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研究生:陳琬昀
論文名稱:利用調適性管制技術同時監控製程平均數和變異數
論文名稱(外文):Joint Monitoring of Process Means and Variances by Using Adaptive Control Schemes
指導教授:楊素芬楊素芬引用關係
學位類別:碩士
校院名稱:國立政治大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:73
中文關鍵詞:管制圖變動參數相依製程選控圖馬可夫鏈
外文關鍵詞:Control ChartsVariable ParametersDependent Process StepsCause-Selecting Control ChartMarkov Chain
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  由近期的研究中發現變動所有參數的管制圖在偵測小幅度偏移時的速度比起傳統的舒華特管制圖來的快,許多文獻也討論到利用調適性管制技術同時監控製程的平均數和變異數。而在這份研究中,為了改善現有管制圖的偵測效率,依序提出了U-V管制圖以及Max-M管制圖來偵測單一製程與兩相依製程的平均數和變異數。採用AATS及ANOS來衡量管制圖的偵測績效,並利用馬可夫鏈推導計算得之。透過兩階段的範例來介紹所提出的管制圖的應用方法並將VP U-V管制圖、VP Max-M管制圖與FP Z(X-bar)-Z(Sx^2)管制圖加以比較。從所研究的數值分析中發現VP Max-M管制圖比另兩種管制圖的表現來的好,再加上只需要單一管制圖在使用上對工程師來說也較為簡便,因此建議Max-M管制圖値得在實務上被使用。
Recent studies have shown that the variable parameters (VP) charts detect small process shifts faster than the traditional Shewhart charts. There have been many papers discussed adaptive control schemes to monitor process mean and variance simultaneously. In the study, to improve the efficiency and performance of the existing control charts, the U-V control charts and Max-M control charts are respectively proposed to monitor the process mean and variance for a single process and two dependent process steps. The performance of the proposed control charts is measured by using adjusted average time to signal (AATS) and average number of observations to signal (ANOS). The calculation of AATS and ANOS is derived by Markov chain approach. The application of the proposed control charts is illustrated by a numerical example for two dependent process steps, and the performance of VP U-V control charts, VP Max-M control charts and FP Z(X-bar)-Z(Sx^2) control charts is compared. From the results of data analyses, it shows that the VP Max-M control charts have better performance than VP U-V control charts and FP Z(X-bar)-Z(Sx^2) control charts. Furthermore, using a single chart to monitor a process is easier than using two charts for engineers. Hence, Max-M control charts are recommended in real industrial process.
1 INTRODUCTION.............................................1
2 DESCRIPTION OF TWO DEPENDENT PROCESS STEPS...............7
3 JOINT VP U-V CONTROL CHARTS FOR ONE STEP AND TWO DEPENDENT STEPS...........................................10
3.1 Description of the Joint VP U-V Control Charts for One Step....................................................11
3.2 Description of the Joint VP U-V Control Charts for Two Dependent Steps...................................................13
3.2.1 The distributions of the U and V statistics under in-control and out-of-control process......................13
3.2.2 Design of the VP U-V control charts...............15
3.2.3 Initial probability calculation...................17
3.2.4 Determination of the warning limit................20
3.2.5 Performance measurement...........................23
4 VP MAX-M CONTROL CHARTS FOR ONE STEP AND TWO DEPENDENT STEPS.....................................................29
4.1 Description of the VP Max-M Control Chart for One Step....................................................29
4.2 Description of the VP Max-M Control Charts for Two Dependent Steps.........................................30
4.2.1 The distributions of the M statistics under in-control and out-of-control process......................30
4.2.2 Design of the VP Max-M control charts.............31
4.2.3 Initial probability calculation...................33
4.2.4 Determination of the warning limit................34
4.2.5 Performance measurement...........................37
5 NUMERICAL ANALYSES FOR THE PROPOSED CONTROL CHARTS......41
5.1 A Real Example of Using FP U-V and FP Max-M Control Charts..................................................41
5.2 Performance Comparisons and Sensitivity Analyses of the FP U-V, FP Max-M and FP Z(X-bar)-Z(Sx^2) Control Charts.49
5.2.1 The effects of parameters on AATS.................49
5.2.2 The effects of parameters on AATS and ANOS........55
5.3 A Real Example of Using VP U-V and VP Max-M Control Charts..................................................57
5.4 Performance Comparisons and Sensitivity Analyses of the VP U-V, VP Max-M and FP Z(X-bar)-Z(Sx^2) Control Charts.65
6 SUMMARY AND FUTURE RESEARCH.............................73
REFERENCES................................................74
APPENDICES................................................78
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