The Birnbaum importance is a well-known measure that evaluates the relative contribution of components to system reliability. There exist certain patterns of the component Birnbaum importance (i.e., the relative order...
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The Birnbaum importance is a well-known measure that evaluates the relative contribution of components to system reliability. There exist certain patterns of the component Birnbaum importance (i.e., the relative order of the Birnbaum importance values to the individual components) for linear consecutive-k-out-of-n (Lin/Con/k/n) systems when all components have the same reliability p. Previous research has shown that based on the Birnbaum importance, plausible patterns and conjectures exist. This article summarizes and annotates the Birnbaum importance patterns for Lin/Con/k/n systems, proves new Birmbaum importance patterns conditioned on the value of p, disproves some patterns that were conjectured or claimed in the literature, and makes new conjectures based on comprehensive computational tests and analysis. More important, this article defines a concept of segment in Lin/Con/k/n systems for analyzing the Birnbaum importance patterns and investigates the relationship between the Birnbaum importance and the common component reliability p and the relationship between the Birnbaum importance and the system size n. One can then use these relations to further understand the proved, disproved, and conjectured Birnbaum importance patterns.
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 ad...
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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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