# Reliability Model of Fuzzy Consecutive k-out-of-n: F System

Document Type : Original Research Article

Authors

1 mathematics and engineering physics dep., faculty of engineering, tanta university

2 Department of Mathematics (Section of Statistics), Faculty of Science, Tanta University, Tanta, Egypt

3 Department of Mathematics and Engineering physics, Faculty of Engineering, Tanta University, Tanta, Egypt

Abstract

Redundancy can be used to increase system reliability. The most popular type of redundancy, k-out-of-n system structure, finds wide applications in both industrial and military systems. Aspecial type of this system is the consecutive k-out-of-n:F system C(k,n:F) which have been proposed for reliability evaluation and integrated circuits design, microwave relay stations in telecommunication system, oil pipelines systems, vacuum systems in accelerators, computer ring networks, and spacecraft relay stations.
In this paper, we will discuss a new algorithm for evaluating the fuzzy reliability of any fuzzy linear consecutive k-out-of-n:Fsystem (Lin/C(k,n:F)) with independent, unrepairable, and non-identical components.Later,we will introduce a model of unrepairable system consists of parallel subsystems if each subsystem is Lin/C(k,n:F). Due to uncertainty and insufficient data, failure time of each component follows fuzzy Rayleigh distribution with one fuzzy parameter. This fuzzy parameter is represented by triangular membership function and estimated from statistical data taken from random samples of each component. Furthermore, a numerical example for a fuzzy unrepairable parallel system with three subsystems is given while eachsystem is represented by Lin/C(k,n:F).Also, the failure time of each component follows fuzzy Rayleigh distribution to get analytically and represents the fuzzy reliability function of this fuzzy system graphically.

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Main Subjects

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### History

• Receive Date: 10 November 2018
• Revise Date: 18 December 2018
• Accept Date: 07 January 2019
• First Publish Date: 01 June 2019