Importance index of components in uncertain random systems

Importance measure is an index to describe the importance of an individual component or a group of components within a reliability system. Up to now, importance measures for components in stochastic reliability systems have been investigated. And importance index for a component and a group of components in an uncertain reliability system has also been studied. In the real world, components with samples and components without samples always coexist in a complex system which is actually an uncertain random reliability system. For describing the importance extent of an individual component and a group of components in an uncertain random reliability system, this paper aims at introducing a new concept of importance index and presenting some formulas to calculate the importance index. Furthermore, this paper takes several examples including uncertain random series, uncertain random parallel, uncertain random parallel-series, uncertain random series-parallel and uncertain random bridge systems to illustrate how to calculate an importance index.