Joint Importance Measures for Repairable Multistate Systems

In order to identify the vulnerable components whose joint effect would have changedsystem performance and ensure the required reliability of various multistate systems, jointimportance measures of relevant components are used in the early design of systems. Due tothe complexity of multistate systems that have the properties of non-linearity, uncertainty,and randomness, which make it difficult to analyze the reasons of failure mechanisms, modelthe system, estimate its reliability, and evaluate the joint importance measures of its compo-nents. This paper discussed measures of joint importance of three components for repairablemultistate systems based on the classical Birnbaum measure. Eight importance measuresare studied in detail. These joint importance measures provide a time-dependent analysis ofthe relevancy of components, thus adding insights on the contributions of the joint effect ofthree components on the system reliability or performance over time. An illustrative exam-ple is given. The results of the study show that joint importance measures can be a valuable decision-support tool for designers and engineers in the design of systems.