A Birnbaum-importance based genetic local search algorithm for component assignment problems

We propose the consecutive-k r -out-of-n r :F linear zigzag structure and circular polygon structure, which extend the consecutive-k-out-of-n:F system model. By employing the finite Markov chain imbedding approach, we have proven the equations for calculating the reliability of consecutive-k-out-of-n:F system with different patterns given the state of the first and(or) the last component(s). Based on those reliability equations, we provide the rules for obtaining the reliability of the linear zigzag structure and circular polygon structure. Numerical examples are presented as an illustration of our new system model and demonstrate the use of the equations and rules proposed in this paper.Index Terms-Birnbaum importance, circular polygon structure, consecutive-k-out-of-n:F system, finite Markov chain imbedding approach (FMCIA), joint reliability importance (JRI), linear zigzag structure.

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“…For more research on JRI, one can refer to Eryilmaz [15], Zhu et al [45], Armstrong [4], Hagstrom [22], Hong and Lie [23], Yao et al [39] …”

Section: Literature Reviewmentioning

confidence: 99%

Reliability Modeling on Consecutive-<inline-formula> <tex-math notation="LaTeX">$k_r $</tex-math> </inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">$n_r $</tex-math> </inline-formula>:F Linear Zigzag Structure and Circular Polygon Structure

et al. 2016

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“…Cai et al [27] proposed an improved genetic algorithm based on heuristic method (BGA) to deal with the CAP, and the research illustrates that BGA is more effective for the systems with arbitrary reliable components. Yao et al [28] constructed a Birnbaum importance-based genetic local search algorithm (BIGLS), which is a comprehensive genetic algorithm to reduce the solution space of the optimal solution based on the local search. When the components of CAP are less, local search could improve the accuracy and convergence speed of the algorithm, but it will take longer time.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

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

Zhang

Zhao

et al. 2017

Mathematical Problems in Engineering

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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.

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“…Cai et al 29 proposed the GA based on the importance to improve the system performance for multicomponent maintenance, and the local search makes GA more effective and efficient. Yao et al 30 constructed an integrated genetic algorithm, which referred as Birnbaum importance-based genetic local search (BIGLS). The local search of BIGLS is based on the ZK-type heuristics, which can gradually reduce the solution space and find the optimal solution effectively.…”

Section: Introductionmentioning

confidence: 99%

Reliability optimization of linear consecutive k-out-of-n: F systems with Birnbaum importance–based quantum genetic algorithm

Zhang

Zhao

Zhu

et al. 2019

Advances in Mechanical Engineering

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Component assignment problem is a common challenge of reliability optimization, which is a non-deterministic polynomial hard problem widely used in the linear consecutive k-out-of-n systems. In consideration of the advantages of quantum computing and importance measure, this article proposed a novel algorithm, which is Birnbaum importance-based quantum genetic algorithm, to improve the efficiency and accuracy for solving component assignment problem. First, the model of reliability optimization for linear consecutive k-out-of-n systems is established. Second, the detailed procedure of Birnbaum importance-based quantum genetic algorithm is introduced to solve the component assignment problem. Moreover, the effectiveness and the convergence of the quantum genetic algorithm, Birnbaum importance-based genetic local search, and Birnbaum importance-based quantum genetic algorithm is discussed through two comparative experiments. Finally, the case of production monitor systems is introduced to illustrate the effectiveness of Birnbaum importance-based quantum genetic algorithm comparing with the Birnbaum importance-based two-stage approach.

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A Birnbaum-importance based genetic local search algorithm for component assignment problems

Cited by 50 publications

References 18 publications

Reliability Modeling on Consecutive-<inline-formula> <tex-math notation="LaTeX">$k_r $</tex-math> </inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">$n_r $</tex-math> </inline-formula>:F Linear Zigzag Structure and Circular Polygon Structure

Reliability Modeling on Consecutive-<inline-formula> <tex-math notation="LaTeX">$k_r $</tex-math> </inline-formula>-out-of-<inline-formula> <tex-math notation="LaTeX">$n_r $</tex-math> </inline-formula>:F Linear Zigzag Structure and Circular Polygon Structure

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

Reliability optimization of linear consecutive k-out-of-n: F systems with Birnbaum importance–based quantum genetic algorithm

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