Abstract: In order to characterize the reliability of multi-state system in performance degradation condition effectively and determine the effects of each component ( state) on the system,this paper makes a performance state analysis and presents dynamic reliability metrics as well as an importance calculation method considering performance level restrictions.Firstly,the failure probability,reliability,performance state expectation,average performance state expectation and performance state duration of system ( component) are calculated by using the universal generating function to avoid the combinatorial explosion of Markov model in multi-state system.Then,four importance indexes under certain performance level restrictions,namely Birnbaum importance,Fussell-Vesely importance,risk assessment worth and risk reduction worth,are defined with performance expectation value to comprehensively evaluate the effects of each component ( state) on the system and meet different performance requirements of system ( component) .The application results to the fuel supply system of four-cylinder diesel engine indicate that the proposed approach can not only accurately solve the failure probability,reliability,performance state expectation,average performance state expectation and performance state duration of system ( component) ,but also comprehensively assess the effects of each component ( state) on the system according to the four importance values under performance level restrictions.Therefore,it helps improve system reliability through identifying the weakest parts in the system.

Key words: multi-state system, reliability, Markov processes, dynamic reliability metric, performance level restriction, importance