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| Title: | 監控多維度品質變異數比的EWMA管制圖
EWMA Control Charts for Monitoring Multi-Dimensional Ratios of Process Variances |
| Authors: | 林正和
Lin, Cheng-Ho |
| Contributors: | 楊素芬
Yang, Su-Fen
林正和
Lin, Cheng-Ho |
| Keywords: | 多元統計製程控制
變異數比值
不偏估計式
資料深度
指數加權移動平均
無分佈假設
Multivariate statistical process control
Ratios of variances
Unbiased estimators
Data depth
Exponentially weighted moving average
Distribution-Free |
| Date: | 2024 |
| Issue Date: | 2024-09-04 14:56:11 (UTC+8) |
| Abstract: | 近年來，在工業製造或服務過程中，多變量品質變數的多維度變異數比的監控在某些實務製程中至關重要，但是，在統計製程管制 (SPC) 的研究中，尚無文獻探討。因此，本研究提出了新的管制圖以追蹤多個兩相依母體變異數之比值製程是否穩定的狀況。
在此研究中，我們分別考慮已知分佈為多元常態分配 (multivariate normal distribution) 、多元伽瑪分配 (multivariate gamma distribution) 和多元偏態分配 (multivariate skew normal distribution) 之下，以三個不同方法建立指數加權移動平均 (EWMA) 管制圖來追蹤多個相依母體變異數之比值。第一種方法是將兩個母體變異數線性組合的不偏估計量轉為T^2統計量，再分別根據樣本大小來建立EWMA-DT管制圖與近似的卡方管制圖，第二種方法則是使用資料深度 (data depth)的方法來建立EWMA-DU管制圖監控多個變異數之比值。第三種方法是以符號方法 (sign method) 來建立EWMA-DS管制圖監控多個變異數之比值。接著，以數值分析計算此三種管制圖之管制界線並考慮在失控的變動幅度相同下的平均連串長度來評估此三種管制圖的偵測能力。
最後，我們選出兩個偵測能力比較好的管制圖，並以牛奶與半導體的實際數據來說明它們的應用，並驗證其偵測能力。
In recent years, monitoring the multiple ratios of variances of multiple quality variables has become crucial in industrial manufacturing and service processes. However, there is a lack of research on this topic in statistical process control study. To address this gap, we propose three control charts for tracking the stability and variations of variance ratios for the multiple dependent process variables.
In this study, we consider the multivariate normal, multivariate gamma and multivariate skew normal distributions, and develop three new exponentially weighted moving average (EWMA) control charts to monitor the multiple ratios of variances. The first method transforms the unbiased estimators of linear combinations of two population variances into T² statistic to construct the EWMA-DT control chart and the approximate chi-square control charts based on small or large sample sizes. The second method uses data depth procedure to create the EWMA-DU control chart. The third method employs the sign method to develop the EWMA-DS control chart. We evaluate the detection capabilities of these three control charts by calculating the average run length under the out-of-control processes.
Finally, we select two better performance control charts to demonstrate their application and effectiveness in the real data using the milk and semiconductor processes respectively. |
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[23] 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.
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| Description: | 碩士
國立政治大學
統計學系
111354017 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0111354017 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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