Joint Importance Measures for Repairable Multistate Systems

Abstract

In order to identify the vulnerable components whose joint effect would have changed system performance and ensure the required reliability of various multistate systems, joint importance measures of relevant components are used in the early design of systems. Due to the 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, model the system, estimate its reliability, and evaluate the joint importance measures of its components. This paper discussed measures of joint importance of three components for repairable multistate systems based on the classical Birnbaum measure. Eight importance measures are studied in detail. These joint importance measures provide a time-dependent analysis of the relevancy of components, thus adding insights on the contributions of the joint effect of three components on the system reliability or performance over time. An illustrative example 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.