博碩士論文 101225020 詳細資訊




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姓名 何逸庭(Yi-Ting Ho)  查詢紙本館藏   畢業系所 統計研究所
論文名稱
(A robust change point estimator for binomial CUSUM control charts)
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摘要(中) 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。
摘要(英) 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.
關鍵字(中) 關鍵字(英) ★ np-chart
★ Quality control
★ statistical decision theory
★ Sequential analysis
★ SPRT
論文目次 Contents
摘要 i
Abstract ii
致謝詞 iii
List of Figures v
List of Tables vi
Chapter 1 Introduction 1
Chapter 2 Background 4
2.1 Binomial CUSUM chart 4
2.2 Sequential Probability Ratio Test 6
2.3 Maximum Likelihood Estimator 11
2.4 Page′s estimator 13
Chapter 3 Method 14
3.1 Idea 14
3.2 Proposed method 16
Chapter 4 Simulation 18
4.1 Simulation designs 18
4.2 Simulation results 23
4.3 Additional simulations 26
Chapter 5 Data Analysis 31
Chapter 6 Conclusion 38
Appendix A1 39
Appendix A2 40
Appendix A3 41
Appendix A4 44
References 46
參考文獻 References
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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.
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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.
指導教授 江村剛志(Takshi Emura) 審核日期 2014-7-24
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