Title: GERT analysis of m-consecutive-k-out-of-n:F system with overlapping runs and (k–1)-step Markov dependence

Authors: Manju Agarwal, Pooja Mohan

Addresses: Department of Operational Research, University of Delhi, Delhi 110007, India. ' Department of Operational Research, University of Delhi, Delhi 110007, India

Abstract: An m-consecutive-k-out-of-n:F system is a system of n linearly ordered components which fails if and only if at least m non-overlapping sequences of k consecutive components fail. When m = 1, we have the classic consecutive-k-out-of-n:F system about which there is an extensive literature. In this paper, we study the situation in which a system consisting of n linearly ordered sequence of components fails if and only if there are at least m overlapping runs of k consecutive failed components. Graphical Evaluation and Review Technique (GERT) analysis is used for reliability evaluation of the system for both, i.i.d. components and (k–1)-step Markov dependent components, in a unified manner. Software Mathematica is used for systematic computation. Illustrative numerical examples are presented to substantiate the theory.

Keywords: graphical evaluation and review technique; GERT; m-consecutive-k-out-of-n:F system; overlapping runs; (k–1)-step Markov dependence; system reliability; operational research.

DOI: 10.1504/IJOR.2008.016153

International Journal of Operational Research, 2008 Vol.3 No.1/2, pp.36 - 51

Published online: 07 Dec 2007 *

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