On the s-Importance of Elements and Prime Implicants of Non-Coherent Systems

This paper extends methods for evaluating the s-importance of elements and cut-sets of s-coherent systems to elements and prime implicants of non-coherent systems. Existing measures of s-importance are redefined to provide general expressions for the system elements and prime implicants when non-coherent systems are encountered. The redefined measures utilize the methodology of I&H and the absolute value of the influence of event i (or prime implicant j) on the top-event occurrence probability (or unavailability). An example illustrates the evaluation of the extended Birnbaum and critically measures of s-importance for a non-coherent system. Further research is required to implement the extended measures in procedures for determining optimum restoration sequences (assuming such sequences exist and are meaningful).