# 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

, Volume 22 (1) – Apr 1, 2007
17 pages

/lp/de-gruyter/gert-analysis-of-m-consecutive-k-out-of-n-f-systems-with-dependence-ys1ge0KAX1
Publisher
de Gruyter
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