政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/153370

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/153370

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政大典藏 > College of Commerce > Department of Statistics > Theses > Item 140.119/153370

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/153370

Title:	監控多元品質變數比之EWMA變異數管制圖 EWMA Variability Control Charts for Monitoring Ratios of Multivariate Quality Variables
Authors:	林郁嘉 Lin, Yu-Chia
Contributors:	楊素芬 Yang, Su-Fen 林郁嘉 Lin, Yu-Chia
Keywords:	多元相依變數比統計過程管制資料深度管制圖指數加權移動平均符號檢定 Ratios of multiple correlated variables Multivariate statistical process control Data depth Control chart Exponentially weighted moving average Sign method Quality variable
Date:	2024
Issue Date:	2024-09-04 14:57:34 (UTC+8)
Abstract:	近年來，維持和改進產品品質的重要議題，也是多元統計過程管制（MSPC）之重要研究領域。但是，在追蹤多變量品質變數比的分散程度的議題文獻中尚少探討。因此，我們提出了無分配假設下的管制圖來追蹤多個相依品質變數比之變異數以了解製程在穩定或失控的狀況。在本研究中，我們分別提出兩種無分佈假設的方法，以建立兩個不同的EWMA管制圖。第一種我們提出使用資料深度 (data depth) 方法來建立EWMAD管制圖來監控多個相依變數比之變異數，第二種我們考慮符號方法 (sign method)，定義指標變數分配以建立管制圖來監控多個相依變數比之變異數。我們分別再以數值分析評估母體在三元常態和伽瑪分配下，兩個管制圖的管制界線與失控下的偵測效率。最後，我們透過實際多元牛奶數據來展示它們的應用和驗證失控的偵測能力。 In recent years, the variability of ratios of multivariate quality variables has become a crucial study of Multivariate Statistical Process Control (MSPC). However, there has been little exploration for the variability of ratios of dependent quality variables in the MSPC literature. Therefore, we propose control charts considering the distribution free assumption to track the variance stability and instability of the ratios of multiple dependent quality variables. In this study, we propose two methods of establishing EWMA control charts without the specified distribution of multivariate quality variables. Firstly, we introduce the ZEWMAD control chart using data depth methods monitor the variance of ratios of multiple dependent quality variables. Secondly, we consider the sign method defining indicator variable distribution to establish a control chart for monitoring the variance of ratios of multiple dependent quality variables. We calculate the control limits of the proposed charts and evaluate their out-of-control detection ability considering three-dimensional normal and gamma distributions through numerical analysis. Finally, we demonstrate the out-of-control detection performance of these proposed charts using a real multivariate milk data.
Reference:	[1] Alt, F. B. (1985). Multivariate quality control. Encyclopedia of Statistical Sciences, 6, 110–122. John Wiley, New York. [2] Aitchison, J. (2005). A concise guide to compositional data analysis. In Compositional Data Analysis Workshop. [3] Celano, G., Castagliola, P., Faraz, A., & Fichera, S. (2014). Statistical performance of a control chart for individual observations monitoring the ratio of two normal variables. Quality and Reliability Engineering International, 30(8), 1361-1377. [4] Chen, N., Zi, X., & Zou, C. (2016). A distribution-free multivariate control chart. Technometrics, 58(4), 448-459. [5] Marsaglia, G. (2006) Ratios of Normal Variables. Journal of Statistical Software, 16, 1-10. [6] Hinkley DV (1969). On the Ratio of Two Correlated Normal Random Variables. Biometrika, 56, 635–639. [7] Hotelling, H. (1947). Multivariate quality control. Techniques of statistical analysis. McGraw-Hill, New York. [8] Izawa, T. (1965). Two or Multi-dimensional Gamma-type Distribution and Its Application to Rainfall Data. Meteorology and Geophysics, 15, 167-200. [9] Kibble, W. F. (1941). A Two-Variate Gamma Type Distribution. Sankhya , 5, 137-150. [10] Lee, R. Y., Holland, B. S., & Flueck, J. A. (1979). Distribution of a ratio of correlated gamma random variables. SIAM Journal on Applied Mathematics, 36(2), 304-320. [11] Liu, R. Y. (1995). Control charts for multivariate processes. Journal of the American Statistical Association, 90(432), 1380-1387. [12] Lowry, C. A., Woodall, W. H., Champ, C. W., & Rigdon, S. E. (1992). A multivariate exponentially weighted moving average control chart. Technometrics, 34(1), 46-53. [13] Marsaglia, G. (1965). Ratios of Normal Variables and Ratios of Sums of Uniform Variables. Journal of the American Statistical Association, 60, 193–204. [14] Montgomery, D. C. (2020). Introduction to statistical quality control, 8. John Wiley & Sons, Hoboken. [15] Nadarajah S (2006). On the Ratio X/Y for Some Elliptically Symmetric Random Variables. Journal of Multivariate Analysis, 97, 342–358. [16] Nguyen, H. D., Tran, K. P., & Heuchenne, C. (2019). Monitoring the ratio of two normal variables using variable sampling interval exponentially weighted moving average control charts. Quality and Reliability Engineering International, 35(1), 439- 460. [17] Panaretos, J., Psarakis, S. & Xekalaki, E. (1997). The Correlated Gamma-Ratio Distribution in Model Evaluation and Selection. Technical Report no. 33, Department of Statistics, Athens University of Economics and Business. [18] William R. Atchley, Charles T. Gaskins and Dwane Anderson. (1976). Statistical Properties of Ratios. I. Empirical Results. Systematic Zoology, 25(2), 137-148. [19] Yang, S. F., Lin, J. S., & Cheng, S. W. (2011). A new nonparametric EWMA sign control chart. Expert Systems with Applications, 38(5), 6239-6243. [20] Yang, S. F. (2016). An improved distribution-free EWMA mean chart. Communications in Statistics-Simulation and Computation, 45(4), 1410-1427. [21] Yang, S. F., & Barry C. Arnold. (2016). A new approach for monitoring process variance. Journal of Statistical Computation and Simulation, 86(14), 2749-2765. [22] Yang, S. F., Lin, Y. C., & Yeh, A. B. (2021). A Phase II depth‐based variable dimension EWMA control chart for monitoring process mean. Quality and Reliability Engineering International, 37(6), 2384-2398. [23] Yang S-F, Arnold BC, Liu Y-l, Lu M-C, Lu S-L. (2022). A new phase II EWMA dispersion control chart. Quality and Reliability Engineering International. 1635–1658. [24] Zou, C., & Tsung, F. (2011). A multivariate sign EWMA control chart. Technometrics, 53(1), 84-97.
Description:	碩士國立政治大學統計學系 111354030
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0111354030
Data Type:	thesis
Appears in Collections:	[Department of Statistics] Theses

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