臺灣博碩士論文加值系統

近年來，計數值管制圖之發展著重於事件時間間隔管制圖(time-between-events, TBE 管制圖) 之研究，此種管制圖特別適用於不合格率或缺點率很低的高產出製程。TBE 管制圖因其統計特性之需求，一般皆採用機率界限。本研究所使用之累積合格品數管制圖 (cumulative counts of conforming chart, CCC 管制圖) 為 TBE 管制圖的一種，用以監控高產出製程的不合格率變化。而 CCC-r 管制圖為 CCC 管制圖之延伸，可有效提高管制圖偵測製程偏移之靈敏度。過去研究大多僅探討獨立性之高產出製程，但在實際製程中，產品間通常存在相依性，故學者提出相依性 CCC-r 管制圖。然而，此管制圖具有 ARL-biased 之缺點，且當製程處於統計管制外時，其平均連串長度相當高，使管制圖無法快速發出製程異常之警訊。且當相依程度愈大則要選擇 r 愈大之管制圖，造成使用上的不便。
本研究考慮三種統計特性，將管制圖之統計設計轉換為最佳化搜尋問題。由於機率界限並不像傳統 k 倍標準差界限容易求得，在此情況下若又要符合統計特性則更難以計算，故本研究以基因演算法尋找符合統計特性之最佳管制界限。過去之統計設計大多為單一目標最佳化，而本研究則是採用多目標最佳化設計，並提出將多目標式納入基因演算法中存活篩選的求解過程之方法。本研究分別以平均連串長度與平均檢驗個數作為績效評估指標，研究結果顯示統計設計可有效提升相依性 CCC-r 管制圖之偵測績效，同時也突破原本相依性之限制範圍，提供一個更有效率的管制方法來監控高產出製程。

Time-between-events charts (TBE charts) are suitable in monitoring a high-yield process. The Cumulative Count of Conforming chart (CCC chart), one of the TBE chart, is studied in this research. The CCC-r chart is an extension and improvement of the CCC chart. Generally, it is assumed that the production process follows an independent and identically distributed Bernoulli pattern. However, the production of the conforming item may be serially dependent in practical manufacturing. The serially dependent CCC-r chart was developed to monitor processes with high quality and serial dependence. However, average run length (ARL) of this chart is too long to alarm in time that the process is out-of-control. Moreover, this chart shows an ARL-biased property. In this study, we propose statistical designs to derive modified control limit for the serially dependent CCC-r chart that can decrease ARL when process is out-of-control and produce ARL-unbiased performance.
We consider three statistical criteria transformed into multi-objective optimizations to improve the performance of the serially dependent CCC-r chart. The purpose of this study is to investigate how to choose values of probability limits with multi-objective optimization using genetic algorithm (GA) in order that the serially dependent CCC-r chart meets the statistical criteria in different statistical designs. ARL and average number inspected (ANI) are used to evaluate the chart’s performance in different designs. The control schemes proposed in this study provide more effective alternatives for monitoring the modern manufacturing production processes, especially in high-yield processes.

中文摘要 i
英文摘要 ii
致謝 iii
表目錄 v
圖目錄 vi
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 3
第二章 文獻探討 4
2.1 傳統計數值管制圖 4
2.2 高產出製程之管制方法 5
2.3 管制圖之評估指標 9
2.3.1 平均連串長度 9
2.3.2 平均檢驗個數 11
2.4 多目標最佳化求解方法 12
2.5 基因演算法 14
2.5.1 基因演算法之概述 15
2.5.2 基因演算法之運算流程 16
第三章 相依性 管制圖 21
3.1 相依性製程之馬可夫鏈模型 21
3.2 相依性 管制圖之統計模型 23
第四章 相依性 管制圖之統計設計 28
4.1 統計設計 29
4.2 基因演算法求解流程 33
第五章 效益評估 36
5.1 以 ARL 為評估指標 36
5.1.1 統計設計個別之績效評估 36
5.1.2 三種統計設計之績效比較 45
5.2 以 ANI 為評估指標 47
第六章 結論與未來研究 50
6.1 結論 50
6.2 未來研究 51
參考文獻 52

Acosta-Mejia, C. A., “Improved p charts to monitor process quality,” IIE Transactions, 31, 6, 509-516 (1999).
Bhat, U. N. and Lal, R., “Number of successes in Markov trials,” Advances in Applied Probability, 20, 3, 677-680 (1988).
Bhat, U. N. and Lal, R., “Attribute control charts for Markov dependent production processes,” IIE Transactions, 22, 2, 181-188 (1990).
Broadbent, S. R., “The inspection of a Markov process,” Journal of the Royal Statistical Society. Series B (Methodological), 20, 1, 111-119 (1958).
Calvin, T. W., “Quality control techniques for "Zero Defects",” IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 6, 3, 323-328 (1983).
Chan, L. Y., Xie, M. and Goh, T. N., “Cumulative quantity control charts for monitoring production processes,” International Journal of Production Research, 38, 2, 397-408 (2000).
Chen, J. T.,”A new approach to setting control limits of cumulative count of conforming charts for high-yield processes,” Quality and Reliability Engineering International, 25, 8, 973-986 (2009).
Chen, P. W. and Cheng, C. S., “An ARL-unbiased approach to setting control limits of CCC-r chart for high-yield processes,” Journal of Quality, 17, 6, 435-452 (2010).
Chen, P. W. and Cheng, C. S., “A modified control scheme for fraction nonconforming under Markov dependent processes,” in Proceedings of The 8th Asia-Pacific Conference on Industrial Engineering and Management Systems APIEMS’2007 (2007).
Chen, P. W., Cheng, C. S., Hsu, Y. H. and Chen, S. S., “A study on the optimal setting of control limits for CCC-r chart in monitoring high-yield processes,” in Proceedings of The 7th Asian Network for Quality Congress (2009).
Chen, Y. K., “Economic design of variable sampling interval control chart- A hybrid Markov Chan approach with genetic algorithms,” Expert System with Applications, 33, 3, 683-689 (2007).
Cheng, C. S. and Chen, P. W., “The design of cumulative count of conforming chart with supplementary runs rules,” in Proceedings of The 9th Asia Pacific Industrial Engineering and Management Conference (2008).
Chou, C. Y., Chen, J. C. and Lia, W. T., “Economic design of variable sampling intervals EWMA charts with sampling at fixed times using genetic algorithms,” Expert System with Applications, 34, 1, 419-426 (2008).
Cohon, J. L., Multiobjective programming and planning, New York (1978).
Deligonul, Z. S. and Mergen, A. E., “Dependence bias in conventional -charts and its correction with an approximate lot quality distribution,” Journal of Applied Statistics, 14, 1, 75-81 (1987).
Goh, T. N., “A control chart for very high yield processes,” Quality Assurance, 13, 1, 18-22 (1987).
Goh, T. N. and Xie, M., “Statistical control of a six sigma process,” Quality Engineering, 15, 4, 587-592 (2003).
Goldberg, D. E., Genetic algorithms in search optimization and machine learning, Addison-Wesley Longman Publishing Co. Inc., MA (1989).
Grant, E. L. and Leavenworth, R. S., Statistical Quality Control, McGraw-Hill Book Company., NY (1988).
Holland, J. H., Adaptation in natural and artificial systems, University of Michigan Press, Ann Arbor (1975).
Johnson, N. L. and Kotz, S., Distributions in Statistics, Vol1：Discrete Distributions, John Wiley and Sons., NY (1969).
Khoo, M. B. C., “Increasing the sensitivity of control chart for fraction nonconforming,” Quality Engineering, 16, 2, 307-319 (2003).
Klein, M., “Two alternatives to the Shewhart control chart,” Journal of Quality Technology, 32, 4, 427-431 (2000).
Kuralmani, V., Xie, M., Goh, T. N. and Gan, F. F., “A conditional decision procedure for high yield processes,” IIE Transactions, 34, 12, 1021-1030 (2002).
Lai, C.D. and Govindaraju K.,”Reduction of control-chart signal variability for high-quality processes,” Journal of Applied Statistics, 35, 6, 671-679 (2008).
Lai, C. D., Xie, M. and Govindaraju, K., “Study of a Markov model for a high-quality dependent process,” Journal of Applied Statistics, 27, 4, 461-473 (2000).
Liu, J. Y., Xie, M., Goh, T. N. and Ranjan, P., “Time-between-events charts for on-line process monitoring,” IEEE International Engineering Management Conference, 3, 1061-1065 (2004).
Marglin, D. C., Public Investment Criteria, MIT press, Cambridge, Massachusetts (1967).
Nelson, L. S., “The Shewhart control chart – tests for special causes,” Journal of Quality Technology, 16, 4, 255-256 (1984).
Shepherd, D. K., Champ, C. W., Rigdon, S. E. and Fuller, H. T., “Attribute charts for monitoring a dependent process,” Quality Reliability Engineering International, 23, 3, 341-365 (2007).
Stimson, W. A. and Mastrangelo, C. M., “Monitoring serially-dependent processes with attribute data,” Journal of Quality Technology, 28, 3, 279-288 (1996).
Tsai, T. R., “An adjusted normal approximation method,” Technical Report No.4, Department of Statistics, Tamkang University (2001).
Western Electric Company, Statistical Quality Control Handbook, Western Electric Co. Inc., Indianapolis, Indiana (1956).
Woodall, W. H., “Control charts based on attribute data: bibliography and review,” Journal of Quality Technology, 29, 2, 172-183 (1997).
Xie, M., Goh, T. N. and Ranjan, P., “Some effective control chart procedures for reliability monitoring,” Reliability Engineering and System Safety, 77, 2, 143-150 (2002).
Xie, M., Lu, X. S. and Goh, T. N., “A quality monitoring and decision-making scheme for automated production processes,” International Journal of Quality and Reliability Management, 16, 2, 148-157 (1999).
Zadeh, L.A., “Optimality and nonscalar-valued performance criteria,” IEEE Transactions on Automatic Control, 8, 1, 59-60 (1963).
Zhang, C. W., Xie, M. and Goh, T. N., “Design of exponential control charts using a sequential sampling scheme,” IIE Transactions, 38, 12, 1105-1116 (2006).
Zhang, L., Govindaraju, K., Bebbington, M. and Lai, C. D., “On the statistical design of geometric control charts,” Quality Technology and Quantitative Management, 1, 2, 233-243 (2004).
徐郁涵，「建構累積合格品數管制圖監控具相依性之高產出製程」，元智大學工業工程與管理所碩士論文，桃園 (2010)。
鄭春生，「品質管理：現代化觀念與實務應用」，全華圖書有限公司，台北 (2010)。