Importance measures for multi-state systems with multiple components under hierarchical dependences

This paper explicitly modeled the hierarchical dependences existing in multi-state systems (MSSs) and proposed novel importance measures (IMs) to rank the criticality of failure-induced factors in different levels. Dependence existing within the component is specified as that arrived shocks make the components become more susceptible to the inherent multi-state degradation. The interaction among components refers to the fact that the degradation of a particular component can be accelerated by others. A comprehensive framework based on Semi-Markov process is constructed to jointly analyze the dependences above. By using the proposed IMs, contributions of each comprising component are firstly measured under hierarchical dependences. Secondly, influences brought by the triggering components on the influenced component are ranked so that the dependence strength among components can be measured. Then, criticality analysis for the suffered failure processes is conducted to specify how the failure processes affect the component reliability level. At last, an illustrative example about a wind turbine generator is presented to show how the proposed IMs can be applied for identifying the key component and its critical failure process.