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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iAbstract ii誌謝iiiList of Figures viList of Tables viiChapter 1 Introduction 1Chapter 2 Control Chart and ARL 42.1 3-sigma control chart 42.2 Exponentially Weighted Moving Average Control Chart 52.3 Moving Centerline Exponentially Weighted Moving Average Control Chart 72.4 Average Run Length 9Chapter 3 Monte Carlo simulation and control variates 103.1 Our model 103.1.1 Generating data 113.2 Simulating ARL by Crude Monte Carlo 123.3 Control variates 13Chapter 4 Simulation Studies 144.1 Simulating ARL with control variates of a 3- control chart 144.2 Simulating ARL with control variates of a EWMA control chart 164.3 Simulating ARL with control variates of a MCEWMA control chart 18Chapter 5 Applications 215.1 Data 1 215.2 Data 2 23Chapter 6 Another control variate 26Chapter 7 Conclusion 30References 31Appendices 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 andSimulation 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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 1 相關性資料管制圖之研究 2 非對稱管制界限設定方式之討論與比較-以管制圖為例- 3 二元不良數計數管制圖 4 ARTA過程的Xbar管制圖統計設計

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