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

Shuai Zhang,Ning Wang,Hong-Guang Li,Jiang-Bin Zhao

doi:10.1155/2017/1831537

Abstract

The circular-consecutive k-out-of-n:F(G) system (Cir/Con/k/n:F(G) system) usually consists of n components arranged in a circle where the system fails (works) if consecutive k components fail (work). The optimization of the Cir/Con/k/n 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/k/n 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/k/n system. Finally, three typical cases of Cir/Con/k/n systems are introduced to demonstrate the relationships among the component reliability, optimal permutation, and component importance.

Highlights

The component assignment problem (CAP) [1] is a kind of classic problem in the optimization of system reliability
The system is composed of n positions and n components with different reliabilities, and the n components should be assigned into n different positions to find the optimal assignment with the maximum system reliability
It can be clearly seen that BIGLS is slightly more efficient than BIGA in the low reliable systems, but less effective and inferior to BIGA in the high and arbitrary systems

Summary

Introduction

The component assignment problem (CAP) [1] is a kind of classic problem in the optimization of system reliability. The optimization of consecutive k-outof-n system (Con/k/n system) is a typical case of CAP, and its purpose is to ensure that the system reliability remains largest. A linear-consecutive k-out-of-n:F(G) system (Lin/Con/ k/n:F(G) system) is an ordered sequence of n components arranged in a line such that the system fails (works) if and only if at least k consecutive components fail (work). Lin/Con/k/n systems are used in most system designs, such as telecommunication or pipeline networks, the allocation of microwave towers and street lamps, and arrangement of spacecraft relay stations [3]. If a pump is failed, the pipeline system can work normally unless the k consecutive pumps all failed. The pipeline system is a Lin/Con/k/n:F system which is widely used in the practical engineering

Results

Discussion

Conclusion