Skip to main content

Advertisement

SpringerLink
Log in

Bi-objective sequence optimization in reliability problems with a matrix-analytic approach

  • S.I.: Statistical Reliability Modeling and Optimization
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

The redundancy allocation problem (RAP) is an intriguing area in the field of reliability optimization to which a lot of research has been devoted in recent years. In this paper, a bi-objective model is developed for RAP with a heterogeneous backup scheme and a mixed redundancy strategy. Elimination of the lower bound estimation and the exact calculation of the reliability of the mixed strategy forms one of the most striking features of the proposed model. Investigating the optimal sequence of components in each subsystem, the study modifies a non-dominated sorting genetic algorithm (NSGA-II), as a powerful multi-objective evolutionary one, to solve the proposed bi-objective model. Two numerical examples will then be used to verify the efficiency of the model in achieving enhanced system reliability. Finally, the results of Pareto optimal set are used to demonstrate that the assumptions made enable the proposed model to improve system reliability by offering various structures while simultaneously considering system limitations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  • Abouei Ardakan, M., Mirzaei, Z., Zeinal Hamadani, A., & Elsayed, E. A. (2017). Reliability optimization by considering time-Dependent reliability for components. Quality and Reliability Engineering International, 33(8), 1641–1654.

    Article  Google Scholar 

  • Abouei Ardakan, M., Sima, M., Zeinal Hamadani, A., & Coit, D. W. (2016). A novel strategy for redundant components in reliability–redundancy allocation problems. IIE Transactions, 48(11), 1043–1057.

    Article  Google Scholar 

  • Amari, S. V, & Dill, G. (2009). A new method for reliability analysis of standby systems. In Reliability and Maintainability Symposium, 2009. RAMS 2009. Annual (pp. 417–422). IEEE.

  • Ardakan, M. A., & Hamadani, A. Z. (2014). Reliability optimization of series–parallel systems with mixed redundancy strategy in subsystems. Reliability Engineering & System Safety, 130, 132–139.

    Article  Google Scholar 

  • Ardakan, M. A., Hamadani, A. Z., & Alinaghian, M. (2015). Optimizing bi-objective redundancy allocation problem with a mixed redundancy strategy. ISA transactions, 55, 116–128.

    Article  Google Scholar 

  • Cha, J. H., Mi, J., & Yun, W. Y. (2008). Modelling a general standby system and evaluation of its performance. Applied Stochastic Models in Business and Industry, 24(2), 159–169.

    Article  Google Scholar 

  • Chambari, A., Najafi, A. A., Rahmati, S. H. A., & Karimi, A. (2013). An efficient simulated annealing algorithm for the redundancy allocation problem with a choice of redundancy strategies. Reliability Engineering & System Safety, 119, 158–164.

    Article  Google Scholar 

  • Chambari, A., Rahmati, S. H. A., & Najafi, A. A. (2012). A bi-objective model to optimize reliability and cost of system with a choice of redundancy strategies. Computers & Industrial Engineering, 63(1), 109–119.

    Article  Google Scholar 

  • Coit, D. W. (2003). Maximization of System Reliability with a Choice of Redundancy Strategies. IIE Transactions, 35(6), 535–543. https://doi.org/10.1080/07408170304420.

    Article  Google Scholar 

  • COIT, D. W. . (2001). Cold-standby redundancy optimization for nonrepairable systems. IIE Transactions, 33(6), 471–478. https://doi.org/10.1080/07408170108936846.

    Article  Google Scholar 

  • Dammak, K., & El Hami, A. (2019). Multi-objective reliability based design optimization of coupled acoustic-structural system. Engineering Structures, 197, 109389.

    Article  Google Scholar 

  • Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation, 6(2), 182–197.

    Article  Google Scholar 

  • dos Santos Coelho, L. (2009). An efficient particle swarm approach for mixed-integer programming in reliability–Redundancy optimization applications. Reliability Engineering & System Safety, 94(4), 830–837.

    Article  Google Scholar 

  • Fyffe, D. E., Hines, W. W., & Lee, N. K. (1968). System reliability allocation and a computational algorithm. IEEE Transactions on Reliability, 17(2), 64–69.

    Article  Google Scholar 

  • Garg, H., & Sharma, S. P. (2013). Multi-objective reliability-redundancy allocation problem using particle swarm optimization. Computers & Industrial Engineering, 64(1), 247–255.

    Article  Google Scholar 

  • Gholinezhad, H., & Hamadani, A. Z. (2017). A new model for the redundancy allocation problem with component mixing and mixed redundancy strategy. Reliability Engineering & System Safety, 164, 66–73.

    Article  Google Scholar 

  • Guilani, P. P., Juybari, M. N., Ardakan, M. A., & Kim, H. (2020). Sequence optimization in reliability problems with a mixed strategy and heterogeneous backup scheme. Reliability Engineering & System Safety, 193, 106660. https://doi.org/10.1016/j.ress.2019.106660.

    Article  Google Scholar 

  • Hsieh, T.-J., & Yeh, W.-C. (2012). Penalty guided bees search for redundancy allocation problems with a mix of components in series–parallel systems. Computers & Operations Research, 39(11), 2688–2704.

    Article  Google Scholar 

  • Kasprzak, E. M., & Lewis, K. E. (2000). An approach to facilitate decision tradeoffs in pareto solution sets. Journal of Engineering Valuation and Cost Analysis, 3(1), 173–187.

    Google Scholar 

  • Kim, H. (2018). Maximization of system reliability with the consideration of component sequencing. Reliability Engineering & System Safety, 170(Supplement C), 64–72. https://doi.org/10.1016/j.ress.2017.10.020

  • Kim, H., & Kim, P. (2017a). Reliability models for a nonrepairable system with heterogeneous components having a phase-type time-to-failure distribution. Reliability Engineering & System Safety, 159, 37–46. https://doi.org/10.1016/j.ress.2016.10.019.

    Article  Google Scholar 

  • Kim, H., & Kim, P. (2017b). Reliability–redundancy allocation problem considering optimal redundancy strategy using parallel genetic algorithm. Reliability Engineering & System Safety, 159(Supplement C), 153–160. https://doi.org/10.1016/j.ress.2016.10.033

  • Konak, A., Coit, D. W., & Smith, A. E. (2006). Multi-objective optimization using genetic algorithms: A tutorial. Reliability Engineering & System Safety, 91(9), 992–1007.

    Article  Google Scholar 

  • Kulturel-Konak, S., Smith, A. E., & Coit, D. W. (2003). Efficiently solving the redundancy allocation problem using tabu search. IIE Transactions, 35(6), 515–526.

    Article  Google Scholar 

  • Kuo, W., & Prasad, V. R. (2000). An annotated overview of system-reliability optimization. IEEE Transactions on Reliability, 49(2), 176–187.

    Article  Google Scholar 

  • Latouche, G., & Ramaswami, V. (1999). Introduction to matrix analytic methods in stochastic modeling (Vol. 5). SIAM.

  • Levitin, G., Xing, L., & Dai, Y. (2013). Optimal sequencing of warm standby elements. Computers & Industrial Engineering, 65(4), 570–576. https://doi.org/10.1016/j.cie.2013.05.001.

    Article  Google Scholar 

  • Levitin, G., Xing, L., & Dai, Y. (2013). Cold-standby sequencing optimization considering mission cost. Reliability Engineering & System Safety, 118, 28–34.

    Article  Google Scholar 

  • Liang, Y.-C., & Lo, M.-H. (2010). Multi-objective redundancy allocation optimization using a variable neighborhood search algorithm. Journal of Heuristics, 16(3), 511–535.

    Article  Google Scholar 

  • O’Connor, P., & Kleyner, A. (2012). Practical reliability engineering. . Wiley.

    Google Scholar 

  • Okafor, E. G., & Sun, Y.-C. (2012). Multi-objective optimization of a series–parallel system using GPSIA. Reliability Engineering & System Safety, 103, 61–71. https://doi.org/10.1016/j.ress.2012.03.014.

    Article  Google Scholar 

  • Sadjadi, S. J., & Soltani, R. (2012). Alternative design redundancy allocation using an efficient heuristic and a honey bee mating algorithm. Expert Systems with Applications, 39(1), 990–999. https://doi.org/10.1016/j.eswa.2011.07.099.

    Article  Google Scholar 

  • Safari, J. (2012). Multi-objective reliability optimization of series-parallel systems with a choice of redundancy strategies. Reliability Engineering & System Safety, 108, 10–20.

    Article  Google Scholar 

  • Salazar, D., Rocco, C. M., & Galván, B. J. (2006). Optimization of constrained multiple-objective reliability problems using evolutionary algorithms. Reliability Engineering & System Safety, 91(9), 1057–1070.

    Article  Google Scholar 

  • Soltani, R., Sadjadi, S. J., & Tofigh, A. A. (2014). A model to enhance the reliability of the serial parallel systems with component mixing. Applied Mathematical Modelling, 38(3), 1064–1076. https://doi.org/10.1016/j.apm.2013.07.035.

    Article  Google Scholar 

  • Soltani, R., Safari, J., & Sadjadi, S. J. (2015). Robust counterpart optimization for the redundancy allocation problem in series-parallel systems with component mixing under uncertainty. Applied Mathematics and Computation, 271, 80–88. https://doi.org/10.1016/j.amc.2015.08.069.

    Article  Google Scholar 

  • Soylu, B., & Ulusoy, S. K. (2011). A preference ordered classification for a multi-objective max–min redundancy allocation problem. Computers & Operations Research, 38(12), 1855–1866.

    Article  Google Scholar 

  • Sun, G., Li, G., Zhou, S., Li, H., Hou, S., & Li, Q. (2011). Crashworthiness design of vehicle by using multiobjective robust optimization. Structural and Multidisciplinary Optimization, 44(1), 99–110.

    Article  Google Scholar 

  • Tavakkoli-Moghaddam, R., Safari, J., & Sassani, F. (2008). Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm. Reliability Engineering & System Safety, 93(4), 550–556.

    Article  Google Scholar 

  • Wang, Z., Chen, T., Tang, K., & Yao, X. (2009). A multi-objective approach to redundancy allocation problem in parallel-series systems. In 2009 IEEE Congress on Evolutionary Computation (pp. 582–589). IEEE.

  • Yeh, W.-C. (2014). Orthogonal simplified swarm optimization for the series–parallel redundancy allocation problem with a mix of components. Knowledge-Based Systems, 64, 1–12. https://doi.org/10.1016/j.knosys.2014.03.011.

    Article  Google Scholar 

  • Zhai, Q., Yang, J., Peng, R., & Zhao, Y. (2015). A Study of Optimal Component Order in a General 1-Out-of-$ n $ Warm Standby System. IEEE Transactions on Reliability, 64(1), 349–358.

    Article  Google Scholar 

  • Zhao, J., Zeng, S., Guo, J., & Yang, C. (2015). Redundancy allocation with non-identical component and uncertainty. In 2015 Annual Reliability and Maintainability Symposium (RAMS) (pp. 1–6). https://doi.org/10.1109/RAMS.2015.7105092

  • Zhuang, J., & Li, X. (2015). Allocating Redundancies to k-out-of-n Systems with Independent and Heterogeneous Components. Communications in Statistics - Theory and Methods, 44(24), 5109–5119. https://doi.org/10.1080/03610926.2013.813046.

    Article  Google Scholar 

  • Zio, E. (2007). An introduction to the basics of reliability and risk analysis (Vol. 13). World scientific.

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

    Mohammad N. Juybari, Pardis Pourkarim Guilani & Mostafa Abouei Ardakan

Authors
  1. Mohammad N. Juybari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pardis Pourkarim Guilani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mostafa Abouei Ardakan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mostafa Abouei Ardakan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Juybari, M.N., Guilani, P.P. & Ardakan, M.A. Bi-objective sequence optimization in reliability problems with a matrix-analytic approach. Ann Oper Res 312, 275–304 (2022). https://doi.org/10.1007/s10479-021-04039-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-021-04039-7

Keywords

Search

Navigation