Combinatorial Algorithm for Reliability Analysis of Multistate Systems With Propagated Failures and Failure Isolation Effect

This paper considers the reliability analysis of multistate systems (MSSs) subject to propagated failure with global effect (PFGE) and failure isolation effect. The PFGE can be caused by an imperfect fault coverage despite the presence of fault-tolerant mechanism or by a destructive effect of failures that originate from some system components on other components. The failure isolation effect is caused by functional dependence among system components, where the failure of some component can prevent the propagation of failures that originate from other components within the same system. Existing approaches for simultaneously addressing PFGE and failure isolation are limited to binary-state systems in which the system and its components exhibit two and only two states: operation or failure. In practice, however, many systems are MSS in which the system and/or its components may exhibit multiple performance levels corresponding to different states ranging from perfect operation to complete failure. In this paper, a separable and combinatorial methodology is proposed for evaluating the reliability of MSS subject to both PFGE and the failure isolation effect. The proposed method has no limitation on the type of time-to-failure distributions for the system components and is applicable to MSS with any arbitrary system structure. Application and advantages of the proposed method are illustrated through a detailed analysis of an example of a multistate memory system.