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Mathematical Problems in Engineering
Volume 2017, Article ID 1831537, 17 pages
Research Article

Reliability Optimization and Importance Analysis of Circular-Consecutive -out-of- System

1Department of Industrial Engineering, School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, China
2School of Automobile, Chang’an University, Xi’an, Shaanxi 710064, China

Correspondence should be addressed to Jiang-bin Zhao; nc.ude.upwn.liam@nibgnaijoahz

Received 8 March 2017; Accepted 29 May 2017; Published 15 August 2017

Academic Editor: David Bigaud

Copyright © 2017 Shuai Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The circular-consecutive -out-of-: system (Cir/Con//: system) usually consists of components arranged in a circle where the system fails (works) if consecutive components fail (work). The optimization of the Cir/Con// system is a typical case in the component assignment problem. In this paper, the Birnbaum importance-based genetic algorithm (BIGA), which takes the advantages of genetic algorithm and Birnbaum importance, is introduced to deal with the reliability optimization for Cir/Con// system. The detailed process and property of BIGA are put forward at first. Then, some numerical experiments are implemented, whose results are compared with two classic Birnbaum importance-based search algorithms, to evaluate the effectiveness and efficiency of BIGA in Cir/Con// system. Finally, three typical cases of Cir/Con// systems are introduced to demonstrate the relationships among the component reliability, optimal permutation, and component importance.