Joint importance measures for multistate reliability systems

Abstract

Importance and joint importance measures in reliability engineering are used to identify the weak areas of a system and signify the roles of components in either causing or contributing to proper functioning of the system. Existing joint reliability importance measure of a multistate system with n components provides the joint reliability importance of k (k ≤ n) components. This paper introduces, for two multistate components, joint performance achievement worth, joint performance reduction worth, joint performance Fussell–Vesely measure and joint performance Birnubaum importance measure, using reliability, availability and risk as output performance measures (OPMs) of the multistate system. With reference to a predefined threshold of component performance, the component’s reachable states are restricted to those corresponding to performances either larger or not larger than the threshold level. A steady state performance level distribution with restriction to the component’s states is used to obtain the introduced measures. Use of universal generating function (UGF) for the evaluation of proposed joint importance measures is given. An illustrative example is provided.