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研究生:吳柏辰
研究生(外文):Po-Chen Wu
論文名稱(外文):Simulating average run lengths of a copula-based control chart with the use of control variates
指導教授:鄧惠文鄧惠文引用關係
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:英文
論文頁數:56
中文關鍵詞:平均串聯長度管制圖相關性資料降低變異數copula
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管制圖 (controlchart) 在工業和財務上都是常見的品質管制方法。平均串聯長度(averagerunlength,ARL)是管制圖的重要指標,它可以用來評斷一個管制圖的表現。因此計算平均串聯長度來選擇合適的管制圖是一項重要的工作。在資料是獨立的假設下,計算 ARL 是很簡單的。但現實生活中存在許多有相關性的資料,ARL 的計算就變的困難許多。我們使用copula-based 模型模擬出據有相關性的資料後,再使用蒙地卡羅模擬方法來計算不同管制圖之下的 ARL,並使用控制變異法(controlvariates) 方法以提高蒙地卡羅估計量的效率。
Control charts are commonly used for quality control in industry. The average run length (ARL) of the series is an important indicator of control charts, which can determine whether a control chart is suitable or not.
Hence, calculating the ARL to select the appropriate control chart is critical. Under the assumption that the information is independently, calculating ARL is simple.
But in practice data is usually dependent, and this makes the calculation of ARL challenging. We use a copula-based model to simulate the dependent data, and then use the Monte Carlo simulation method to calculate the ARL of different control charts. Furthermore, we propose a control variate method to improve the efficiency of the standard Monte Carlo estimator.
摘要i
Abstract ii
誌謝iii
List of Figures vi
List of Tables vii
Chapter 1 Introduction 1
Chapter 2 Control Chart and ARL 4
2.1 3-sigma control chart 4
2.2 Exponentially Weighted Moving Average Control Chart 5
2.3 Moving Centerline Exponentially Weighted Moving Average Control Chart 7
2.4 Average Run Length 9
Chapter 3 Monte Carlo simulation and control variates 10
3.1 Our model 10
3.1.1 Generating data 11
3.2 Simulating ARL by Crude Monte Carlo 12
3.3 Control variates 13
Chapter 4 Simulation Studies 14
4.1 Simulating ARL with control variates of a 3- control chart 14
4.2 Simulating ARL with control variates of a EWMA control chart 16
4.3 Simulating ARL with control variates of a MCEWMA control chart 18
Chapter 5 Applications 21
5.1 Data 1 21
5.2 Data 2 23
Chapter 6 Another control variate 26
Chapter 7 Conclusion 30
References 31
Appendices 32
Busaba, J., S. Sukparungsee, and Y. Areepong (2012). Numerical approximations of average run length for ar(1) on exponential cusum. Proceeding of the International MultiConference of Engineers and Computer Scientists, 1268–1273.
Chen, G. (1997). The mean and standard deviation of the run length distribution of X charts when control limits are estimated. Statistica Sinica, 789–798.
Konrath, A. C., G. D. Donatelli, and D. H. Piekar (2006). The application of monte carlo simulation to evaluate the uncertainty of control chart performance indices. IMEKO World Congress Metrology for a Sustainable Development.
Lia, Z., C. Zoua, Z. Gonga, and Z. Wang (2008). The computation of average run length and average time to signal: An overview. Journal of Statistical Computation and
Simulation January, 1–26.
Long, T.-H. (2014). A control chart based on copula-based markov time series models. Master’s thesis, National Central University.
Pan, X. and J. Jarrett (2012). On Quality Control Chart Construction and Simulation. Ph. D. thesis, University of Rhode Island.
Shao, Y. and Y.-I. Lee (2000). Monitoring an autocorrelated process by spc control charts: the comparison among three approaches. Asia Pacific Management Review, 75–93.
Vanbrackle, L. (1999). A study of the average run length characteristics of the national notifiable diseases surveillance system. Statistics in Medicine, 3309–3319.

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