A linear weighted system for non-homogeneous Markov-dependent components

Xiaoyan Zhu and Mahmoud Boushaba

IISE Transactions, 2017, vol. 49, issue 7, 722-736

Abstract: We study a linear weighted (n, f, k) system, denoted by L(n, f, k, w) system and consider the situation where components are non-homogeneous Markov-dependent. An L(n, f, k, w) system consists of n components ordered in a line, and each component u has a positive integer weight wu for u = 1, 2, …, n and w = (w1, w2, …, wn). The L(n, f, k, w):F (G) system fails (works) if the total weight of failed (working) components is at least f or the total weight of consecutive failed (working) components is at least k. For the L(n, f, k, w):F system with non-homogeneous Markov-dependent components, we derive closed-form formulas for the system reliability, the marginal reliability importance measure of a single component, and the joint reliability importance measure of multiple components using a conditional probability generating function method. We extend these results to the L(n, f, k, w):G systems, the weighted consecutive-k-out-of-n systems, and the weighted f-out-of-n systems. Our numerical examples and a case study on a bridge system demonstrate the use of derived formulas and provide the insights on the L(n, f, k, w) systems and the importance measures. In addition, the two failure modes associated with the L(n, f, k, w):F systems are analyzed by comparing to the single failure mode associated with the weighted consecutive-k-out-of-n:F systems and the single failure mode associated with the weighted f-out-of-n:F systems.

Date: 2017
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DOI: 10.1080/24725854.2016.1269977

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