Rare-event component importance for the consecutive-k system

Various indices of component importance with respect to system reliability have been proposed. The most popular one is the Birnbaum importance. In particular, a special case called uniform Birnbaum importance in which all components have the same reliabilityphas been widely studied for the consecutive-k system. Since it is not easy to compare uniform Birnbaum importance, the literature has looked into the case p = 1 ;p! 1 ,o rp 1 . In this paper, we look into the case p ! 0 to complete the spectrum of examining Birnbaum importance over the whole range of p. c 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 159{166, 2002; DOI