multilevel inspection activities. The procedure of the proposed InsIM contains four steps: 1) calculating the efficiency of the optimal maintenance policy identified without inspections, 2) updating the system's state distribution by multilevel inspection activities, 3) calculating the efficiency of the optimal maintenance policy identified with inspections, and 4) evaluating the expected improvement of maintenance policy. A five-component system and a real-world programmable logic controller control system are exemplified to demonstrate the accuracy and effectiveness of the proposed method. The results indicate that the InsIM can significantly enhance the efficiency of the subsequent proactive maintenance decision.