OBDD-based evaluation of reliability and importance measures for multistate systems subject to imperfect fault coverage

Algorithms for evaluating the reliability of a complex system such as a multistate fault-tolerant computer system have become more important recently. They are designed to obtain the complete results quickly and accurately even when there exist a number of dependencies such as shared loads (reconfiguration), degradation, and common-cause failures. This paper presents an efficient method based on Ordered Binary Decision Diagram (OBDD) for evaluating the multistate system reliability and the Griffith's importance measures which can be regarded as the importance of a system-component state of a multistate system subject to imperfect fault-coverage with various performance requirements. This method combined with the conditional probability methods can handle the dependencies among the combinatorial performance requirements of system modules and find solutions for multistate imperfect coverage model. The main advantage of the method is that its time complexity is equivalent to that of the methods for perfect coverage model and it is very helpful for the optimal design of a multistate fault-tolerant system.