臺灣博碩士論文加值系統

針對退化生產系統之生產批量的研究中，經常以兩狀態(控制狀態及失控狀態)的馬可夫過程來描述系統的退化過程，並假設系統的狀態轉移機率為已知的常數，然後再根據這馬可夫過程建構決策模型並推導最佳生產批量。然而，在實務上系統的狀態轉移機率通常是未知而需要進行估計，而這估計的準確度在生產批量的決策上將扮演著關鍵的角色。因此，本論文提出一個逐次估計程序以解決狀態轉移機率未知下的批量決策問題。首先以歷史生產資訊透過最大概似法估計狀態轉移機率，再以此估計量推導下一批的最佳生產批量，使得單位時間總成本最低。此外，針對缺乏歷史資訊的生產系統，本論文進一步提供一個貝氏估計程序，藉以加入生產經驗、專家意見、或主觀機率。最後，以數值模擬說明逐次生產批量之決策機制，並探討最佳生產批量對估計準確度的敏感性。

The two-state (in-control and out-of-control) Markov process is usually employed to describe the deteriorating process of a production system. By assuming the transition probability is known and fixed, a production cost model is then established and an optimal production lot size can be obtained based on the model. However, in practice, the transition probability is usually unknown and need to be estimated. And, this estimation plays an important role in deciding the production lot sizes. Therefore, a sequential estimating procedure is developed in this thesis to derive the optimal lot size when the transition probability is unknown. We first use the past production information to estimate the transition probability by Maximum Likelihood Estimation (MLE) process. Then, the optimal lot size for next run is derived based on the estimate. For those systems without past information, a Bayesian estimation procedure is developed to incorporate the experience, expert opinions, or subjective probabilities. Furthermore, a simulation study is given to illustrate the sequential procedure. Finally, a sensitivity analysis is carried out to investigate the effects of the estimation on the optimal lot sizes.

中文摘要I
英文摘要II
誌謝III
目錄IV
表目錄VI
圖目錄VII
第一章 緒論1
1.1 研究背景1
1.2 研究動機與目的1
1.3 相關文獻探討3
1.4 論文架構5
第二章 系統描述7
2.1 符號定義與基本假設9
2.2 已知參數之退化系統模型10
2.2.1成本模式10
2.2.2最佳批量及演算法12
2.3 未知參數之退化系統模型16
第三章 最佳生產批量18
3.1 最大概似估計量估計程序18
3.1.1最大概似估計量18
3.1.2建構決策系統模型22
3.2 貝氏估計程序25
3.2.1後驗機率分配與損失成本25
3.2.2建構決策系統模型28
第四章 數值模擬與分析33
4.1 數值範例33
4.1.1 MLE估計程序之數值範例33
4.1.2 貝氏估計程序之數值範例35
4.2 維修成本和重估成本比例對逐次決策模式的影響38
4.2.1 模擬設計40
4.2.2 分析與比較42
4.2.3 綜合分析43
第五章 結論與未來研究方向52
5.1 結論52
5.2 未來研究方向53
參考文獻55
附錄 系統模擬程式58
作者簡介68

[1] 黃棨杉，「免費小修保證策略下之產品品質管制」，台灣工業技術學院管理技術研究所工業管理學程，碩士論文(1997)。
[2] 羅惠瓊，「保固產品之品質管制與售後維護策略分析」，國立台灣科技大學工業管理系，博士論文(2000)。
[3] Ben-Daya, M., "Integrated production maintenance and quality model for imperfect processes," IIE Transactions, 31, 491-501 (1999).
[4] Ben-Daya, M. and M. Makhdoum, "Integrated production and quality model under various preventive maintenance policies," Journal of the Operational Research Society, 49, 840-853 (1998).
[5] Dekker, R., "Applications of maintenance optimization models: a review and analysis," Reliability Engineering & System Safety, 51, 229-240 (1996).
[6] Dekker, R. and P. A. Scarf, "On the impact of optimisation models in maintenance decision marking: the state of the art," Reliability Engineering & System Safety, 60, 111-119 (1998).
[7] Djamaludin, I., D. N. P. Murthy and R.J. Wilson, "Quality Control through Lot Sizing for items Sold with Warranty," International Journal of Production Economics, 33, 97-107 (1994).
[8] Hariga, M. and M. Ben-Daya, "Note: The economic manufacturing lot-sizing problem with imperfect production processes: bounds and optimal solutions," Naval Research Logistics Quarterly, 45, 423-433 (1998).
[9] Hax, A. C. and D. Candea, Production and Inventory Management, Prentice Hall, 1984.
[10] Johnson, L. A. and D. C. Montgomery, Operations Research Wiley and Sons, Inc., Now York, 1974.
[11] Lui, K., "Estimation of the Geomertric Survival Distribution," IEEE Transactions on Reliability, 46(1), 134-141 (1997).
[12] Lee, H. L. and M. J. Rosenblantt, "Simultaneous determination of production cycle and inspection schedules in a production system," Management Science, 33(9), 1125-1136 (1987).
[13] Lin, T. M., S. T. Tseng and M. J. Liou, "Optimal inspection schedule in the imperfect production system under general shift distribution," Journal of the Chinese Institute of Industrial Engineers, 8(2), 73-81 (1991).
[14] Liou, M. J., S. T. Tseng and T. M. Lin, "The effects of inspection errors to the imperfect EMQ model," IIE Transactions, 26(2), 42-51 (1994).
[15] McCall, J.J., "Maintenance policies for stochastically failing equipment: a survey," Management Science, 11, 493-524 (1965).
[16] Murthy, D. N. P. and I. Djamaludin, "Quality control in a single staage production system: open and closed loop policies," International Journal of Production Research, 28, 2219-2242 (1990).
[17] Pham, H. and H. Wang, "Imperfect maintenance," European Journal of Operational Research, 94, 425-438 (1996).
[18] Pierskalla, W. P. and J. A. Voelker, "A survey of maintenance models: the control and surveillance of deteriorating systems." Naval Research Logistics Quarterly, 23(3), 353-388 (1976).
[19] Porteus, E. L., "Optimal lot sizing, process quality improvement and setup cost reduction," Operations Research, 34(1), 137-144 (1986).
[20] Rahim, M.A., "Joint determination of production quantity, inspection schedule, and control chart design," IIE Transactions, 26(6), 2-11 (1994).
[21] Rahim, M.A. and M. Ben-Daya, "A generalized economic model for the jont determination of production run, inspection schedules and control chart design," International Journal of Production Research, 36, 277-289 (1996).
[22] Rosenblantt, M. J. and H. L. Lee, "Economic production cycles with imperfect production processes," IIE Transactions, 18, 48-55 (1986).
[1] Sherif, Y. S. and M. L. Smith, "Optimal maintenance models for systems subject to failure－a review," Naval Research Logistics Quarterly, 28, 47-74 (1981).
[24] Scheaffer, R. L. "A note on approximate confidence limits for the negative binomial model," Commun. Statis.-Theor. Meth., A5(2), 149-158, (1976).
[25] Osaki, S. and X. Li, "Characterizations of Gamma and Negative Binomial Distributions," IEEE Transactions on Reliability, 37(4), 379-382 (1988).
[26] Valdez-Flores, C. and R. M. Feldman, "A survey of preventive maintenance models for stochastically deteriorating single-unit systems," Naval Research Logistics Quarterly, 36, 419-446 (1989).
[27] Yeh, R. H., and H. Lo, "A Markovian EPQ Model for Deteriorating Production Systems," International Journal of Operations and Quantitative Management, 6, 45-57 (2000).