Joint importance of multistate systems

Importance measures in reliability engineering are used to identify weak areas of a system and signify the roles of components in either causing or contributing to proper functioning of the system. Traditional importance measures for multistate systems mainly concern reliability importance of an individual component and seldom consider the utility performance of the systems. This paper extends the joint importance concepts of two components from the binary system case to the multistate system case. A joint structural importance and a joint reliability importance are defined on the basis of the performance utility of the system. The joint structural importance measures the relationship of two components when the reliabilities of components are not available. The joint reliability importance is inferred when the reliabilities of the components are given. The properties of the importance measures are also investigated. A case study for an offshore electrical power generation system is given.