Non-Recursive Algorithms for SystemReliability and Component Importance in Consecutive-k-out-of-n Systems

In this paper, the evaluation of reliability function, VeselyFussell measure of component importance and Birnbaum reliability measure of component importance in a consecutive-k-out-of-n:F system and a consecutive-k-out-of-n:G system are considered. Using the minimal cut (path) sets of a consecutive-k-out-of-n:G(F) system, we present nonrecursive algorithms or determining the system reliability and measures of component importance of these systems. We show that these algorithms leads to explicit formulas for determining the reliability function and measures of component importance in a κ-out-of-n:F system with independent but not identical components