Reliability and Importance Measures for Combined m-Consecutive-k-out-of-n: F and Consecutive-kb-out-of-n: F Systems with Non-Homogeneous Markov-Dependent Components  
Author Mahmoud Boushaba
Co-Author(s) Azzedine Benyahia
Abstract A Combined m-Consecutive-k-out-of-n and Consecutive-kb-out-of-n: F System is consists of n components ordered in a line such that the system fails if there exist at least kb consecutive failed components, or at least m non-overlapping runs of k consecutive failed components, where kb< mk. This system was been introduced by Mohan et al. [8] where they propose an algorithm to evaluate system reliability by using the (GERT) technique, in the independent case. In this paper, we propose a new formula of the reliability of this system for nonhomogeneous Markov-dependent components. For a Combined m-Consecutive-k-out-of-n and Consecutive- kb-out-of-n: F System with non-homogenous Markov-dependent components, we derive closed-form formulas for the marginal reliability importance measure of a single component, and the joint reliability importance measure of two or more than two components using probability generating function (pgf) and conditional pgf methods.
Keywords system reliability, marginal reliability importance, joint reliability importance, Combined m-Consecutive-k-out-of-n and Consecutive-kb-out-of-n: F System, non-homogenous Markov-dependent components, probability generating function
    Article #:  23-317
Proceedings of the 23rd ISSAT International Conference on Reliability and Quality in Design
August 3-5, 2017 - Chicago, Illinois, U.S.A.