Bi-objective optimization of active redundancy allocation in the electrical power distribution system of a marine vessel considering load sharing and a single repairman

Document Type : Original Article

Authors

Department of Industrial Management and Engineering, Malek Ashtar University of Technology, Isfahan, Iran.

Abstract
Purpose: The objective of the present study is to determine an optimal configuration in terms of the type and number of components in order to maximize system availability and reduce costs, using an active redundancy allocation strategy, while considering load-sharing capability and the use of maintenance personnel under maintenance and leave policies, in the electrical power distribution system of a marine vessel. In the active redundancy strategy, all additional components and subsystems are operated simultaneously from the start of system operation, and the system fails only when all components have failed.
Methodology: In this study, a bi-objective model is developed for an electrical power distribution system with active redundancy in a marine vessel, where the first objective is minimization of total cost and the second objective is maximization of system availability. System behavior is simulated using a Markov chain and a phase-type distribution, and the model is solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Failure of one component affects the failure rates of other components within the same subsystem, leading to an increase in their failure rates. In other words, the problem is analyzed under a load-sharing condition. A single repairman is considered for equipment repair. The maintenance and leave policy is defined such that if a component fails during the repairman’s leave period, the leave is terminated and repair of the failed component begins immediately. If another component fails while a component is under repair, it is placed in a repair queue, and the repairman starts repairing the next failed component immediately after completing the repair of the previous one. When the repairman is on leave and no component failure occurs, the repairman may resume the leave period.
Findings: The results of the study identify the optimal combination of the type and number of electrical power distribution panels in each subsystem of the vessel’s electrical power distribution system, aimed at increasing system availability and reducing costs through the use of active redundancy. In addition, the results provide the probability of the repairman being busy, which can support managerial decision-making regarding maintenance and leave policies.
Originality/Value: Considering the innovative aspects of the study, the results can be effectively used for engineering analyses, particularly in evaluating system availability, as well as for managerial analyses, including cost estimation and the allocation of maintenance personnel.

Keywords

Subjects

[1]      Ebling, C. E. (2021). An introduction to reliability and maintainability engineering. Akhtar negar. https://ketabnak.com/book/123841/
[2]      Jafarnejad, A., Esmaeeilian, M. (2012). Maintenance and reliability management. https://samta.samt.ac.ir/content/9539/
[3]      Golmohammadi, E., & Ardakan, M. A. (2022). Reliability optimization problem with the mixed strategy, degrading components, and a periodic inspection and maintenance policy. Reliability engineering & system safety, 223, 108500. https://doi.org/10.1016/j.ress.2022.108500
[4]      Oszczypała, M., Ziółkowski, J., & Malachowski, J. (2024). Redundancy allocation problem in repairable k-out-of-n systems with cold, warm, and hot standby: A genetic algorithm for availability optimization. Applied soft computing. https://doi.org/10.1016/j.asoc.2024.112041
[5]      Noormohammadi, G., Safari, J., Najafi, S. E., & Movahedi Sobhani, F. (2025). Defense and attack strategy optimization for reliability systems with virtual components and active redundancy with a game theory approach. Journal of decisions and operations research, 10(1), 109–124. https://doi.org/10.22105/dmor.2025.497532.1902
[6]      Jadhav, S., & Kumar, A. (2025). Stochastic modeling and availability optimization of wireless sensor network through particle swarm optimization. Reliability engineering \& system safety, 111538. https://doi.org/10.1016/j.ress.2025.111538
[7]      Jakkula, B., Mandela, G. R., & Tripathi, A. K. (2025). Reliability-based scheduled maintenance (SM) for mining equipment with artificial neural network (ANN) model. Precis. mech. digit. fabr, 2(2), 124–133. https://library.acadlore.com/PMDF/2025/2/2/PMDF_02.02_05.pdf
[8]      Garg, D., Popli, D., Kamboj, P., & Vashishth, N. (2025). Reliability availability maintainability dependability (ramd) optimization: A case study of manufacturing plant. Reliability: theory & applications, 20(2 (84)), 308–323. https://cyberleninka.ru/article/n/reliability-availability-maintainability-dependability-ramd-optimization-a-case-study-of-manufacturing-plant
[9]      Yusuf, I., Auta, K. S., & Kabeer, M. (2024). Optimizing system availability in client-server network through fog computing: a stochastic model with foggy markovian paths. Risk assessment and management decisions, 1(1), 102–118. https://doi.org/10.48314/ramd.v1i1.38
[10]    Juybari, M. N., Zeinal Hamadani, A., & Liu, B. (2022). A Markovian analytical approach to a repairable system under the mixed redundancy strategy with a repairman. Quality and reliability engineering international, 38(7), 3663–3688.
[11]    Peiravi, A., Ardakan, M. A., & Zio, E. (2020). A new Markov-based model for reliability optimization problems with mixed redundancy strategy. Reliability engineering & system safety, 201, 106987. https://doi.org/10.1016/j.ress.2020.106987
[12]    ZhAng, C., & ZhAng, Y. (2020). Common cause and load-sharing failures-based reliability analysis for parallel systems. Eksploatacja i niezawodność, 22(1). http://dx.doi.org/10.17531/ein.2020.1.4
[13]    de Paula, C. P., Visnadi, L. B., & de Castro, H. F. (2019). Multi-objective optimization in redundant system considering load sharing. Reliability engineering & system safety, 181, 17–27. https://doi.org/10.1016/j.ress.2018.08.012
[14]    Xu, H., Fang, Y., & Fard, N. (2018). Optimal design for resilient load-sharing systems with nonidentical components. Quality and reliability engineering international, 34(6), 1254–1270.
[15]    Kayedpour, F., Amiri, M., Rafizadeh, M., & Nia, A. S. (2017). Multi-objective redundancy allocation problem for a system with repairable components considering instantaneous availability and strategy selection. Reliability engineering \& system safety, 160, 11–20. https://doi.org/10.1016/j.ress.2016.10.009
[16]    Zhao, X., Liu, B., & Liu, Y. (2018). Reliability modeling and analysis of load-sharing systems with continuously degrading components. IEEE transactions on reliability, 67(3), 1096–1110. https://doi.org/10.1109/TR.2018.2846649
[17]    Xiao, H., Shi, D., Ding, Y., & Peng, R. (2016). Optimal loading and protection of multi-state systems considering performance sharing mechanism. Reliability engineering & system safety, 149, 88–95. https://doi.org/10.1016/j.ress.2015.12.001
[18]    Sharifi, M., Cheragh, G., Maljaii, K. D., Zaretalab, A., & Fakre Daei, A. V. (2015). Reliability optimization of a series-parallel k-out-of-n system with failure rate depends on working components of system. International journal of industrial engineering, 22(4). https://www.researchgate.net/profile/Arash-Zaretalab/publication/281061933
[19]    Liu, B., Cui, L., Wen, Y., & Shen, J. (2015). A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process. Reliability engineering & system safety, 142, 1–8. https://doi.org/10.1016/j.ress.2015.04.010
[20]    Han, Y., Wen, Y., Guo, C., & Huang, H. (2015). Incorporating cyber layer failures in composite power system reliability evaluations. Energies, 8(9), 9064–9086. https://doi.org/10.3390/en8099064
[21]    Guo, J., Wang, Z., Zheng, M., & Wang, Y. (2014). Uncertain multiobjective redundancy allocation problem of repairable systems based on artificial bee colony algorithm. Chinese journal of aeronautics, 27, 1477–1487. https://doi.org/10.1016/j.cja.2014.10.014
[22]    Zoulfaghari, H., Zeinal Hamadani, A., & Ardakan, M. (2013). Bi-objective redundancy allocation problem for a system with mixed repairable and non-repairable components. ISA transactions, 53. https://doi.org/10.1016/j.isatra.2013.08.002
[23]    Noormohammadi, G., Safari, J., Najafi, A. & Movahedi Sobhani, F. (2025). Defense and attack strategy optimization for reliability systems with virtual components and active redundancy using a game theory approach, 10(1), 109-124. (In Persian). doi.org/10.22105/dmor.2025.497532.1902.
[24]    Wu, R., Li, Y., Guo, S., & Wenxiang, X. (2018). Solving the dual-resource constrained flexible job shop scheduling problem with learning effect by a hybrid genetic algorithm. Advances in mechanical engineering, 10. https://doi.org/10.1177/1687814018804096
[25]    Janbaz, S., Davoodi, S. M., & Abdolbaghi Ataabadi, A. (2023). Presenting a multi-objective mathematical model with an integrated approach to scheduling and financial flow in manufacturing projects using non-dominated sorting genetic algorithm. Journal of decisions and operations research, 8(4), 975-992 (In Persian). https://doi.org/10.22105/dmor.2023.367956.1681
[26]    farughi,  hiva, & Solgi, Z. (2017). Multi-objective optimization of redundancy and reliability allocation in multi-state series-parallel systems. Journal of quality engineering and management, 7(3), 176–185. https://www.pqprc.ir/article_79601.html?lang=en
[27]    Billinton, Roy & Allen, R. (2022). Reliability assessment of engineering systems. https://doi.org/10.1007/978-1-4899-0685-4
[28]    Abouei Ardakan, M., & Zeinal Hamadani, A. (2014). Reliability optimization of series–parallel systems with mixed redundancy strategy in subsystems. Reliability engineering & system safety, 130, 132–139. https://doi.org/10.1016/j.ress.2014.06.001
[29]    Peiravi, A., Karbasian, M., & Abouei Ardakan, M. (2018). K-mixed strategy: A new redundancy strategy for reliability problems. Proceedings of the institution of mechanical engineers, part o: journal of risk and reliability, 232(1), 38–51. https://journals.sagepub.com/doi/abs/10.1177/1748006x17736166
[30]    Robinson, D. G., & Neuts, M. F. (1989). An algorithmic approach to increased reliability through standby redundancy. IEEE transactions on reliability, 38(4), 430–435. https://doi.org/10.1109/24.46457
[31]    Sahoo, L. (2017). Genetic algorithm based approach for reliability redundancy allocation problems in fuzzy environment. International journal of mathematical, engineering and management sciences, 2(4), 259–272. https://dx.doi.org/10.33889/IJMEMS.2017.2.4-020