International Society of Science and Applied Technologies 

Reliability and Importance Measures for Combined mConsecutivekoutofn: F and Consecutivek_{b}outofn: F Systems with NonHomogeneous MarkovDependent Components  
Author  Mahmoud Boushaba  
CoAuthor(s)  Azzedine Benyahia  
Abstract  A Combined mConsecutivekoutofn and Consecutivek_{b}outofn: F System is consists of n components ordered in a line such that the system fails if there exist at least k_{b} consecutive failed components, or at least m nonoverlapping runs of k consecutive failed components, where k_{b}< 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 Markovdependent components. For a Combined mConsecutivekoutofn and Consecutive k_{b}outofn: F System with nonhomogenous Markovdependent components, we derive closedform 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 mConsecutivekoutofn and Consecutivek_{b}outofn: F System, nonhomogenous Markovdependent components, probability generating function  
Article #: 23317 
August 35, 2017  Chicago, Illinois, U.S.A. 