廣泛加權移動平均管制圖在偵測製程平均數與（或）變異數上的推廣

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研究生：	謝育泰 Yu-tai Hsieh
論文名稱：	廣泛加權移動平均管制圖在偵測製程平均數與（或）變異數上的推廣 Extend GWMA Control Charts in Monitoring the Process Mean and/or Variance
指導教授：	徐世輝 Shey-Huei Sheu
口試委員:	王國雄 Kuo-Hsiung Wang 蘇朝墩 Chao-Ton Su 孫智陸 Juh-Luh Sun 林義貴 Yi-Kuei Lin 巫木誠 none 柯沛程 none
學位類別：	博士 Doctor
系所名稱：	管理學院 - 工業管理系 Department of Industrial Management
論文出版年：	2009
畢業學年度：	97
語文別：	英文
論文頁數：	88
中文關鍵詞：	管制圖、指數加權移動平均、廣泛加權移動平均、平均連串長度、雙重廣泛加權移動平均、雙重指數加權移動平均、組合式管制圖
外文關鍵詞：	Control chart, Generally weighted moving average, Exponentially weighted moving average, Average run length, Double generally weighted moving average, Double exponentially weighted moving average, Combined chart
相關次數：	點閱：358 下載：6
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廣泛加權移動平均（GWMA）管制圖建立於2003年，透過增加的調整參數，使得權重函數的設計上更具彈性，進而使GWMA管制圖在偵測小偏移的製程平均數時，較指數加權移動平均（EWMA）管制圖更有效率。然而，除了偵測製程平均數的偏移外，偵測製程變異數或同時監控平均數與變異數亦是我們所感興趣的。因此，本研究主要延伸GWMA的優點，建立偵測製程變異數的管制圖，並結合GWMA的平均數與變異數管制圖來同時監控製程偏移，最後透過簡單的手法，進一步改善GWMA在偵測製程平均數中等偏移的能力。
本論文研究分為三大部份。
第一部份，利用一些樣本統計量來製作GWMA的變異數管制圖。透過數值的模擬來衡量EWMA與GWMA管制圖的平均連串長度（ARL）。透過ARL的比較顯示，在偵測小偏移的製程變異數方面，GWMA比EWMA管制圖來的敏感。
第二部份，結合GWMA的平均數與變異數管制圖來同時監控製程的偏移。透過ARL的比較顯示，當製程平均數與變異數同時發生偏移時，組合式的GWMA管制圖比使用兩個單一的GWMA管制圖要來的敏感，而且，也比組合式的EWMA管制圖要來的有效。
第三部份，利用雙重權重的手法，製作雙重廣泛加權移動平均（DGWMA）管制圖。同樣的，透過模擬來比較ARL，結果顯示DGWMA管制圖在偵測中等偏移上，要比GWMA管制圖和雙重指數加權移動平均（DEWMA）管制圖來的敏感。

The generally weighted moving average (GWMA) control chart was developed in the 2003s. Due to the added adjustment parameter, the weight function of the GWMA is more flexible and the GWMA control chart performs substantially better than the exponentially weighted moving average (EWMA) control chart for monitoring small shifts in the process mean. Besides the process mean shifts, it is also important to monitor either the process variance or both mean and variance simultaneously. The main problem addressed in this study is to develop the new control chart by GWMA techniques for monitoring the process variance, and combine the GWMA mean chart and variance chart for detecting small shifts in the process mean and variance at the same time. Finally, use an easy way to improve the performance of the GWMA control chart for monitoring median shifts in the process mean.
This thesis is divided into three major parts.
Firstly, some GWMA variance charts are applied to the sample statistics. Simulation is utilized to evaluate the average run length (ARL) of the EWMA and GWMA control charts. Numerous comparisons of ARLs indicate that the GWMA control chart is more sensitive than the EWMA control chart for detecting small shifts in the process variance.
Secondly, a combined scheme consisting of the GWMA mean chart and variance chart for detecting process variability is developed. Numerous comparisons of ARLs indicate that the combination of the GWMA charts is more sensitive than using two single GWMA control charts when the process mean and variance shifts occurred at the same time. The combined GWMA control chart is also more sensitive than the combination of the EWMA charts for detecting small shifts in the process mean and variance.
Thirdly, this part extends the GWMA control chart by the double weighted technique. The proposed chart is called the double generally weighted moving average (DGWMA) control chart. A simulation result indicates that the DGWMA control chart with time-varying control limits is more sensitive than the GWMA and the double exponentially weighted moving average (DEWMA) control charts for detecting medium shifts in the mean of a process.

摘要...................................................................I
Abstract..............................................................II
致謝..................................................................IV
Table of Contents......................................................V
List of Notations....................................................VII
List of Figures........................................................X
List of Tables........................................................XI

Chapter 1.  Introduction...............................................1
  1.1   Background.....................................................1
  1.2   Literature Review..............................................3
  1.3   Scope and Purpose..............................................5
Chapter 2.  Description of the GWMA Control Chart......................7
Chapter 3.  The GWMA Variance Charts..................................13
  3.1   Introduction..................................................13
  3.2   Proposed GWMA Variance Charts.................................15
  3.3   Performance Measurements and Comparison.......................18
  3.4   Conclusions...................................................28
Chapter 4.  The Combined GWMA Control Chart...........................29
  4.1   Introduction..................................................29
  4.2   Mean Charts and Variance Charts...............................31
     4.2.1 EWMA Mean Chart............................................31
     4.2.2 GWMA Mean Chart............................................32
     4.2.3 EWMA Variance Chart........................................33
     4.2.4 GWMA Variance Chart........................................34
  4.3   Evaluation of the ARL.........................................35
  4.4   Comparing Performance of Control Charts.......................37
  4.5   Design of a Combined GWMA Chart...............................44
  4.6   Conclusions...................................................48
Chapter 5.  The Double GWMA Control Chart.............................49
  5.1   Introduction..................................................49
  5.2   The DGWMA Control Chart.......................................51
  5.3   Some Special Cases............................................54
     5.3.1 Case 1.....................................................54
     5.3.2 Case 2.....................................................55
     5.3.3 Case 3.....................................................55
     5.3.4 Case 4.....................................................56
  5.4   Performance Measurement and Comparison........................57
  5.5   ARL Profiles of the DGWMA Control Chart.......................60
  5.6   An Example....................................................65
  5.7   Conclusions...................................................68
Chapter 6.  Conclusions and Future Works..............................69
References............................................................71

                                

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