Abstract
The component assignment problem (CAP) is one of the most important problems in reliability engineering. This paper proposes a Birnbaum importance-based simulated annealing (SA) algorithm for the CAP of linear connected-(r, s)-out-of-(m, n):F lattice systems. Here, the CAP is assigning the components to maximize system reliability, and Birnbaum importance is a measure of the importance of a component assigned at a certain position in the CAP. If the number of components is small, this problem can be solved within an acceptable time by enumerating all solution candidates. However, it is difficult to solve the problem by using this approach with large numbers of components, because the required computational time increases rapidly with the number of components. Based on these factors, we propose an algorithm to solve the CAP of large-sized linear connected-(r, s)-out-of-(m, n):F lattice systems within an acceptable time. We performed numerical experiments to evaluate the effectiveness of combining Birnbaum importance and SA because the proposed algorithm could aid in designing reliable systems.
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Acknowledgements
This work was supported by a Grant-in-Aid for Early-Career Scientists, Grant Number JP21K14370, JSPS KAKENHI, Grant Number 20K04964, and the Tokai University General Research Organization Grant.
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This work was supported by Japan Society for the Promotion of Science Grant number (JP21K14370), Japan Society for the Promotion of Science Grant number (20K04964)
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Appendix: comparison of initial assignment generations
Appendix: comparison of initial assignment generations
Here, we investigate the effectiveness of initial assignment generations using the BITA by comparing the SA algorithm that generates an initial solution using the BITA (SA with the BITA) and the SA algorithm that randomly generates an initial solution (SA without the BITA). SA with the BITA is the algorithm excluding Steps 3 and 9 from the flowchart in Fig. 3. SA without the BITA is the algorithm that randomly generates an initial solution in Step 1 and excludes Steps 3 and 9 from the flowchart in Fig. 3. Accordingly, the only difference between the two algorithms is the initial solution generation method.
Five instances were solved twenty times with each algorithm and the results were compared. Table 3 shows the experimental results when the two algorithms use the same parameters. In this case, SA with the BITA obtained assignments with higher system reliability with less computation time than SA without the BITA. These results confirm the effectiveness of generating the initial solution with the BITA within the scope of the numerical experiments.
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Nakamura, T., Homma, I. & Yamamoto, H. Birnbaum importance-based simulated annealing algorithm for solving the component assignment problem of linear connected-(r, s)-out-of-(m, n):F lattice systems. Int J Syst Assur Eng Manag 15, 1407–1414 (2024). https://doi.org/10.1007/s13198-022-01848-2
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DOI: https://doi.org/10.1007/s13198-022-01848-2