運用遺傳演算法求解可維修串並聯系統參數

A Genetic Algorithms Approach to Determining Parameters of Repairable Series-Parallel Systems

林水順(Shui-Shun Lin)；劉子麟(Tzu-Lin Liu)；莊英慎(Ying-Shen Juang)

可用度 ； 平均失效間隔時間 ； 平均修護時間 ； 遺傳演算法 ； Availability ； MTBF ； MTTR ； Genetic Algorithms

品質學報

14卷1期（2007 / 03 / 01）

69 - 84

繁體中文

系統可用度關係著可靠度及系統建置成本，在工業系統設計領域中是一重要課題。隨著系統結構日趨複雜，當系統中有一零件發生失效時，導致系統功能無法發揮的弊害有時相當嚴重。提升系統可靠度的同時，成本也會相對增加，故決定可用度參數是一複雜的尋優問題。串並聯系統的複置配置問題，大多仰賴系統設計人員的經驗。本研究的運用最佳化技術於可維修串並聯系統之設計，輔助系統設計人員進行系統元件參數擬定之決策，亦即在既定的系統架構下，決定各組件的平均失效時間與平均修護時間的最佳策略。本研究提出－最佳化模式與方法，先列出系統可用度估算式以及系統的總成本計算式，再以單位成本之系統可用度形成目標函數並建構最佳化數學模式，使用遺傳演算法求解模式。在遺傳演算法平行搜尋與世代演化的特性下，可快速得到符合成本效益下之系統可用度最佳化參數，輔助系統設計人員制定組件之選用策略與修復策略。

As the system structure becomes more and more complicated, failure of system function will result in huge damage. System availability is an important subject in the design field of industrial system as it is associated with reliability and allocation cost of systems. While improving the system's reliability, the cost is also on the upswing. Thus, the parameter of availability depends upon complex optimization. Redundancy Allocation Problem (RAP) of series-parallel system is traditionally resolved via the help of experienced system designers. We utilized optimization technology to assist the designers, during design of repairable series-parallel system, in setting up system component parameters, namely, determining the most economical policy of components' mean-time-between-failure (MTBF) and mean time-to-repair (MTTR). We proposed a three-phase method. The first phase is to list the approximate expression of system availability and total cost's computation. The second phase is to use the system availability and total cost to form an objective function and thereafter a mathematical model. The third phase is to solve the RAP model by Genetic Algorithms. With the characteristics of parallel search and generation evolution for Genetic Algorithms, it is possible to obtain rapidly and cost-effectively the optimal system parameters, so that assist the system designers in preparing component options and related repair policies.

1. Bellman, R. E.,Dreyfus, E.(1958).Dynamic programming and reliability of multi-component devices.Operations Research,6,200-206.
2. Birolini, A.(1999).Reliability Engineering Theory and Practice.New York:Springer.
3. Bris, R.,Chatelet, E.,Yalaoui, F.(2003).New method to minimize the preventive maintenance cost of series-parallel systems.Reliability Engineering and System Safety,82,247-255.
4. Bulfin, R. L.,Liu, C. Y.(1985).Optimal allocation of redundant components for large systems.IEEE Transactions on Reliability,34,241-247.
5. Chern, M. S.(1992).On the computational complexity of reliability redundancy allocation in a series system.Operations Research Letters,11,309-315.
6. Chisman, J. A.(1998).Using discrete simulation modeling to study large-scale system reliability/availability.Computers and Operations Research,25,169-174.
7. Coit, D. W.,Smith, A. E.(1996).Solving the redundancy allocation problem using a combined neural network/genetic algorithm approach.Computers and Operations Research,23,515-526.
8. Coit, D. W.,Smith, A. E.(1996).Reliability optimization of series-parallel systems using genetic algorithm.IEEE Transactions on Reliability,45,254-260.
9. Elegbede, C.,Adjallah, K.(2003).Availability allocation to repairable systems with genetic algorithms: a multi-objective formulation.Reliability Engineering and System Safety,82,319-330.
10. Fisher, M.(1981).The lagrangian relaxation method for solving integer programming problems.Management Science,27,1-18.
11. Fyfee, D. E.,Hines, W. W.,Lee, N. K.(1968).System reliability allocation and a computational algorithm.IEEE Transactions on Reliability,17,64-69.
12. Gen, M.,Cheng, R.(1996).Optimal design of system reliability using interval programming and genetic algorithms.Computers and Industrial Engineering,31,237-240.
13. Gen, M.,Ida, K.,Tsujimura, Y.,Kim, C. E.(1993).Large-scale 0-1 fuzzy goal programming and its application to reliability optimization problem.Computers and Industrial Engineering,24,539-549.
14. Goldberg, D. E.(1989).Genetic Algorithm in Search, Optimization, and Machine Learning.MA.:Addison-Wesley.
15. Gopal, K.,Aggarwal, K. K.,Gupta, J. S.(1978).An improved algorithm for reliability optimization.IEEE Transactions on Reliability,27,325-328.
16. Gordan, J.(1996).Computational methods for reliability data analysis.Annual Reliability and Maintainability Symposium
17. Hamersma, B.,Chodos, M. S.(1992).Availability and maintenance considerations in telecommunication network design and the use of simulation.Proceedings of AFRICON 1992 Conference
18. Henley, E. J.,Kumampto, H.(1985).Design for Reliability and Safety Control.New Jersey:Prentice-Hall.
19. Holland, J. H.(1975).Adaptation in Natural and Artificial Systems.Ann Arbor:The University of Michigan Press.
20. Huang, H. Z.(1997).Fuzzy multi-objective optimization decision-making of reliability of series system.Microelectron Reliability,37,447-449.
21. Jeang, A.(2001).Computer-aided tolerance synthesis with statistical method and optimization techniques.Quality and Reliability Engineering International,17,131-139.
22. Jeang, A.(1999).Optimal process parameter determination for computer-aided manufacturing.Quality and Reliability Engineering International,15,3-16.
23. Kim, J. H.,Yum, B. J.(1993).A heuristic method for solving reliability redundancy optimization problems in complex systems.IEEE Transactions on Reliability,42,572-578.
24. Kohda, T.,Inoue, K.(1982).A reliability optimization method for complex systems with the criterion of local optimality.IEEE Transactions on Reliability,31,109-111.
25. Kumral, M.(2005).Reliability-based optimisation of a mine production system using genetic algorithms.Journal of Loss Prevention in the Process Industries,18,186-189.
26. Kuo, W.,Hwang, C. L.,Tillman, F. A.(1978).A note on heuristic methods in optimal system reliability.IEEE Transactions on Reliability,27,320-324.
27. Kuo, W.,Lin, H.,Xu, Z.,Zhang, W.(1987).Reliability optimization with the lagrange multiplier and branch-and-bound technique.IEEE Transactions on Reliability,36,624-630.
28. Lapa, C. M. F.,Pereira, C. M.,De Barros, M. P.(2006).A model for preventive maintenance planning by genetic algorithms based in cost and reliability.Reliability Engineering and System Safety,91,233-240.
29. Li, D.,Haimes, Y. Y.(1992).A decomposition method for optimization of large-system reliability.IEEE Transactions on Reliability,41,183-188.
30. Lieber, D.,Nemirovskii, A.,Rubinstein, R. Y.(1999).A fast monte carlo method for evaluating reliability indexes.IEEE Transactions on Reliability,48,256-261.
31. Lin, S. S.,Wang, H. P.,Zhang, C.(1997).Statistical tolerance analysis based on beta distributions.Journal of Manufacturing Systems,16,150-158.
32. Lin, S. S.,Zhang, C.,Wang, H. P.(1995).On mixed-discrete nonlinear optimization problems: a comparative study.Engineering Optimization,23,287-300.
33. Misra, K. B.,Sharma, U.(1991).An efficient algorithm to solve integer programming problems arising in system reliability design.IEEE Transactions on Reliability,40,81-91.
34. Mitchell, B. F.,Murry, R. J.(1996).Predicting operational availability for systems with redundant, repairable components and multiple sparing levels.Annual Reliability and Maintainability Symposium
35. Mohan, C.,Shanker, K.(1998).Reliability optimization of complex systems using random search technique.Microelectronics and Reliability,28,513-518.
36. Nakagawa, Y.,Miyazaki, K.(1981).Surrogate constraints algorithm for reliability optimization problem with two constraints.IEEE Transactions on Reliability,30,175-180.
37. Nakagawa, Y.,Miyazaki, S.(1981).An experimental comparison of the heuristic methods for solving reliability optimization problems.IEEE Transactions on Reliability,30,181-184.
38. Nakagawa, Y.,Nakashima, K.(1977).A heuristic method for determining optimal reliability allocation.IEEE Transactions on Reliability,26,156-161.
39. Painton, L.,Campbell, J.(1995).Genetic algorithms in optimization of system reliability.IEEE Transactions on Reliability,44,172-178.
40. Prasad, V. R.,Kuo, W.(2000).Reliability optimization of coherent systems.IEEE Transactions on Reliability,49,323-330.
41. Propst, J. E.,Doan, D. R.(2001).Improvements in modeling and evaluation of electrical power system reliability.IEEE Transactions on Industry Applications,37,1413-1422.
42. Samrout, M.,Yalaoui, F.,Chatelet, E.,Chebbo, N.(2005).New methods to minimize the preventive maintenance cost of series-parallel systems using ant colony optimization.Reliability Engineering and System Safety,89,346-354.
43. Sharma, J.,Venkateswaran, K. V.(1971).A direct method for maximizing the system reliability.IEEE Transactions on Reliability,20,256-259.
44. Tillman, F. A.(1969).Optimization by integer programming of constrained reliability problems with several modes of failure.IEEE Transactions on Reliability,18,47-53.
45. Tillman, F. A.,Hwang, C. L.,Kuo, W.(1980).Optimization of Systems Reliability.New York:Marcel Dekker.
46. Wang, W. D.(2000).Confidence limits on the inherent availability of equipment.Annual Reliability and Maintainability Symposium
47. Yang, J. E.,Hwang, M. J.,Sung, T. Y.,Jin, Y.(2000).Application of genetic algorithm for reliability allocation in nuclear power plants.Reliability Engineering and System Safety,65,229-238.
48. Yokota, T.,Gen, M.,Ida, K.(1995).System reliability of optimization problems with several failure modes by genetic algorithm.Japanese Journal of Fuzzy Theory and Systems,7,117-135.
49. Yokota, T.,Gen, M.,Li, Y. X.(1996).Genetic algorithm for non-linear mixed integer programming problems and its applications.Computers and Industrial Engineering,30,905-917.
50. Yun, W. Y.,Kim, J. W.(2004).Multi-level redundancy optimization in series systems.Computers and Industrial Engineering,46,337-346.
51. 王宗華(1992)。可靠度工程技術的理論與實用。台北:中華民國品質管制學會。
52. 李正龍(2000)。碩士論文(碩士論文)。逢甲大學工業工程研究所。