International Journal of Nonlinear Analysis and Applications

Optimizing redundancy allocation problem with repairable components based on the Monte Carlo simulation

Document Type : Research Paper

Authors

1 Faculty of Industrial Management, South Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Business Management, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran

Abstract

The optimization of reliability is crucial across various engineering domains. The redundancy allocation problem (RAP) is among the key challenges within reliability. This study introduces an RAP incorporating repairable components and a k-out-of-n sub-systems structure. The objective function aims to maximize system reliability while adhering to cost and weight constraints. The goal is to determine the optimal number of components for each subsystem, including the appropriate allocation of repairmen to each subsystem. Given that this model is classified as an Np-Hard problem, we employed a genetic algorithm (GA) to solve the proposed model. Additionally, response surface methodology (RSM) was utilized to fine-tune the algorithm parameters. To calculate the reliability of each subsystem, as well as the overall system reliability, a Monte Carlo simulation was employed. Lastly, a numerical example was solved to assess the algorithm's performance.

Keywords

[1] K.K. Aggarwal, Redundancy optimization in general systems, IEEE Trans. Reliabil. 25 (1976), 330–332.
[2] K.K. Aggarwal, J.S. Gupta, and K.B. Misra, A new heuristic criterion for solving a redundancy optimization problem, IEEE Trans. Reliabil. 24 (1975), 86–87.
[3] M.S. Chern, On the computational complexity of reliability redundancy allocation in a series system, Oper. Res. Lett. 11 (1992), 309–315.
[4] D.W. Coit, Maximization of system reliability with a choice of redundancy strategies, IIE Trans. 35 (2003), no. 6, 535–544.
[5] D.W. Coit and A. Smith, Considering risk profiles in design optimization for series-parallel systems, Proc. Reliabil. Maintain. Symp., Philadelphia, 1997, pp. 271–277.
[6] D.W. Coit and A. Smith, Redundancy allocation to maximize a lower percentile of the system time-to-failure distribution, IEEE Trans. Reliabil. 47 (1998), 79–87.
[7] D.W. Coit and A. Smith, Stochastic formulations of the redundancy allocation problem, Proc. Fifth Ind. Engin. Res. Conf., Minneapolis, 1996.
[8] Q. Ding and C. Li, Reliability optimization for series-parallel system with multi-state components under repairable and nonrepairable conditions, Comput. Ind. Eng. 105 (2017), 256–266.
[9] D.E. Fyffe, W.W. Hines, and N.K. Lee, System reliability allocation and computational algorithm, IEEE Trans. Reliabil. 17 (1968), 64–69.
[10] K. Gopal, K.K. Aggarwal, and J.S. Gupta, An improved algorithm for reliability optimization, IEEE Trans. Reliabil. 27 (1978), 325–328.
[11] C. Ha and W. Kuo, Reliability redundancy allocation: an improved realization for non-convex nonlinear programming problems, Eur. J. Oper. Res. 171 (2006), 24–38.
[12] J. Holland, Adaptation Natural and Artificial Systems, University of Michigan, 1992.
[13] K. Ida, System reliability optimization with several failure modes by genetic algorithm, Proc. 16th Int. Conf. Comp. Indust. Engg., 1994, pp. 349–352.
[14] X. Liu, D.Q. Li, Z.J. Cao, and Y. Wang, Adaptive Monte Carlo simulation method for system reliability analysis of slope stability based on limit equilibrium methods, Eng. Geo. 264 (2020), 105384.
[15] M. Miriha, S.T.A. Niaki, B. Karimi, and A. Zaretalab, Bi-objective reliability optimization of switch-mode k-out of-n series–parallel systems with active and cold standby components having failure rates dependent on the number of components, Arab. J. Sci. Eng. 42 (2017), 5305–5320.
[16] Y. Nakagawa and S. Miyazaki, Surrogate constraints algorithm for reliability optimization problems with tow constraints, IEEE Trans. Reliabil. 30 (1981), 175–180.
[17] Y. Nakagawa and K. Nakashima, A heuristic method for determining optimal reliability allocation, IEEE Trans. Reliabil. 26 (1977), 156–161.
[18] P. Pourkarim Guilani, A. Zaretalab, S.T. A Niaki and P. Pourkarim Guilani, A bi-objective model to optimize reliability and cost of k-out-of-n series-parallel systems with tri-state components, Sci. Iranica 24 (2017), no. 3, 1585–1602.
[19] M. Shahriari, Using genetic algorithm to optimize a system with repairable components and multi-vacations for repairmen, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 2, 3139–3144.
[20] M. Shahriari, Redundancy allocation optimization based on the fuzzy universal generating function approach in the series-parallel systems, Int. J. Ind. Math. 15 (2023), no. 1, 69–77.
[21] M. Sharifi, G. Cheragh, K. Dashti Maljaii, A. Zaretalab, and M. Shahriari, Reliability and cost optimization of a system with k-out-of-n configuration and choice of decreasing the components failure rates, Sci. Iranica 28 (2021), no. 6, 3602–3616.
[22] M. Sharifi, T.A. Moghaddam, and M. Shahriari, Multi-objective redundancy allocation problem with weighted-kout-of-n subsystems, Heliyon, 5 (2019), no. 12.
[23] M. Sharifi, M. Mousa Khani, and A. Zaretalab, Comparing parallel simulated annealing, parallel vibrating damp optimization and genetic algorithm for joint redundancy-availability problems in a series-parallel system with multi-state components, J. Optim. Ind. Eng. 7 (2014), no. 14, 13–26.
[24] M. Sharifi, P. Pourkarim Guilani, A. Zaretalab and A. Abhari, Reliability evaluation of a system with active redundancy strategy and load-sharing time-dependent failure rate components using Markov process, Communic. Statist.-Theory Meth. 52 (2021), no. 13, 1–20.
[25] M. Sharifi, M. Shahriari, A. Khajehpoor, and S.A. Mirtaheri, Reliability optimization of a k-out-of-n series-parallel system with warm standby components, Sci. Iranica 29 (2022), no. 6, 3523–3541.
[26] M. Sharifi, M.R. Shahriari, and A. Zaretalab, The effects of technical and organizational activities on redundancy allocation problem with choice of selecting redundancy strategies using the memetic algorithm, Int. J. Ind. Math. 11 (2019), no. 3, 165–176.
[27] M. Sharifi, A. Shojaie, S. Naserkhaki and M. Shahriari, A bi-objective redundancy allocation problem with time-dependent failure rates, Int. J. Ind. Eng. 25 (2018), no. 4.
[28] J. Sharma and K.V. Venkateswaran, A direct method for maximizing the system reliability, IEEE Trans. Reliabil. 20 (1971), 256–259.
[29] M. Takeshi, A Monte Carlo simulation method for system reliability analysis, Nuclear Safety Simul. 4 (2013), no. 1, 44–52.
[30] F.A. Tillman, C.L. Hwang, and W. Kuo, Determining component reliability and redundancy for optimum system reliability, IEEE Trans. Reliabil. 26 (1977), 162–165.
[31] G.G.Wang and M.C. Bell, Advances in metaheuristic algorithms for optimal design of engineering systems, Engin. Optim. 40 (2008), no. 5, 439–465.
[32] T. Yokota, M. Gen, and K. Ida, System reliability of optimization problems with several failure modes by genetic algorithm, Japan. J. Fuzzy Theory Syst. 7 (1995), 117.
International Journal of Nonlinear Analysis and Applications
Volume 15, Issue 2
February 2024
Pages 115-124
  • Receive Date: 19 July 2023
  • Revise Date: 29 July 2023
  • Accept Date: 19 January 2024