雙元件系統受衝擊與故障率交互作用雙重影響下的置換策略

簡易檢索 / 詳目顯示

回結果列表

研究生：	宋建國 Chien-kuo Sung
論文名稱：	雙元件系統受衝擊與故障率交互作用雙重影響下的置換策略 Replacement Policy for a Two-Unit System with Failure Rate Interaction and Shocks
指導教授：	許總欣 Tsung-shin Hsu 徐世輝 Shey-huei Sheu
口試委員:	王國雄 Kuo-hsiung Wang 王福琨 Fu-kwun Wang 林義貴 Yi-kuei Lin 柯沛程 Jau-chuan Ke 簡郁紘 Yu-Hung Chien
學位類別：	博士 Doctor
系所名稱：	管理學院 - 工業管理系 Department of Industrial Management
論文出版年：	2012
畢業學年度：	100
語文別：	英文
論文頁數：	81
中文關鍵詞：	雙元件系統、週期型置換策略、年齡置換策略、離散型置換策略、小修理、故障率交互作用、純生過程
外文關鍵詞：	two-unit system, periodic replacement policy, age replacement policy, discrete replacement policy, minimal repair, failure rate interaction, pure birth process
相關次數：	點閱：282 下載：10
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

允許小修理之雙元件系統在受到衝擊與故障率交互作用雙重影響下，探討週期型置換策略(periodic replacement policy)的經濟性。非齊次卜瓦松過程(non-homogeneous Poisson process)的外部衝擊(external shocks)分為兩類：「第I型衝擊(Type I shock)」會使得元件A輕微故障(minor failure)，所有元件A的故障可經由小修理修復，同時也會某程度的增加元件B之故障率，此外元件B故障會使得系統完全故障；「第II型衝擊(Type II shock)」屬嚴重故障(catastrophic failure)，會造成系統完全故障。在此置換模式下，系統將被置換於年齡T、系統完全故障或發生元件A第n次故障時，端視何先發生。此外針對衝擊的發生屬非齊次純生過程(non-homogeneous pure birth process)，且衝擊發生的類型與最近一次置換後衝擊發生的次數存在隨機性之關係(random mechanism)。在最小化單位時間期望成本下，求得NHPP模式的最佳置換策略T*及n*；以及NHPBP模式的最佳年齡置換策略T*，並分析其存在性及唯一性。

This dissertation presents an extended replacement policy for a two-unit system that is subject to shocks and exhibits interaction of failure rates. The shocks were simulated using a non-homogeneous Poisson process (NHPP). There are two types of system shocks considered: (1) a Type I shock causes a minor failure of Unit A, and the damage that is caused by such a failure affects Unit B, and (2) a Type II shock which causes a total failure of the system (catastrophic failure). All Unit A failures can be corrected by making minimal repairs. The system also exhibits interaction among the failure rates of units; a failure of any Unit A causes an internal shock that increases the failure rate of Unit B, while a failure of a Unit B causes instantaneous failure of Unit A. Furthermore, the shocks occur according to a non-homogeneous pure birth process (NHPBP) is presented. The shock type is based on a random mechanism that depends on the number of shocks that have occurred since the last replacement. The goal of this dissertation is to derive the expected cost per unit time of replacement by introducing relative costs as a factor in determining optimality. The optimal replacement period (T*), the optimal number of Unit A failures (n*) assuming NHPP, and optimal age replacement policy assuming NHPBP which minimize that cost were determined.

中文摘要 ................................................ I
英文摘要 ............................................... II
誌謝 .................................................. III
目錄 ................................................... IV
List of Notations ...................................... VI
List of Figures and Tables .............................. X
Chapter 1 Introduction .................................. 1
1.1 Background .......................................... 1
1.2 Literature Review ................................... 1
1.3 Subject and Assumptions ............................. 9
1.4 Research Process and Dissertation Content .......... 11
Chapter 2 Age and Discrete Replacement Policy for a Two-Unit System with Failure Rate Interaction and Shocks ... 12
2.1 Introduction ....................................... 12
2.2 Mathematical Model ................................. 13
2.2.1 Model I: Age Replacement Policy .................. 15
2.2.2 Model II: Discrete Replacement Policy ............ 20
Chapter 3　Extended Optimal Replacement Policy for a Two-Unit System with Failure Rate Interaction and Shocks ... 25
3.1Introduction ........................................ 25
3.2 General Model ...................................... 25
3.3 Long-run Cost Per Unit Time ........................ 26
3.4 Numerical Example .................................. 36
Chapter 4 Age Replacement Policy for a Two-Unit System Subject to Non-Homogeneous Pure Birth Shocks ........... 40
4.1 Introduction ....................................... 40
4.2 Model Formulation and Cost Functions ............... 43
4.2.1 The Shock Model .................................. 43
4.2.2 Expected Cost Functions .......................... 46
4.3 Optimization ....................................... 51
4.4 Numerical Example .................................. 54
Chapter 5　Conclusions and Future Research ............. 57
5.1 Conclusions ........................................ 57
5.2 Suggestions for Future Research .................... 58
References ............................................. 59
作者簡介 ............................................... 66

                                

[1] Abdel-Hameed, M. and Proschan, F., “Shock models with underlying birth process,” Journal of Applied Probability, Vol. 12, No. 1, pp. 18-28 (1975).
[2] Abdel-Hameed, M. S. and Proschan, F., “Nonstationary shock models,” Stochastic Processes and their Applications, Vol. 1, No. 4, pp. 383-404 (1973).
[3] Barlow, R. and Hunter, L., “Optimum preventive maintenance policies,” Operations Research, Vol. 8, No. 1, pp. 90-100 (1960).
[4] Barlow, R. E. and Proschan, F., Muthematical Theory of Reliability, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania (1996).
[5] Berg, M., “General trigger-off replacement procedures for two-unit systems,” Naval Research Logistics Quarterly, Vol. 25, No. 1, pp. 15-29 (1978).
[6] Berg, M. and Cléroux, R., “The block replacement problem with minimal repair and random repair costs,” Journal of Statistical Computation and Simulation, Vol. 15, No. 1, pp. 1-7 (1982).
[7] Boland, P. J. and Proschan, F., “Optimum replacement of a system subject to shocks,” Operations Research, Vol. 31, No. 4, pp. 697-704 (1983).
[8] British Standard, Glossary of Maintenance Management Terms Used in Terotechnology - BS 3811:1993, British Standards Publishing Limited, London (1993).
[9] Chang, C.-C., Sheu, S.-H. and Chen, Y.-L., “Optimal number of minimal repairs before replacement based on a cumulative repair-cost limit policy,” Computers & Industrial Engineering, Vol. 59, No. 4, pp. 603-610 (2010).
[10] Chen, C. S. and Savits, T. H., “A discounted cost relationship,” Journal of Multivariate Analysis, Vol. 27, No. 1, pp. 105-115 (1988).
[11] Chen, C. S. and Savits, T. H., “Some remarks on compound nonhomogeneous Poisson processes,” Statistics & Probability Letters, Vol. 17, No. 3, pp. 179-187 (1993).
[12] Chien, Y. H. and Sheu, S. H., “Extended optimal age-replacement policy with minimal repair of a system subject to shocks,” European Journal of Operational Research, Vol. 174, No. 1, pp. 169-181 (2006).
[13] Chien, Y. H., Sheu, S. H., Zhang, Z. G. and Love, E., “An extended optimal replacement model of systems subject to shocks,” European Journal of Operational Research, Vol. 175, No. 1, pp. 399-412 (2006).
[14] Cho, D. I. and Parlar, M., “A survey of maintenance models for multi-unit systems,” European Journal of Operational Research, Vol. 51, No. 1, pp. 1-23 (1991).
[15] European Federation of National Maintenance Societies Vzw., Maintenance Management Competencies, education and best practices in European perspective: Guide to Maintenance Management, Hogeschool Utrecht University of Applied Sciences Utrecht, Brussels, Belgium (2008).
[16] Giri, B. C. and Dohi, T., “Quantifying the risk in age and block replacement policies,” Journal of the Operational Research Society, Vol. 61, No. 7, pp. 1151-1158 (2010).
[17] Japanese Industrial Standards, English of the Glossary of Terms Used in Reliability in JIS Z8115 - 2000, Japanese Standards Association, Janpan (2000).
[18] Jhang, J. P. and Sheu, S. H., “Optimal age and block replacement policies for a multi-component system with failure interaction,” International Journal of Systems Science, Vol. 31, No. 5, pp. 593-603 (2000).
[19] Kececioglu, D., Maintainability, availability, and operational readiness engineering handbook, Prentice-Hall PTR, Upper Saddle River, New Jersey (1995).
[20] Lai, M. T. and Chen, Y. C., “Optimal periodic replacement policy for a two-unit system with failure rate interaction,” International Journal of Advanced Manufacturing Technology, Vol. 29, No. 3-4, pp. 367-371 (2006).
[21] Lai, M. T. and Chen, Y. C., “Optimal replacement period of a two-unit system with failure rate interaction and external shocks,” International Journal of Systems Science, Vol. 39, No. 1, pp. 71-79 (2008).
[22] Lai, M. T. and Leu, B. Y., “An economic discrete replacement policy for a shock damage model with minimal repairs,” Microelectronics Reliability, Vol. 36, No. 10, pp. 1347-1355 (1996).
[23] Lai, M. T., Shih, W. and Tang, K. Y., “Economic discrete replacement policy subject to increasing failure rate shock model,” International Journal of Advanced Manufacturing Technology, Vol. 27, No. 11-12, pp. 1242-1247 (2006).
[24] Lam, Y., “A geometric process δ-shock maintenance model,” IEEE Transactions on Reliability, Vol. 58, No. 2, pp. 389-396 (2009).
[25] Li, Z., Chan, L.-Y. and Yuan, Z., “Failure Time Distribution Under a δ-Shock Model and Its Application to Economic Design of Systems,” International Journal of Reliability, Quality & Safety Engineering, Vol. 6, No. 3, pp. 237-247 (1999).
[26] Murthy, D. N. P. and Iskandar, B. P., “New shock damage model. Part I. Model formulation and analysis,” Reliability Engineering and System Safety, Vol. 31, No. 2, pp. 191-208 (1991).
[27] Murthy, D. N. P. and Iskandar, B. P., “New shock damage model. Part II. Optimal maintenance policies,” Reliability Engineering and System Safety, Vol. 31, No. 2, pp. 211-231 (1991).
[28] Murthy, D. N. P. and Nguyen, D. G., “Study of a multi-component system with failure interaction,” European Journal of Operational Research, Vol. 21, No. 3, pp. 330-338 (1985).
[29] Murthy, D. N. P. and Nguyen, D. G., “Study of two-component system with failure interaction,” Naval Research Logistics Quarterly, Vol. 32, No. 2, pp. 239-247 (1985).
[30] Nakagawa, T., “Generalized models for determining optimal number of minimal repairs before replacement,” Journal of the Operations Research Society of Japan, Vol. 24, No. 4, pp. 325-337 (1981).
[31] Nakagawa, T. and Murthy, D. N. P., “Optimal replacement policies for a two-unit system with failure interactions,” Rairo-Recherche Operationnelle-Operations Research, Vol. 27, No. 4, pp. 427-438 (1993).
[32] Ohashi, M. and Nishida, T., “Optimal Replacement Policy for Two-Unit System,” Journal of the Operations Research Society of Japan, Vol. 24, No. 4, pp. 283-294 (1981).
[33] Osaki, S., Applied stochastic system modeling, Springer-Verlag, New York (1992).
[34] Park, J. H., Lee, S. C., Hong, J. W. and Lie, C. H., “An optimal block preventive maintenance policy for a multi-unit system considering imperfect maintenance,”Asia-Pacific Journal of Operational Research, Vol. 26, No. 6, pp. 831-847 (2009).
[35] Peng, W. and Tongdan, J., “Optimal replacement of safety-critical aircraft parts with utilization uncertainties,” In Reliability and Maintainability Symposium (RAMS), 2010 Proceedings - Annual, pp. 1-6 (2010).
[36] Pham, H., Handbook of reliability Engineering, Springer-Verlag London Limited, London (2003).
[37] Pham, H. and Wang, H. Z., “Imperfect maintenance,” European Journal of Operational Research, Vol. 94, No. 3, pp. 425-438 (1996).
[38] Purl, P. S. and Singh, H., “Optimum replacement of a system subject to shocks: a mathematical lemma,” Operations Research, Vol. 34, No. 5, pp. 782-789 (1986).
[39] Radner, R. and Jorgenson, D. W., "Optimal replacement and inspection of stochastically failing equipment," Studies in Applied Probability and Management Science, K. J. Arrow, H. Scarf and S. Karlin (eds.), Stanford Univ. Press, Stanford, California, pp. 184-206 (1962).
[40] Ross, S. M., Introduction to Probability Models, 9th ed., Academic Press, San Diego, California (2007).
[41] Satow, T. and Osaki, S., “Optimal replacement policies for a two-unit system with shock damage interaction,” Computers and Mathematics with Applications, Vol. 46, No. 7, pp. 1129-1138 (2003).
[42] Satow, T., Teramoto, K. and Nakagawa, T., “Optimal replacement policy for a cumulative damage model with time deterioration,” Mathematical and Computer Modelling, Vol. 31, No. 10, pp. 313-319 (2000).
[43] Scarf, P. A. and Deara, M., “On the development and application of maintenance policies for a two-component system with failure dependence,” IMA Journal of Mathematics Applied in Business and Industry, Vol. 9, No. 2, pp. 91-107 (1998).
[44] Scarf, P. A. and Deara, M., “Block replacement policies for a two-component system with failure dependence,” Naval Research Logistics, Vol. 50, No. 1, pp. 70-87 (2003).
[45] Sethi, D., "Opportunistic replacement policies," The Theory and Applications of Reliability, D. Tsokos and S. Shirvi (eds.), Academic Press, New York, pp. 433-447 (1977).
[46] Sheu, S.-H., “A general replacement of a system subject to shocks,” Microelectronics Reliability, Vol. 32, No. 5, pp. 657-662 (1992).
[47] Sheu, S.-H., “A generalized model for determining optimal number of minimal repairs before replacement,” European Journal of Operational Research, Vol. 69, No. 1, pp. 38-49 (1993).
[48] Sheu, S.-H., “A generalized age and block replacement of a system subject to shocks,” European Journal of Operational Research, Vol. 108, No. 2, pp. 345-362 (1998).
[49] Sheu, S.-H., Chang, C.-C., Zhang, Z. G. and Chien, Y.-H., “A note on replacement policy for a system subject to non-homogeneous pure birth shocks,” European Journal of Operational Research, Vol. 216, No. 2, pp. 503-508 (2012).
[50] Sheu, S.-H., Griffith, W. S. and Nakagawa, T., “Extended optimal replacement model with random minimal repair costs,” European Journal of Operational Research, Vol. 85, No. 3, pp. 636-649 (1995).
[51] Sheu, S. H. and Chang, C. C., “Extended periodic imperfect preventive maintenance model of a system subjected to shocks,” International Journal of Systems Science, Vol. 41, No. 10, pp. 1145-1153 (2010).
[52] Sheu, S. H., Chang, C. C., Chen, Y. L. and Zhang, Z. G., “A periodic replacement model based on cumulative repair-cost limit for a system subjected to shocks,” IEEE Transactions on Reliability, Vol. 59, No. 2, pp. 374-382 (2010).
[53] Tang, Y.-Y. and Lam, Y., “A δ-shock maintenance model for a deteriorating system,” European Journal of Operational Research, Vol. 168, No. 2, pp. 541-556 (2006).
[54] Thomas, L. C., “A survey of maintenance and replacement models for maintainability and reliability of multi-item systems,” Reliability Engineering, Vol. 16, No. 4, pp. 297-309 (1986).
[55] Valdez-Flores, C., “A survey of preventive maintenance models for stochastically deteriorating single-unit systems,” Naval Research Logistics, Vol. 36, No. 4, pp. 419-446 (1989).
[56] Vergin, R. C., “Optimal renewal policies for complex systems,” Naval Research Logistics Quarterly, Vol. 15, pp. 523-534 (1968).
[57] Wang, G. J. and Zhang, Y. L., “A geometric process repair model for a two-component system with shock damage interaction,” International Journal of Systems Science, Vol. 40, No. 11, pp. 1207-1215 (2009).
[58] Wang, H. Z., “A survey of maintenance policies of deteriorating systems,” European Journal of Operational Research, Vol. 139, No. 3, pp. 469-489 (2002).

簡易檢索 / 詳目顯示

相關論文