A New Recursive Formulation for the Mixed Redundancy Strategy in Reliability Optimization Problems
Authors
Abstract
One of the common approaches for improving the reliability of a specific system is to use parallel redundant components in subsystems. This approach, which is known as the redundancy allocation problem (RAP), includes the simultaneous selection of the component type and its level for each subsystem in order to maximize the system reliability.Traditionally, there are two redundancy strategies, namely active and standby, for the redundant components. Recently, a new powerful strategy called mixed strategy has been developed. It has been proved that the mixed strategy has a better performance when compared to both previous strategies. The main issue in utilizing the mixed strategy is its complicated formulation and sophisticated calculations, leading to a time-consuming procedure for solving the problems. Hence, in this paper, a new formulation based on the recursive approach is introduced to ease the calculation of the mixed strategy. In the new formulation, the complex double integral calculations are removed and the calculation times is reduced. The proposed recursive formulation provides a general statement for the mixed strategy formula which is not changed by altering the number of components in each subsystem. This flexibility and stability in the formula can be very important, especially for large scale cases. In order to evaluate the new approach and to compare its performances with the previous formulation, a benchmark problem with 14 subsystems is considered and the results of the two formulation are compared with each other.
Keywords
1. Chambari, A., Rahmati, S. H. A. and Najafi, A. A., “A Bi-Objective Model to Optimize Reliability and Cost of System with a Choice of Redundancy Strategies”, Computers and Industrial Engineering, Vol. 63, No. 1, pp. 109-119, 2012.
2. Kuo, w. and Prasad, V. R., “An Annotated Overview of System-Reliability Optimization”, IEEE Transactions on Reliability, Vol. 49, No. 2, pp. 176-187, 2000.
3. Chern, M. S., “On the Computational Complexity of Reliability Redundancy Allocation in a Series System”, Operations Research Letters, Vol. 11, No. 5, pp. 309-315, 1992.
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6. Ng, K. Y. and Sancho, N., “A hybrid ‘Dynamic Programming/ Depth-First Search’ algorithm, with an Application to Redundancy Allocation”, IISE Transactions, Vol. 33, No. 12, pp. 1047-1058, 2001.
7. Coit, D. W., “Maximization of System Reliability with a Choice of Redundancy Strategies”, IISE Transactions, Vol. 35, No. 6, pp. 535-543, 2003.
8. Misra, K. B. and Sharma, U., “An Efficient Algorithm to Solve Integer-Programming Problems Arising in System-Reliability Design”, IEEE Transactions on Reliability, Vol. 40, No. 1, pp. 81-91, 1991.
9. Misra, K. B., “Reliability Optimization of a Series-Parallel System”, IEEE Transactions on Reliability, Vol. 21, No. 4, pp. 230-238, 1972.
10. Coit, D. W. and Smith, A. E., “Reliability Optimization of Series- Parallel Systems using a Genetic Algorithm”, IEEE Transactions on Reliability, Vol. 45, No. 2, pp. 254-260, 266, 1996.
11. Eslami, A. A., Seyed-esfahani, M., Farsi, M. A. and Mahmoudi, M., “Redundancy Optimization in Series- Parallel Systems and Choice of Redundancy Strategies”, Tenth International Industrial Engineering Conference, 27-28 January, 2014. (In Farsi).
12. Liang, Y.-C. and Smith, A. E., “An Ant Colony Optimization Algorithm for the Redundancy Allocation Problem (RAP)”, IEEE Transactions on reliability, Vol. 53, No. 3, pp. 417-423, 2004.
13. Ouzineb, M., Nourelfath, M. and Gendreau, M., “Tabu Search for the Redundancy Allocation Problem of Homogenous Series–Parallel Multi-State Systems”, Reliability Engineering and System Safety, Vol. 93, No. 8, pp. 1257-1272, 2008.
14. Beji, N., Jarboui, B., Eddaly, M. and Chabchoub, H., “A Hybrid Particle Swarm Optimization Algorithm for the Redundancy Allocation Problem”, Journal of Computational Science, Vol. 1, No. 3, pp. 159-167, 2010.
15. Seyed Esfahani, M., Hajian Heidary, M. and Jaberi, S., “A Simulated Annealing Algorithm for Fuzzy Reliability Optimization Model in Series-Parallel and Standby Systems”, International Journal of Industrial Engineering and Production Management, Vol. 24, No. 4, pp. 413-422, January 2014. (In Farsi).
16. Coit, D. W., “Cold-Standby Redundancy Optimization for Nonrepairable Systems”, Iie Transactions, Vol. 33, No. 6, pp. 471-478, 2001.
17. Robinson, D. and Neuts, M., “Standby Redundancy in Reliability: A Review”, IEEE Transactions on Reliability, Vol. 38, No. 4, pp. 430-435, 1989.
18. Abouei Ardakan, M. and Zeinal Hamadani, A., “Reliability–Redundancy Allocation Problem with Cold-Standby Redundancy Strategy”, Simulation Modelling Practice and Theory, Vol. 42, pp. 107-118, 2014.
19. Sakawa, M., “Multi-Objective Optimization by the Surrogate Worth Trade-Off Method”, IEEE Transaction on Reliability, Vol. 27, No 5, pp. 311-314, 1978.
20. Azizi Boroujerdi, S., Amiri, M. and Garshasbi, D., “A Mathematical Model for Solving a Multi Objective Choice of Redundancy Allocation Strategy Problem by Optimizing MTTF for K out Of N systems”, 13th International Conference on Industrial Engineering, IIEC 2017, Babol, Mazandaran. (In Farsi).
21. Jamshidi, H., and Hejaz, T. H., “A Bi-Objective Mathematical Programing Model to Solve Redundancy Allocation Problems in a Series-Parallel System with Mixed Strategy and Price Discount Policy”, 13 th International Conference on Industrial Engineering, IIEC 2017, Babol, Mazandaran (In Farsi).
22. Feizabadi, M. and Jahromi A. E., “A New Model for Reliabilit Optimization of Series-Parallel Systems with Non-Homogeneous Components”, Reliability Engineering and System Safety, Vol. 157, pp. 101- 112, 2017.
23. Kim, H., “Maximization of System Reliability with the Consideration of Component Sequencing”, Reliability Engineering and System Safety, Vol. 170: 64-72, 2018.
24. Ardakan, M. A. and Rezvan, M. T., “Multi-Objective Optimization of Reliability–Redundancy Allocation Problem with Cold-Standby Strategy Using NSGA-II”, Reliability Engineering and System Safety, Vol. 172, pp. 225-238. 2018.
25. Huang X, Coolen FP, Coolen-Maturi T. “A Heuristic Survival Signature based Approach for Reliability-Redundancy Allocation”, Reliability Engineering and System Safety, Vol. 185, pp. 511-517, 2019.
26. Zoulfaghari, H., Hamadani, A. Z. and Ardakan, M. A., “Bi-Objective Redundancy Allocation Problem for a System with Mixed Repairable and Non-Repairable Components,” ISA Transactions, Vol. 53, No. 1, pp. 17-24, 2014.
27. Ardakan Abouei, M., Sima, M., Zeinal Hamadani, A. and Coit, D. W., “A Novel Strategy for Redundant Components in Reliability-Redundancy Allocation Problems”, IIE Transactions, accepted, 2016.
28. Peiravi, A., Karbasian, M., Ardakan, M. A. and Coit, D. W., “Reliability Optimization of Series-Parallel Systems with K-Mixed Redundancy Strategy”, Reliability Engineering and System Safety, Vol. 183, pp. 17-28. 2019.
2. Kuo, w. and Prasad, V. R., “An Annotated Overview of System-Reliability Optimization”, IEEE Transactions on Reliability, Vol. 49, No. 2, pp. 176-187, 2000.
3. Chern, M. S., “On the Computational Complexity of Reliability Redundancy Allocation in a Series System”, Operations Research Letters, Vol. 11, No. 5, pp. 309-315, 1992.
4. Fyffe, D. E., Hines W. W. and Lee, N. K., “System Reliability Allocation and a Computational Algorithm”, IEEE Transactions on Reliability, Vol. 2, pp. 64-69, 1968.
5. Abouei Ardakan, M. and Zeinal Hamadani, A., “Reliability Optimization of Series– Parallel Systems with Mixed Redundancy Strategy in Subsystems”, Reliability Engineering and System Safety, Vol. 130, pp. 132-139, 10// 2014.
6. Ng, K. Y. and Sancho, N., “A hybrid ‘Dynamic Programming/ Depth-First Search’ algorithm, with an Application to Redundancy Allocation”, IISE Transactions, Vol. 33, No. 12, pp. 1047-1058, 2001.
7. Coit, D. W., “Maximization of System Reliability with a Choice of Redundancy Strategies”, IISE Transactions, Vol. 35, No. 6, pp. 535-543, 2003.
8. Misra, K. B. and Sharma, U., “An Efficient Algorithm to Solve Integer-Programming Problems Arising in System-Reliability Design”, IEEE Transactions on Reliability, Vol. 40, No. 1, pp. 81-91, 1991.
9. Misra, K. B., “Reliability Optimization of a Series-Parallel System”, IEEE Transactions on Reliability, Vol. 21, No. 4, pp. 230-238, 1972.
10. Coit, D. W. and Smith, A. E., “Reliability Optimization of Series- Parallel Systems using a Genetic Algorithm”, IEEE Transactions on Reliability, Vol. 45, No. 2, pp. 254-260, 266, 1996.
11. Eslami, A. A., Seyed-esfahani, M., Farsi, M. A. and Mahmoudi, M., “Redundancy Optimization in Series- Parallel Systems and Choice of Redundancy Strategies”, Tenth International Industrial Engineering Conference, 27-28 January, 2014. (In Farsi).
12. Liang, Y.-C. and Smith, A. E., “An Ant Colony Optimization Algorithm for the Redundancy Allocation Problem (RAP)”, IEEE Transactions on reliability, Vol. 53, No. 3, pp. 417-423, 2004.
13. Ouzineb, M., Nourelfath, M. and Gendreau, M., “Tabu Search for the Redundancy Allocation Problem of Homogenous Series–Parallel Multi-State Systems”, Reliability Engineering and System Safety, Vol. 93, No. 8, pp. 1257-1272, 2008.
14. Beji, N., Jarboui, B., Eddaly, M. and Chabchoub, H., “A Hybrid Particle Swarm Optimization Algorithm for the Redundancy Allocation Problem”, Journal of Computational Science, Vol. 1, No. 3, pp. 159-167, 2010.
15. Seyed Esfahani, M., Hajian Heidary, M. and Jaberi, S., “A Simulated Annealing Algorithm for Fuzzy Reliability Optimization Model in Series-Parallel and Standby Systems”, International Journal of Industrial Engineering and Production Management, Vol. 24, No. 4, pp. 413-422, January 2014. (In Farsi).
16. Coit, D. W., “Cold-Standby Redundancy Optimization for Nonrepairable Systems”, Iie Transactions, Vol. 33, No. 6, pp. 471-478, 2001.
17. Robinson, D. and Neuts, M., “Standby Redundancy in Reliability: A Review”, IEEE Transactions on Reliability, Vol. 38, No. 4, pp. 430-435, 1989.
18. Abouei Ardakan, M. and Zeinal Hamadani, A., “Reliability–Redundancy Allocation Problem with Cold-Standby Redundancy Strategy”, Simulation Modelling Practice and Theory, Vol. 42, pp. 107-118, 2014.
19. Sakawa, M., “Multi-Objective Optimization by the Surrogate Worth Trade-Off Method”, IEEE Transaction on Reliability, Vol. 27, No 5, pp. 311-314, 1978.
20. Azizi Boroujerdi, S., Amiri, M. and Garshasbi, D., “A Mathematical Model for Solving a Multi Objective Choice of Redundancy Allocation Strategy Problem by Optimizing MTTF for K out Of N systems”, 13th International Conference on Industrial Engineering, IIEC 2017, Babol, Mazandaran. (In Farsi).
21. Jamshidi, H., and Hejaz, T. H., “A Bi-Objective Mathematical Programing Model to Solve Redundancy Allocation Problems in a Series-Parallel System with Mixed Strategy and Price Discount Policy”, 13 th International Conference on Industrial Engineering, IIEC 2017, Babol, Mazandaran (In Farsi).
22. Feizabadi, M. and Jahromi A. E., “A New Model for Reliabilit Optimization of Series-Parallel Systems with Non-Homogeneous Components”, Reliability Engineering and System Safety, Vol. 157, pp. 101- 112, 2017.
23. Kim, H., “Maximization of System Reliability with the Consideration of Component Sequencing”, Reliability Engineering and System Safety, Vol. 170: 64-72, 2018.
24. Ardakan, M. A. and Rezvan, M. T., “Multi-Objective Optimization of Reliability–Redundancy Allocation Problem with Cold-Standby Strategy Using NSGA-II”, Reliability Engineering and System Safety, Vol. 172, pp. 225-238. 2018.
25. Huang X, Coolen FP, Coolen-Maturi T. “A Heuristic Survival Signature based Approach for Reliability-Redundancy Allocation”, Reliability Engineering and System Safety, Vol. 185, pp. 511-517, 2019.
26. Zoulfaghari, H., Hamadani, A. Z. and Ardakan, M. A., “Bi-Objective Redundancy Allocation Problem for a System with Mixed Repairable and Non-Repairable Components,” ISA Transactions, Vol. 53, No. 1, pp. 17-24, 2014.
27. Ardakan Abouei, M., Sima, M., Zeinal Hamadani, A. and Coit, D. W., “A Novel Strategy for Redundant Components in Reliability-Redundancy Allocation Problems”, IIE Transactions, accepted, 2016.
28. Peiravi, A., Karbasian, M., Ardakan, M. A. and Coit, D. W., “Reliability Optimization of Series-Parallel Systems with K-Mixed Redundancy Strategy”, Reliability Engineering and System Safety, Vol. 183, pp. 17-28. 2019.
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