政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/159036

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/159036

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题名:	兩比例比值之製程監控 Process Monitoring for Ratio of Two Proportions
作者:	盧杰宏 Lu, Chieh-Hung
贡献者:	楊素芬盧杰宏 Lu, Chieh-Hung
关键词:	兩比例比值兩比例交叉乘積比管制圖指數加權移動平均 Ratio of two proportions Cross-product ratio Control chart Exponentially weighted moving average
日期:	2025
上传时间:	2025-09-01 14:48:53 (UTC+8)
摘要:	近年來，在工業製造與醫療診斷等應用領域中，兩比例比值的監控方法與技術應用逐漸受到重視，於部分實務製程中扮演重要角色。然而，在統計製程管制的相關文獻中，針對兩比例比值進行監控的方法仍屬罕見。有鑑於此，本研究旨在建構監控兩比例比值變化的管制圖，以有效偵測製程是否失控。本研究分為兩個部分。第一部分為監控兩相依二項比例的比值，分別提出三種方法，建構三種不同的標準化指數加權移動平均（ZEWMA）管制圖。第一種方法利用樣本比例比值對數轉換後之近似常態分配建構 ZEWMA-RA 管制圖；第二種方法透過蒙地卡羅法模擬出樣本比例比值對數轉換後的抽樣分配，並以此建構 ZEWMA-RE 管制圖；第三種方法則以樣本比例之差推導出分配以建構 ZEWMA-RD 管制圖。接著，透過數值模擬計算這三種管制圖的管制界限，並在相同失控幅度下，以平均連串長度作為效能指標，評估各圖之偵測能力。最後，選擇偵測能力較佳的 ZEWMA-RE 與 ZEWMA-RD 管制圖應用於兩種新冠肺炎檢測方法（快篩與 RT-PCR）的實際偵測率比值資料，以說明其實務使用過程和偵測力。第二部分則為監控兩獨立二項比例的交叉乘積比，同樣提出三種標準化指數加權移動平均（ZEWMA）管制圖方法。第一種為利用樣本比例交叉乘積比對數轉換後的近似常態分配建構 ZEWMA-CRA 管制圖；第二種為透過蒙地卡羅法模擬出樣本比例交叉乘積比對數轉換後的抽樣分配，並以此建構 ZEWMA-CRE 管制圖；第三種則以兩比例乘積之差推導出分配以建構ZEWMA-CRD 管制圖。接著，透過數值模擬計算這三種管制圖的管制界限，並在相同失控幅度的情境下，以平均連串長度作為效能指標，評估這三種管制圖之偵測能力。最終以偵測能力較佳之 ZEWMA-CRE 與 ZEWMA-CRD管制圖，應用於台灣與日本新冠肺炎確診資料以說明其應用與比值失控偵測能力。 In recent years, the monitoring of the ratio of two proportions has gained increasing attention in industrial manufacturing and medical diagnostics, and playing a critical role in certain practical processes. However, there is a lack of research about this topic in the study of statistical process control. To address this gap, the study aims to develop control charts specifically designed for detecting shifts in the ratio of two proportions. This study is divided into two parts. The first part focuses on monitoring the ratio of two dependent binomial proportions. We propose three methods for constructing standardized Exponentially Weighted Moving Average (ZEWMA) control charts. The first method applies an asymptotic normal distribution after log-transformation of the sample ratio to construct the ZEWMA-RA chart. The second method employs Monte Carlo simulation to generate the sampling distribution of the log-transformed of the sample ratio, which is then used to construct the ZEWMA-RE control chart. The third method performs a difference of the sample proportions to derive a monitoring statistic and construct the ZEWMA-RD chart accordingly. Subsequently, control limits for the three charts are computed via numerical simulation, and their detection performance is evaluated under scenarios with identical shift magnitudes using average run length as the performance metric. Finally, the two charts with superior detection capability, ZEWMA-RE and ZEWMA-RD, are applied to a real-world case involving the detection ratios of two COVID-19 with positive testing proportions, rapid antigen tests and RT-PCR, to demonstrate their practical utility and out-of-control detection power. The second part focuses on monitoring the cross-product ratio of two independent binomial proportions. Similarly, three different ZEWMA control charts are proposed. The first method applies asymptotic normal distribution after log-transformation of the sample cross-product ratio to construct the ZEWMA-CRA chart. The second method employs Monte Carlo simulation to generate the sampling distribution of the log-transformed of the sample cross-product ratio, which is then used to construct the ZEWMA-CRE control chart. The third method performs a difference of the two-proportion product to derive a monitoring statistic and construct the ZEWMA-CRD chart accordingly. Control limits for the three charts are then obtained through numerical simulation, and their detection performance is evaluated using average run length under equal shift magnitudes. Finally, the ZEWMA-CRE and ZEWMA-CRD charts, which demonstrate superior performance, are applied to the real COVID-19 confirmed case data from Taiwan and Japan to demonstrate their practical utility and out-of-control detection power.
參考文獻:	[1] Alyassi, F., Haridy, S., Shamsuzzaman, M., & Alsyouf, I. (2021). Monitoring Multi-Attribute Characteristics using a Combined Scheme of np and EWMA Charts. International Journal of Industrial Engineering and Operations Management, 3098-3104. [2] Bonett, D. G., Price, R. M. (2006). Confidence intervals for a ratio of binomial proportions based on paired data. Statistic in Medicine, 25(17), 3039-3047. [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] Chaimayo, C., Kaewnaphan, B., Tanlieng, N. et al. (2020). Rapid SARS-CoV-2 antigen detection assay in comparison with real-time RT-PCR assay for laboratory diagnosis of COVID-19 in Thailand, Virology Journal, 17, 177–183. [5] Chiu, J. E., & Kuo, T, I. (2010). Control charts for fraction nonconforming in a bivariate binomial process. Journal of Applied Statistics, 37(10), 1717-1728. [6] Chong, N. L., Khoo, M. B., Haridy, S., & Shamsuzzaman, M. (2019). A multiattribute cumulative sum‐np chart. Stat, 8(1), e239, 1-9. [7] DelRocco, N., Wang, Y., Wu, D. et al. (2023). New Confidence Intervals for Relative Risk of Two Correlated Proportions. Statistic in Biosciences, 15, 1–30. [8] Goodman, L. A. (1964). Simultaneous confidence limits for cross‐product ratios in contingency tables. Journal of the Royal Statistical Society: Series B (Methodological), 26(1), 86-102. [9] Haridy, S., Wu, Z., Abhary, K., Castagliola, P., & Shamsuzzaman, M. (2014). Development of a multiattribute synthetic-np chart. Journal of Statistical Computation and Simulation, 84(9), 1884-1903. [10] Jolayemi, J. K. (1999). A statistical model for the design of multiattribute control charts. Sankhyā: The Indian Journal of Statistics, Series B, 351-365. [11] Kokaew, A., Bodhisuwan, W., Yang, S. F. & Volodin, A. (2022). Logarithmic confidence estimation of a ratio of binomial proportions for dependent populations. Journal of Applied Statistics, 50(8), 1750-1771. [12] Kokaew, A., Thaithanan, J., Bodhisuwan, W., & Volodin, A. (2021). Confidence estimation of a ratio of binomial proportions for dependent populations. Lobachevskii Journal of Mathematics, 42, 394-403. [13] Lidstone, G. J. (1920). Note on the general case of the Bayes-Laplace formula for inductive or a posteriori probabilities. Transactions of the Faculty of Actuaries, 8(13), 182-192. [14] Lu, X. S. (1998). Control chart for multivariate attribute processes. International Journal of Production Research, 36(12), 3477-3489. [15] Miettinen, O., & Nurminen, M. (1985). Comparative analysis of two rates. Statistics in medicine, 4(2), 213-226. [16] Nam, J. M. & Blackwelder, W. C. (2002). Analysis of the ratio of marginal probabilities in a matched-pair setting. Statistic in Medicine, 21(5), 689–699. [17] Nam, J. M. (2009). Efficient interval estimation of a ratio of marginal probabilities in matched-pair data: Non-iterative method. Statistic in Medicine, 28(23), 2929–2935. [18] Nguyen, H. D., Tran, K. P. & Goh, T. N. (2020). Variables sampling interval control charts for monitoring the ratio of two normal variables. Journal of Testing and Evaluation, 48(3), 2505-2529. [19] Pauphilet, J. (2024). Robust and heterogenous odds ratio: Estimating price sensitivity for unbought items. Manufacturing & Service Operations Management, 26(1), 11-27. [20] Roberts, S. W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics, 239-250. [21] Roldán-Nofuentes, J. & Sidaty-Regad, S. (2024). Asymptotic Confidence Intervals for the Difference and the Ratio of the Weighted Kappa Coefficients of Two Diagnostic Tests Subject to a Paired Design. REVSTAT-Statistical Journal, 20(3), 309-336. [22] Shamsuzzamana, M., Haridy, S., & Zhang, L. (2018). Design of multiattribute EWMA chart. International Journal of Industrial Engineering and Operations Management, 538-543. [23] Shewhart, W. A. (1924). Some applications of statistical methods to the analysis of physical and engineering data. Bell System Technical Journal, 3(1), 43-87. [24] Sungboonchoo, C., Ngamkham, T., Panichkitkosolkul, W., & Volodin, A. (2021). Confidence estimation of the cross-product ratio of binomial proportions under different sampling schemes. Lobachevskii Journal of Mathematics, 42, 435-450. [25] Sungboonchoo, C., Yang, S. F., Panichkitkosolkul, W., & Volodin, A. (2023). Logarithmic confidence intervals for the cross-product ratio of binomial proportions under different sampling schemes. Communications in Statistics-Simulation and Computation, 52(6), 2686-2704. [26] Tang, M.-L., Li, H.-Q. & Tang, N.-S. (2012). Confidence interval construction for proportion ratio in paired studies based on hybrid method. Statistical Methods in Medical Research, 21(4), 361–378. [27] Tenny, S., & Hoffman, M. R. (2023). Odds ratio. StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing. [28] Tran, K. P., Castagliola, P. & Celano, G. (2016). Monitoring the ratio of two normal variables using run rules type control charts. International Journal of Production Research, 54(6), 1670-1688. [29] Wang, W. & Shan, G (2015). Exact confidence intervals for the relative risk and the odds ratio. Biometric Methodology, 71(4), 985-995. [30] Yang, S. F., Yeh, A. B., & Chou, C. C. (2023). A phase II multivariate EWMA chart for monitoring multi-dimensional ratios of process means with individual observations. Computers & Industrial Engineering, 183, 109490, 1-15.
描述:	碩士國立政治大學統計學系 112354004
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0112354004
数据类型:	thesis
显示于类别:	[統計學系] 學位論文

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