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| Title: | 追蹤品質變數分配變化的Phase II管制圖
Phase II Control Charts for Monitoring Abnormal Process Distributions |
| Authors: | 潘禹翔
Pan, Yu-Hsiang |
| Contributors: | 楊素芬
Yang, Su-Fen
潘禹翔
Pan, Yu-Hsiang |
| Keywords: | 管制圖
指數移動平均
平均連串長度
累積分配函數
control chart
exponentially weighted moving average
average run length
CDF (cumulative distribution function) |
| Date: | 2023 |
| Issue Date: | 2023-09-01 14:56:35 (UTC+8) |
| Abstract: | 近年來，用於監測單維品質變數整個分配是否有變化的管制圖有新的發展。目前的文獻多以CDF服從均勻分配據以建立管制圖，用來偵測整個分配是否發生變化，且部分研究考慮樣本數為一(n=1)的情況。實務上，在製程管制中樣本數為一的情況較少，於是我們的研究動機是延伸1991年Hackl和Ledolter的研究，考慮樣本數大於一並且品質變數不受限制下的Phase II管制圖，用以監測品質變數分配是否發生變化。
在本研究中，我們建立兩個Phase II管制圖(SEWMA-R ̅ 管制圖和SEWMA-T管制圖)以監測品質變數的分配變化，並使用平均連串長度(ARL)作為管制圖偵測能力指標。我們考慮四個不同的失控分配，分別為常態、雙指數、偏斜常態和伽瑪分配，數據分析結果顯示在偏移平均數時，SEWMA-R ̅ 管制圖的偵測能力在伽瑪分配下最佳；在偏移變異數時，SEWMA-T管制圖的偵測能力在伽瑪分配表現最佳。最後，我們將SEWMA-R ̅ 管制圖和SEWMA-T管制圖與兩種現有的管制圖進行比較，在伽瑪分配下，SEWMA-R ̅ 管制圖在偵測平均數的偏移方面表現出較好的檢測性能，SEWMA-T管制圖在監測平均數和變異數同時偏移時表現出較好的偵測能力。
In recent years, there have been new developments in univariate control charts for monitoring changes in distribution. Current literature mostly focuses on control charts based on the cumulative distribution function (CDF) following a uniform distribution and used to detect distributional changes. Some studies consider the case where the sample size is one (n=1). However, in practice, the case of sample size one is less common in process control. Hence, our research motivation is considering sample size greater than one and developing the Phase II distribution-free control charts for monitoring abnormal process distributions by extending Hackl and Ledolter’s (1991) research.
In this study, we establish two Phase II control charts, the SEWMA-R ̅ chart and the SEWMA-T chart, to monitor changes in distribution. We use the average run length (ARL) as the performance measurement indicator for the control charts. We consider four different out-of-control distributions including normal, double exponential, skew normal and gamma distribution. The data analyses results show that, when mean shifts only, the SEWMA-R ̅ chart with gamma distributed performs the best. When variance shifts only, the SEWMA-T chart with gamma distributed performs the best. Finally, we compare the SEWMA-R ̅ chart and SEWMA-T chart with two existing control charts. Considering the gamma distribution, the SEWMA-R ̅ chart shows better detection performance in detecting shifts in process mean, while the SEWMA-T control chart exhibits better detection ability in monitoring shifts in the both mean and variance. |
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| Description: | 碩士
國立政治大學
統計學系
110354015 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0110354015 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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