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

GERT Analysis of m -consecutive- k -out-of- n : F Systems with Dependence 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, and Model 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

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

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Publisher
de Gruyter
Copyright
Copyright © 2007 by the
ISSN
1869-6147
eISSN
1869-6147
DOI
10.1515/EQC.2007.141
Publisher site
See Article on Publisher Site

Abstract

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, and Model 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.

Journal

Economic Quality Controlde Gruyter

Published: Apr 1, 2007

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