The birnbaum importance and the optimal replacement for the consecutive-k-out-of-n： F system

Abstract

This paper deals with the problem that given a new component and a consecutive-k-ot-of-n:F system,shich component should be replaced with the new one such that the resulting system reliability is maximized.Based on the B-importance, we propose an O(n) time algorithm for the linear system and an O(n²)time algorithm for the circular system.Both algorithms are far more efficient than the straightforward algorithms.As a special case, if the reliability of the original circular system is 0,the optimal replacement for this system can be found in O(kn)time by our modified circular algorithm