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| 研究生： |
蘇惠君 |
|---|---|
| 論文名稱： |
兩相依製程之調適性管制圖 Adaptive Control Charts for Two Dependent Process Steps |
| 指導教授： | 楊素芬 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2004 |
| 畢業學年度： | 92 |
| 語文別： | 英文 |
| 論文頁數： | 168 |
| 中文關鍵詞： | 調適性管制圖 、兩相依製程 、馬可夫鍊 |
| 外文關鍵詞： | Adaptive control chart, Two dependent process steps, Markov chain, ATS |
| 相關次數： | 點閱：61 下載：0 |
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近年來,許多調適性管制圖都只探討單一製程,然而現今存在許多相依製程的問題.因此本論文提出兩相依製程之調適性管制圖,並以ATS測量管制圖的績效.本論文所提出的變動抽樣間隔時間之調適性管制圖對於偵測製程中幅度及小幅度的偏移有良好的績效.此外,本論文所提出的變動抽樣樣本大小及變動抽樣間隔時間之調適性管制圖對於偵測製程極小幅度的偏移有良好的績效.
In recent years, many research papers about adaptive control charts all consider a single process step. However, there are many multiple process steps in industry process. In this article, we propose adaptive control charts to monitor two dependent process steps, and their average time to signal (ATS) is calculated by Markov chain approach to measure the performance of these proposed control charts. It has been shown that the performance of the adaptive sampling interval (ASI) control charts in detecting small and moderate shifts in process means is better than the fixed sampling interval control charts, especially for small shifts, and the proposed adaptive sample size and sampling interval (ASSI) control charts have better performance in detecting very small shifts in process means than the fixed sample size and sampling interval control charts and the adaptive sample size control charts.
PARTⅠ: ADAPTVIE SAMPLING INTERVAL AND CONTROL CHARTS
CONTENTS
1 INTRODUCTION.....................................................................................................1
2 PROCESS DESCRIPTION.......................................................................................7
3 PRINCIPLES OF THE ASI AND CONTROL CHARTS FOR TWO DEPENDENT PROCESS STEPS……………….………………………………….8
4 DETERMINATION OF THE WARNING LIMITS ON THE ASI AND CONTROL CHARTS………………………...…………………………..……..….13
5 PERFORMANCE MEASUREMENT FOR THE ASI AND CONTROL CHARTS……………………….……………………………..……………………15
6 AN EXAMPLE…………………………………………………………….………17
7 SENSITIVITY ANALYSES……………………….………………………………21
8 COMPARISONS BETWEEN ASI AND FSI AND CONTROL CHARTS……………………………………………………………………….…..22
9 CONCLUSIONS………………………..………………………….……………....23
REFERENCES……………………………………………………………..………...50
APPENDICES………………………………………………………………………..53
Appendix 1.…………………………………………………………………………..53
Appendix 2…………………………………………………………………………...54
Appendix 3…………………………………………………………………………...60
Appendix 4…………………………………………………………………………...61
Appendix 5…………………………………………………………………………...63
Appendix 6…………………………………………………………………………...64
LIST OF TABLES
Table 2.1 Possible distributions of X and Y……………………...…………………..25
Table 3.1 Possible distributions of X and e………………………………...…..…….25
Table 5.1 The 36 process states………………………………..…………..…………25
Table 7.1 Values of the ATS for the ASI and FSI and control charts when and …………………………..……………………..27
Table 7.2 Values of the ATS for the ASI and FSI and control charts when and …………………………..……………………..32
Table 7.3 Values of the ATS for the ASI and FSI and control charts when and ……………………..…………………………..37
Table 7.4 Values of the ATS for the ASI and FSI and control charts when and …………………………..……………………..42
Table 7.5 Summary of sensitivity analyses for the ASI and control chart..47
Table 8.1 Comparisons the ATS of the ASI and FSI and control charts when =0.03 and =0.04…………….…………….……………………..…..48
Table 8.2 Comparisons the ATS of the ASI and FSI and control charts when and …………..….…………………………….……49
LIST OF FIGURES
Figure 2.1 A two-step process………………………………………………………...7
Figure 3.1 The FSI X and cause-selecting control charts……………………………10
Figure 3.2 The ASI X and cause-selecting control charts………………...…..…..….11
Figure 3.3 The ASI and control charts……………………………………12
PARTⅡ: ADAPTVIE SMAPLE SIZE AND SAMPLING INTERVAL AND CONTROL CHARTS
CONTENTS
1 INTRODUCTION.......................................................................................................1
2 PROCESS DESCRIPTION.........................................................................................7
3 PRINCIPLES OF THE ASSI AND CONTROL CHARTS FOR TWO DEPENDENT PROCESS STEPS……………….…………………………………..8
4 DETERMINATION OF THE WARNING LIMITS ON THE ASSI AND CONTROL CHARTS.………………………………..…………………………….14
5 PERFORMANCE MEASUREMENT FOR THE ASSI AND CONTROL CHARTS……….……………………………………………………….………….17
6 AN EXAMPLE………………………………………………………….…………19
7 SENSITIVITY ANALYSES………………………….……………………………23
8 COMPARISONS BETWEEN ASSI AND FSSI AND CONTROL CHARTS………………………………..…………………………….……………25
9 COMPARISONS BETWEEN ASSI AND ASS AND CONTROL CHARTS…………………………..………………….…………………………....27
10 CONCLUSIONS..…………………………………………….…………………..28
REFERENCES……………………………………………………………..………...75
APPENDICES………………………………………………………………..………78
Appendix 1.…………………………………………………………………………..78
Appendix 2…………………………………………………………………………...79
Appendix 3…………………………………………………………………………...84
Appendix 4…………………………………………………………………………...86
Appendix 5…………………………………………………………………………...87
LIST OF TABLES
Table 2.1 Possible distributions of X and Y…………………………...……………..30
Table 3.1 Possible distributions of and …………………………...………….30
Table 5.1 The 36 process states…………..……………………………..……………31
Table 7.1 Values of the ATS for the ASSI and FSSI control charts when and ……………………………………………………………..33
Table 7.2 Values of the ATS for the ASSI and FSSI control charts when and ……………………………………………………………..39
Table 7.3 Values of the ATS for the ASSI and FSSI control charts when and ……………………………………………………………..45
Table 7.4 Values of the ATS for the ASSI and FSSI control charts when and ……………………………………………………………..51
Table 7.5 Summary of sensitivity analyses for the ASSI and control charts…………………………………………….…………………………57
Table 8.1 Comparisons the ATS of the ASSI and FSSI control charts when =0.03 and =0.04…….………………………………………………………...58
Table 8.2 Comparisons the ATS of the ASSI and FSSI control charts when and ………….…………………………………………….……59
Table 9.1 Values of the ATS for the ASS and FSS and control charts when and ………………………………...……………….60
Table 9.2 Values of the ATS for the ASS and FSS and control charts when and …………………...…………………………….62
Table 9.3 Values of the ATS for the ASS and FSS and control charts when and ……………………...………………………….64
Table 9.4 Values of the ATS for the ASS and FSS and control charts when and ………………………...……………………….66
Table 9.5 Comparisons the ATS of the ASSI and ASS and control charts when =0.03 and =0.04…………………………………….………..68
Table 9.6 Comparisons the ATS of the ASSI and ASS and control charts when and ……………………………….…………71
Table 9.7 The ATS of the ASSI and ASS and control charts for very small shifts in process means…………………………………..………………...74
LIST OF FIGURES
Figure 3.1 The FSSI and control charts…………………………………….10
Figure 3.2 The ASSI and control charts……………….……………………11
Figure 3.3 The ASSI and control charts……………….………………….12
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