GERT Analysis of m-consecutive-k-out-of-n:F Systems with Dependence

Agarwal Manju, Mohan Pooja and Sen Kanwar
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Agarwal Manju: Department of Operational Research, University of Delhi, Delhi-110007, India
Mohan Pooja: Department of Operational Research, University of Delhi, Delhi-110007, India
Sen Kanwar: Department of Statistics, University of Delhi, Delhi-110007, India

Stochastics and Quality Control, 2007, vol. 22, issue 1, 141-157

Abstract: In this paper the reliability analysis of two new models generalizing the m-consecutive-k-out-of-n:F system is carried out using GERT:Model I: m-consecutive-k-out-of-n:F system with (k-1)-step Markov dependence, andModel II: m-consecutive-k-out-of-n:F system with Block-k dependence.For both the models, the system consists of n linearly ordered components. In Model I, the system fails, if and only if there are at least m non-overlapping runs of k consecutive failed components having (k-1)-step Markov dependence. We call such a system m-consecutive-k-out-of-n:F with (k-1)-step Markov dependence. Model II represents an m-consecutive-k-out-of-n:F system, in which each subsequent occurrence of a block of k-consecutive failures increases the failure probability of the remaining components. We define such a system as m-consecutive-k-out-of-n:F with Block-k dependence. GERT provides a visual picture of the system and helps to analyze the system in a less inductive manner. Mathematica Software is used for systematic computations. Illustrative numerical examples for reliability evaluation of these systems showing the time efficiency of GERT analysis are also provided.

Keywords: m-consecutive-k-out-of-n:F system; (k-1)-step Markov dependence; Block-k dependence; system reliability; GERT (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1515/EQC.2007.141

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