Optimization of Availability-Redundancy in Multiple Multi-State Parallel-Series Systems Considering Multi-Stage Failures and Supplier Selection

Document Type : Original Article

Authors

1 Associate Professor, Department of Industrial Management, South Tehran Branch, Islamic Azad University, Tehran, Iran.

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

Abstract

Introduction: Given the competitive and globalized nature of markets, availability has become a crucial aspect of product design in recent decades. Modern availability includes functional requirements, adherence to standards, design considerations, predictability of availability, modeling, and evaluation. One objective of availability is to design systems with maximum accessibility. System availability is often improved by enhancing the availability of individual components or by allocating redundant components. These improvements are achieved through better materials, improved manufacturing processes, and the application of design principles.
 Method: This paper introduces an innovative approach to optimizing multiple parallel-series multi-state systems. Unlike traditional methods that focus on optimizing a single system, this approach simultaneously optimizes multiple systems to enhance their overall efficiency and performance. These systems contain parallel subsystems with multi-state components that can operate in various states, providing different performance outcomes. A significant aspect of this model is the impact of multi-stage failure rates on the systems, analyzed through state diagrams. The model also considers various assumptions, including the capability to select suppliers with different conditions and constraints. Additionally, the effects of technical and organizational activities on continuous optimization intervals are analyzed. The model is refined using a genetic algorithm, showing considerable improvements in system performance.
Results and discussion: An optimization mathematical model is presented to address the problem under specified assumptions. A numerical example is provided where the state transition distribution function is exponential, and technical and organizational activities have varying performance intensities. In this example, the performance rate of each subsystem equals the sum of the performance rates of its components, and the system's performance is at least as good as the minimum performance rate of its subsystems. Based on these assumptions, the system's availability probability and cost can be calculated using the model's objective function. The example problems are then solved using a genetic algorithm, and the results are reported.
 Conclusions: Recent research indicates that scholars in the field of redundancy allocation models for both binary and multi-state systems have continuously aimed to make these problems more realistic by incorporating new assumptions or eliminating simplifying ones. These efforts underscore the importance of developing mathematical optimization models that consider all system conditions and constraints, addressing the broader issues faced by decision-makers. Our research demonstrates that expanding the dimensions of optimization problems related to redundancy allocation can produce models that better reflect real-world conditions.

Keywords

Main Subjects

References

  1. Amiri, M., Azizi Boroujerdi, S., & Pourbakhsh, S. H. (2015). A Mathematical Model for Solving a Multi Objective Choice of Redundancy Allocation Strategy Problem by Optimizing Reliability for K out of N Systems. The Journal of Industrial Management Perspective, 4(4), 117-134. (In Persian)
  2. Chern, M. S. (1992). On the computational complexity of reliability redundancy allocation in a series system. Operations research letters, 11(5), 309-315.
  3. Coit, D. W. (2003). Maximization of system reliability with a choice of redundancy strategies. IIE transactions, 35(6), 535-543.
  4. Coit, D. W., & Smith, A. E. (1996). Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Transactions on reliability, 45(2), 254-260.
  5. Ding, Y., & Lisnianski, A. (2008). Fuzzy universal generating functions for multi-state system reliability assessment. Fuzzy Sets and Systems, 159(3), 307-324.
  6. Guilani, P. P., Sharifi, M., Niaki, S. T. A., & Zaretalab, A. (2014). Reliability evaluation of non-reparable three-state systems using Markov model and its comparison with the UGF and the recursive methods. Reliability Engineering & System Safety, 129, 29-35.
  7. 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.
  8. Levitin, G., Lisnianski, A., Ben-Haim, H., & Elmakis, D. (1998). Redundancy optimization for series-parallel multi-state systems. IEEE transactions on reliability, 47(2), 165-172.
  9. Levitin, G., Xing, L., Ben-Haim, H., & Dai, Y. (2013). Reliability of series-parallel systems with random failure propagation time. IEEE Transactions on Reliability, 62(3), 637-647.
  10. Li, W., & Zuo, M. J. (2008). Reliability evaluation of multi-state weighted k-out-of-n systems. Reliability engineering & system safety, 93(1), 160-167.
  11. Liang, Y. C., & Chen, Y. C. (2007). Redundancy allocation of series-parallel systems using a variable neighborhood search algorithm. Reliability Engineering & System Safety, 92(3), 323-331.
  12. Liang, Y. C., & Smith, A. E. (2004). An ant colony optimization algorithm for the redundancy allocation problem (RAP). IEEE Transactions on reliability, 53(3), 417-423.
  13. Lisnianski, A., & Levitin, G. (2003). Multi-state system reliability: assessment, optimization and applications. World scientific.
  14. Lisnianski, A., Levitin, G., Ben-Haim, H., & Elmakis, D. (1996). Power system structure optimization subject to reliability constraints. Electric Power Systems Research, 39(2), 145-152.
  15. Maatouk, I., Châtelet, E., & Chebbo, N. (2013). Availability maximization and cost study in multi-state systems. In 2013 Proceedings Annual Reliability and Maintainability Symposium (RAMS)(pp. 1-6). IEEE.
  16. Mansouri, A., & Alem Tabriz, A. (2023). Presenting an Exact Solution Method to Optimize the Bi-Objective Problem of Reliability and Cost of Redundancy Allocation in the Satellite Attitude Determination and Control System. The Journal of Industrial Management Perspective, 13(2), 241-266. (In Persian)
  17. Mousavi, S. M., Alikar, N., Niaki, S. T. A., & Bahreininejad, A. (2015). Two tuned multi-objective meta-heuristic algorithms for solving a fuzzy multi-state redundancy allocation problem under discount strategies. Applied Mathematical Modelling, 39(22), 6968-6989.
  18. Ouzineb, M., Nourelfath, M., & Gendreau, M. (2008). Tabu search for the redundancy allocation problem of homogenous series–parallel multi-state systems. Reliability Engineering & System Safety, 93(8), 1257-1272.
  19. Ouzineb, M., Nourelfath, M., & Gendreau, M. (2011). A heuristic method for non-homogeneous redundancy optimization of series-parallel multi-state systems. Journal of Heuristics, 17(1), 1-22.
  20. Radfar, A., & Mohammaditabar, D. (2019). Bi-Objective Optimization of Vendor Managed Inventory Problem in a Mult Echelon Green Supply Chain. Journal of Industrial Management Perspective, 9(3), 109-134. (In Persian)
  21. Ramirez-Marquez, J. E., & Coit, D. W. (2004). A heuristic for solving the redundancy allocation problem for multi-state series-parallel systems. Reliability Engineering & System Safety, 83(3), 341-349.
  22. Sharifi, M., Shahriari, M. R., & Zaretalab, A. (2019). The effects of technical and organizational activities on redundancy allocation problem with choice of selecting redundancy strategies using the memetic algorithm. International Journal of Industrial Mathematics, 11(3), 165-176.
  23. Sharma, V. K., & Agarwal, M. (2009, July). Ant colony optimization approach to heterogeneous redundancy in multi-state systems with multi-state components. In 2009 8th International Conference on Reliability, Maintainability and Safety(pp. 116-121). IEEE.
  24. 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.
  25. Tian, Z., Levitin, G., & Zuo, M. J. (2009). A joint reliability–redundancy optimization approach for multi-state series–parallel systems. Reliability Engineering & System Safety, 94(10), 1568-1576.
  26. Tian, Z., & Zuo, M. J. (2006). Redundancy allocation for multi-state systems using physical programming and genetic algorithms. Reliability Engineering & System Safety, 91(9), 1049-1056.
  27. Tian, Z., Zuo, M. J., & Huang, H. (2008). Reliability-redundancy allocation for multi-state series-parallel systems. IEEE Transactions on Reliability, 57(2), 303-310.
  28. Ushakov, I. A. (1987). Optimal standby problems and a universal generating function. Soviet journal of computer and systems sciences, 25(4), 79-82.
  29. Vaziri, S., Zaretalab, A., Esmaeili, M., & Niaki, S. T. A. (2018). An integrated production and procurement design for a multi-period multi-product manufacturing system with machine assignment and warehouse constraint. Applied Soft Computing, 70, 238-262.
  30. Zaretalab, A., Hajipour, V., Sharifi, M., & Shahriari, M. R. (2015). A knowledge-based archive multi-objective simulated annealing algorithm to optimize series–parallel system with choice of redundancy strategies. Computers & Industrial Engineering, 80, 33-44.
  31. Zuo, M. J., & Tian, Z. (2006). Performance evaluation of generalized multi-state k-out-of-n systems. IEEE Transactions on Reliability, 55(2), 319-327.

Files

Share

How to cite

Statistics