A Complete Importance Ranking for Components of Binary Coherent Systems,with Extensions to Multi-State Systems.

摘要

Given a system composed of many components, a question of considerable interest is which components are most relevant or crucial to the proper functioning of the system. In response to this question, a number of importance measures and rankings have been proposed. This paper investigates a new ranking and compares it to existing rankings, principally the ranking induced by the Birnbaum reliability importance measure. The new ranking is based upon minimal cuts and provides a complete ordering of all the system's components relative to their importance to the system reliability. This ranking has three main points in its favor: (i) the calculations involved require only readily obtainable information; (ii) the calculations are usually quite simple; and (iii) the ranking is designed for use with systems consisting of highly reliable components, the most common case. The final section of the paper deals with extensions of importance measures and rankings to systems in which both the system and its components may be in any of a finite number of states. Many of the results about importance measures and rankings for binary systems established in preceding sections are shown to extend to the more sophisticated multi-state systems. Also, the multi-state importance measures and rankings are shown to be decomposable into a number of sub-importance measures and rankings. (Author)