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研究生： 林政憲
論文名稱： 適應性累積和損失管制圖之研究
The Study of Adaptive CUSUM Loss Control Charts
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： 2010
畢業學年度： 98
語文別： 英文
論文頁數： 59
中文關鍵詞： 累積和管制圖 、適應性管制圖 、VSI管制圖 、VSS管制圖 、VSSI管制圖 、損失函數 、馬可夫鍊 、基因演算法
外文關鍵詞： CUSUM control chart, Adaptive control chart, VSI control chart, VSS control chart, VSSI control chart, Loss function, Markov chain, Genetic algorithm
相關次數： 點閱：96  下載：24 
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    • The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process.

    The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process.

    1. INTRODUCTION 1
    2. DESCRIPTION OF IN-CONTROL AND OUT-OF-CONTROL PROCESS QUALITY VARIABLES 3
    3. OPTIMAL FP CUSUM LOSS CHART 4
    3.1 Description of the optimal FP CUSUM Loss chart 4
    3.2 Design of the optimal FP CUSUM Loss chart 6
    3.2.1 The Performance Measurement 6
    3.2.2 ARL calculation based on Markov chain approach 6
    3.2.3 Computing the upper control limit H under a specified k 9
    3.2.4 The procedure of acquiring the optimal reference value k and upper control limit H 9
    3.3 Numerical analyses for the optimal FP CUSUM Loss chart 10
    3.4 Example for the optimal FP CUSUM Loss Chart 16
    4. OPTIMAL VSI CUSUM LOSS CHART 19
    4.1 Description of the optimal VSI CUSUM Loss chart 19
    4.2 Design of the optimal VSI CUSUM Loss chart 21
    4.2.1 The performance measurement 21
    4.2.2 ATS calculation based on Markov chain approach 22
    4.2.3 Computing the warning control limit W under k and H 24
    4.2.4 The procedure of acquiring the optimal process parameters 24
    4.3 Numerical analyses for the optimal VSI CUSUM Loss chart 25
    4.4 Example for the optimal VSI CUSUM Loss Chart 29
    5. OPTIMAL VSSI CUSUM LOSS CHART 32
    5.1 Description of the optimal VSSI CUSUM Loss chart 32
    5.2 Design of the optimal VSSI CUSUM Loss chart 35
    5.2.1 The performance measurement 35
    5.2.2 ATS and ANOS calculations based on Markov chain approach 36
    5.2.3 Computing the warning control limit W under k and H 38
    5.2.4 Computing the long sampling interval t1 38
    5.2.5 The procedure of acquiring the optimal process parameters 39
    5.3 Numerical analyses for the optimal VSSI CUSUM Loss chart 40
    5.4 Example for the optimal VSSI CUSUM Loss Chart 44
    6. CONCLUSION AND FUTURE STUDY 47
    REFERENCES 48
    APPENDIX 51

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