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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Agarwal Manju & Mohan Pooja & Sen Kanwar, 2007. "GERT Analysis of m-consecutive-k-out-of-n:F Systems with Dependence," Stochastics and Quality Control, De Gruyter, vol. 22(1), pages 141-157, January.
    • Handle: RePEc:bpj:ecqcon:v:22:y:2007:i:1:p:141-157:n:4
    DOI: 10.1515/EQC.2007.141
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