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

Abstract

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.

New Bounds for All Types of Multi-state Consecutive $k$ -Out-of-$r$ -From-$n$ : F System Reliability

“…When k = r, the system is named consecutive-k-out-of-n: F system (e.g. Eryilmaz [8], Dăuş and Beiu [9], and Zhang et al [10]), when r = n, the system is named k-out-of-n: F system (e.g. Pham [11], and Eryilmaz [12], [27]).…”