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 在工業統計中，統計製程管制(Statistical process control) 是一個非常重要的品質管制工具。 在檢測過程中，我們注重產品的品質是否保持一致良好，使用管制圖來監控產品品質是否有所改變。當管制圖偵測到品質有所改變時，下一步我們有興趣的是如何找到從哪一個時間點開始產生改變，我們稱此時間點為改變點(change point)。np管制圖、二項累積管制圖、最大概似估計量法目前較為普遍用來估計監控的為不合格個數的change point. 在本文，我們主要目的為發展新的方法來估計change point 改善二項累積管制圖、最大概似估計量的方法。 進一步的我們也利用模擬比較新方法與二項累積管制圖、最大概似估計量方法在各種不同情況下的均方誤差(MSE)。我們發現新方法並非總是最好的，但在不同參數設定之下是較為穩健的。最後，我們用實例分析再一次證明新方法的優點。
 Detecting when the process has changed is very important in quality control and industrial statistics. For the binomial CUSUM control chart, a maximum likelihood estimator (Samuel and Pignatiello 2001) has been proposed to estimate the change point. Using some decision theoretic approach, we develop a new estimator which aims to improve the existing methods. We compare our proposed method with the Page’s last zero estimator (Page, 1954) and the maximum likelihood estimator in terms of mean squared error (MSE) by simulations. We find that the proposed method is not always the best, but is robust under various parameter designs. We analyze jewelry manufacturing data for illustration.Keywords: -chart; Quality control; statistical decision theory, Sequential analysis, SPRT.
 Contents摘要 iAbstract ii致謝詞 iiiList of Figures vList of Tables viChapter 1 Introduction 1Chapter 2 Background 42.1 Binomial CUSUM chart 42.2 Sequential Probability Ratio Test 62.3 Maximum Likelihood Estimator 112.4 Page's estimator 13Chapter 3 Method 143.1 Idea 143.2 Proposed method 16Chapter 4 Simulation 184.1 Simulation designs 184.2 Simulation results 234.3 Additional simulations 26Chapter 5 Data Analysis 31Chapter 6 Conclusion 38Appendix A1 39Appendix A2 40Appendix A3 41Appendix A4 44References 46
 References1 Assareh H, Mengersen K, Change point Estimation in Monitoring Survival Time. PloS ONE 2012; 7(3): e33630. Doi:10.1371/journal.pone.0033630.2 Assareh H, Mengersen K, Change point detection in risk adjusted control charts. Statistical Methods in Medical Reasearch 2011; 1-22, doi: 10.1177/0962280211426356.3 Burr WI, Elementary Statistical Quality Control (1st edn) Milwaukee: New York and Basel, 1979.4 Casella G, Berger RL. Statistical inference (2nd edn). Cengage Learning: CA, 2001.5 Duran RI, Albin SL. Monitoring a fraction with easy and reliable settings of the false alarm rate. Quality and Reliability Engineering International 2009; 25(8): 1026-1043.6 Emura T, Lin YS, A comparison of normal approximation rules for attribute control charts. Quality and Reliability Enginerring International 2013, doi: 10.1002/qre.1601.7 Emura T, Chen YH, Chen HY, Survival prediction based on compound covariate method under Cox proportional hazard models, PloS ONE 7(10).Doi:10.1371/journal.pone.0047627 (SCI).8 Fuh CD, Mei Y (2008) Optimal stationary binary quantizer for decentralized quickest change detecction in hidden Markov models, 11th International Conference on IEEE Information Fusion.9 Hawkins DM, Olwell DH, Cumulative sum charts and charting for quality improvement ( 1st edn ). Wiley: New York, 1998.10 Khan RA, A note on estimating the mean of a normal distribution with known coefficient of variation. Journal of the American Statistical Association 1968; 63: 1039-1041.11 Montgomery DC. Introduction to Statistical Quality Control. Wiley: New York, NY, 2009.12 Page ES, Continuous inspection schemes. Biometrika 1954; 41:100-114.13 Page ES, A test for a change in a parameter occurring at an unknown point. Biometrika 1955; 523-527.14 Pignatiello JJ Jr, Samuel TR, Identifying the time of a step change in the process fraction nonconforming. Quality Engineering 2001; 13(3): 357-365.15 Pignatiello JJ Jr, Perry MB, Estimation of the change point of the process fraction nonconforming in SPC applications. Interational Journal of Reliability Quality and Safety Engineering 2005; 12: 95-110.16 Pignatiello JJ Jr, Simpson JR, Perry MB, Estimating the change point of the process fraction nonconforming with a monotonic change disturbance in SPC. Quality and Reliability Engineering Inernational 2007; 23: 327-339.17 Rossi G, Sarto SD, Marchi M, A new risk-adjusted Bernoulli cumulative sum chart for monitoring binary health data. Statistical Methods in Medical Reasearch 2014; 1-10, DOI: 10.1177/0962280214530883.18 Wetherill GB, Brown DB, Statistical Process Control. Theory and Practice, 1991.19 Wang H, Comparison of p control charts for low defective rate. Computational Statistics &; Data Analysis 2009; 53:4210-4220.20 Wang YH, Economic design of CUSUM chart with variable sampling. Master thesis, NTHU library, 2008.21 Wald A, Sequential Analysis (1st edn). Wiley: New York, 1947.22 Wencheko E, Wijekoon P, Improved estimation of the mean in one-parameter exponential families with known coefficient of variation. Statistical Papers 2005; 46(1): 101-115.23 Yang SF, Cheng TC, Hung YC, Cheng SW. A new chart for monitoring service process mean. Quality and Reliability Engineering International 2011; 28: 377-386.
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