卜瓦松廣泛加權及雙重廣泛加權移動平均管制圖｜國立臺灣科技大學博碩士論文系統

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研究生：	邱文智 Wen-Chih Chiu
論文名稱：	卜瓦松廣泛加權及雙重廣泛加權移動平均管制圖 Poisson Generally Weighted Moving Average and Double GWMA Control Charts
指導教授：	徐世輝 Shey-Huei Sheu
口試委員:	蘇朝墩 Chao-Ton Su 巫木誠 Muh-Cherng Wu 王國雄 Kuo-Hsiung Wang 陳仁義 Zen-yi Chen 孫智陸 Juh-Luh Sun 謝光進 Kong-King Shieh
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：	2007
畢業學年度：	95
語文別：	英文
論文頁數：	109
中文關鍵詞：	指數加權移動平均、廣泛加權移動平均、平均連串長度、快速起始反應、卜瓦松觀測值
外文關鍵詞：	EWMA, Generally weighted moving average (GWMA), Average run length (ARL), Fast initial response (FIR), Poisson observations
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本論文發展一個新管制圖，稱為「卜瓦松廣泛加權移動平均」(Poisson Generally Weighted Moving Average,簡稱 PGWMA) 管制圖，用以監視服從卜瓦松 (Poisson)分配的觀測值。利用模擬方法，平均連串長度 (ARLs) 及連串長度之標準差 (SDRLs) 被計算並與其他管制圖比較。結果顯示PGWMA 管制圖整體而言優於其他管制圖，尤其是當製程發生輕微偏移時更為適用。另外，PGWMA 管制圖提供一個通用的模式，使得卜瓦松指數加權移動平均 (Poisson EWMA,簡稱 PEWMA) 管制圖及修華特 (Shewhart) c 管制圖均成為它的特例。
本論文亦提出另一個新發展的管制圖，稱為「卜瓦松雙重廣泛加權移動平均」(Poisson Double GWMA, 簡稱 PDGWMA) 管制圖。經由模擬，PDGWMA 管制圖之統計績效被評估並與PEWMA、PGWMA 及卜瓦松雙重EWMA (Poisson DEWMA) 等管制圖比較。結果說明在大部分的製程偏移情況下，PDGWMA 管制圖有較佳的績效，特別是當製程發生向下偏移時PDGWMA 更具優勢。因此，無論是 Poisson 製程平均向上偏移 (製程品質退化) 或向下偏移 (製程品質改善)，PDGWMA 管制圖均可敏捷的檢測出來，以便及時採取適當的管理措施。此外，如前所述，Poisson DEWMA 管制圖亦為 PDGWMA 管制圖之特例。
最近幾年來，有一些論文針對EWMA 管制圖進行快速起始反應 (Fast Initial Response, 簡寫 FIR) 特性之研究。本論文探討各種 FIR 修改模式並應用於 PGWMA 管制圖中，以期快速檢測製程於起始階段發生之品質問題。利用模擬，各種模式管制圖之 ARLs 與 SDRLs 被計算並互相比較。結果顯示 PDGWMA 管制圖在中小偏移時整體表現最佳，尤其是當製程向下偏移時特別敏感。而經調整之變動管制界限 (Adjusted time-varying control limits) PGWMA 管制圖則在製程起始階段發生重大偏移時表現最優。

A generally weighted moving average (GWMA) control chart for monitoring Poisson observations is introduced. Using simulation, its average run lengths (ARLs) and standard deviations of run lengths (SDRLs) are compared with those of other control charts for Poisson data. It is showed that the Poisson GWMA chart outperforms other control charts, especially when the process shift is small. Furthermore, the Poisson GWMA chart provides a generalized model for which the Poisson EWMA and Shewhart c charts are the special cases.
A novel control chart called “Poisson double GWMA” (PDGWMA) chart is also presented for monitoring Poisson-distributed processes. Through simulation, the statistical performance of PDGWMA chart is evaluated and compared with those of other control charts including Poisson EWMA, Poisson GWMA and Poisson double EWMA (PDEWMA). It is showed that this chart is more sensitive than other control charts in detecting an out-of-control signal in most of situations, particularly in the cases of downward process shifts. Consequently, not only the quality deterioration (upward shift) but also the quality improvement (downward shift) can be detected agilely, which is important to a modern advanced system. Moreover, the PDGWMA chart is also a generalized model in which the PDEWMA chart is its special case.
As above mentioned, the Poisson GWMA control chart is an extension model of Poisson EWMA chart. It is relatively sensitive to small process shifts for monitoring Poisson observations. Recently, some approaches have been proposed to modify EWMA charts with fast initial response (FIR) features. In this research, we employ these approaches in Poisson GWMA charts to agilely detect the process shifts caused by the start-up quality problems. Using simulation, various control schemes are designed and their ARLs and SDRLs are computed and compared. Based on the overall performance, it is showed that the PDGWMA chart is the first choice in detecting moderate or small shifts especially when the shifts are downward, and the PGWMA chart with adjusted time-varying control limits performs excellently in detecting great process shifts during the initial stage.

Chapter 1  Introduction……………….…………………………………………………1
1  Basic Principles of Control Charts…………………………………………… 1
2  Control Charts for Attribute Data Based on the Poisson Distribution…2
3  Objectives of Research……………………………………………………………3
4  Scope and Outline of Research………………………………………………… 4
Chapter 2  Poisson GWMA Control Charts…………………………………………… 6
1	Introduction to Poisson GWMA Control Charts………………………… 6
2	General Model of GWMA Charts………………………………………………8
3	Modeling of Poisson GWMA Control Charts……………………………….11
3.1	Average Run Length……………………………………………………………11
3.2	Design of PGWMA Control Charts……………………………………………12
4	Illustrative Examples………….…………………………………………..14
4.1	Simulated Data Example 2-A………………………………………………..16
4.2	Simulated Data Example 2-B…………………………………………………16
5	Comparisons with Other Control Charts………………………………….16
6	Conclusions of Chapter 2……………………………………………………25
Chapter 3  Poisson Double GWMA Control Charts……………………………………26
1	Introduction to Poisson Double GWMA Control Charts…………………26
2	Modeling of Poison Double GWMA Control Charts……………………….28
3	Statistical Performance of PDGWMA Charts………………………………29
4	Comparison with Other Control Charts……………………………………30
5	Illustrative Examples...........................................37
5.1	Simulated Data Example 3-A......................................37
5.2	Simulated Data Example 3-B......................................41
6	Conclusions of Chapter 3.................................  .....44
Chapter 4 Fast Initial Response Features for Poisson GWMA Control Charts..45
1  Introduction to FIR GWMA Control Charts..............................45
2  Poisson GWMA-type Control Charts................ ....................47
2.1  ACLPGW Control Chart...............................................47
2.2  VCLPGW Control Chart...............   .............................48
2.3  FVCLPGW Control Chart..............................................49
2.4  FADJPGW Control Chart..............................................50
2.5  PDGWMA Control Chart...............................................52
3  Performance Measure of Control Charts................................54
4  Comparison Study.....................................................55
5  Illustrative Examples................................................61
6  Conclusions of Chapter 4.............................................64
Chapter 5  Summary and Recommendations....................................65
1  Summary..............................................................65
2  Recommendations for Further Research.................................66
References................................................................67
Appendix A  ARLs and SDRLs of PGWMA charts when ARL0 = 500................70
Appendix B  ARLs and SDRLs of PDGWMA charts when ARL0 = 500...............84
Appendix C  ARLs and SDRLs of ACLPGW charts when ARL0 = 500...............98
Appendix D  ARLs and SDRLs of FVCLPGW charts when ARL0 = 500..............101
Appendix E  ARLs and SDRLs of FADJPGW charts when ARL0 = 500..............104
作者簡介..................................................................107

                                

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