A COUNTER-INTUITIVE ASPECT OF COMPONENT IMPORTANCE IN LINEAR CONSECUTIVE-k-OUT-OF-nSYSTEMS

Abstract

Abstract In this paper we study a certain counter-intuitive aspect of component importance in linear consecutive-k-out-of-n systems, when the components are independent with equal reliability p. It is shown that, in the case of the Birnbaum measure, the importance of the k-th component is greater than that of the (k+ l)-st when 2k+1 ≤ n ≤ 3k+1 for any p on [0,1] or when n > 3k+1 for p and k such that (1 — p k)k ≥ 1 —p. The same pertains in the case of the Barlow-Proschan measure when 2k+1 ≤ n ≤ 3k+l or when n is sufficiently large.