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研究生： 余翊寧
論文名稱： 設計EWMA管制圖以監控相依製程
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： 2009
畢業學年度： 96
語文別： 英文
論文頁數： 92
中文關鍵詞： 管制圖 、相依製程 、馬可夫鏈
相關次數： 點閱：124  下載：87 
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    • Control charts are used to effectively monitor and determine whether a process is in-control or out-of-control. The properties of EWMA control charts on a single process have been discussed by many researchers. They have proved that EWMA control charts detect small shifts in means or variances more quickly than the traditional Shewhart control charts. However, many products are currently produced in several dependent process steps. In this article, (1) we propose three kinds of EWMA control charts, - , - , and a combined control charts, to monitor the process mean and variance for a single process step, and (2) extend the three kinds of EWMA control charts in (1) to control two dependent steps. The performance of the proposed control charts is measured by using the Markov chain approach. The application of the proposed control charts is illustrated by using some numerical examples, and the performance of the proposed charts is compared by using some numerical examples. The adjusted average time to signal (AATS) and the adjusted average samples to signal (ANOS) are calculated to measure the performance of the proposed EWMA control charts by Markov chain approach. A data set consisting of the measurements of the inside diameter of the cylinder bores in an engine block example illustrates the applications of the three kinds of EWMA control charts for a single step and a empirical automobile braking system example illustrates the applications of the three kinds of EWMA control charts for two dependent steps. Moreover, their performances are compared by some numerical analysis results.

    1.INTRODUCTION............................................1
    2.DESIGN OF THREE KINDS OF EWMA CONTROL CHARTS FOR A SINGLE PROCESS STEP .............................................3
    2.1 Description of the EWMAZx-bar-EWMAZlnSx^2 Control Charts for a Single Process Step .........................4
    2.1.1 The distributions of the plotted statistics under in-control and out-of-control process........................4
    2.1.2 The structure of the EWMAZx-bar-EWMAZlnSx^2 control charts ...................................................6
    2.1.3 Performance measurement of the EWMAZx-bar-EWMAZlnSx^2 control charts ...........................................6
    2.2 Description of the EWMAUx-bar-EWMAVx-bar Control Charts for a Single Process Step ...............................10
    2.2.1 The distributions of the plotted statistics under in-control and out-of-control process ......................10
    2.2.2 The structure of the EWMAUx-bar-EWMAVx-bar control charts ..................................................12
    2.2.3 Performance measurement of the EWMAUx-bar-EWMAVx-bar control charts ..........................................13
    2.3 Description of the EWMAMx-bar Control Chart for a Single Process Step .....................................16
    2.3.1 The distributions of the plotted statistics under in-control and out-of-control process ......................16
    2.3.2 The structure of the EWMAMx-bar control charts ....18
    2.3.3 Performance measurement of the EWMAMx-bar control charts ..................................................18
    2.4 Numerical Analyses for a Single Process Step ........21
    2.4.1 A real example of using three kinds of EWMA control charts ..................................................21
    2.4.2 Performance comparisons for the three kinds of EWMA control charts ...........................................27
    3.DESIGN OF THREE KINDS OF EWMA CONTROL CHARTS FOR TWO DEPENDENT PROCESS STEPS ..................................33
    3.1 Description of the EWMAZx-bar-EWMAZlnSx^2 and EWMAZe-bar-EWMAZlnSe^2 Control Charts Under Two Dependent Steps..34
    3.1.1 The distributions of the plotted statistics under in-control and out-of-control process .......................34
    3.1.2 The structure of the EWMAZx-bar-EWMAZlnSx^2 and EWMAZe-bar-EWMAZlnSe^2 control charts ....................37
    3.1.3 Performance measurement of the EWMAZx-bar-EWMAZlnSx^2 and EWMAZe-bar-EWMAZlnSe^2 control charts ................37
    3.2 Description of the EWMAUx-bar-EWMAVx-bar and EWMAUe-bar-EWMAVe-bar Control Charts under Two Dependent Steps.......43
    3.2.1 The distributions of the plotted statistics under in-control and out-of-control process .......................43
    3.2.2 The structure of the EWMAUx-bar-EWMAVx-bar and EWMAUe-bar-EWMAVe-bar control charts ............................45
    3.2.3 Performance measurement of the EWMAUx-bar-EWMAVx-bar and EWMAUe-bar-EWMAVe-bar control charts .................46
    3.3 Description of the EWMAMx-bar and EWMAMe-bar Control Charts Under Two Dependent Steps .........................52
    3.3.1 The distributions of the plotted statistics under in-control and out-of- control process ......................52
    3.3.2 The structure of the EWMAMx-bar and EWMAMe-bar control charts ...........................................53
    3.3.3 Performance measurement of the EWMAMx-bar and EWMAMe-bar control charts .......................................54
    3.4 Numerical Analyses for Two Dependent Steps ...........58
    3.4.1 A real example of using three kinds of EWMA control charts ...................................................56
    3.4.2 Performance comparisons for the three kinds of EWMA control charts ..........................................69
    4.CONCLUTION…………………………………………………………………..71
    REFERENCE ………………………………………………………………………72
    APPENDICES ..............................................74
    Appendix 1: The calculation of all transition probabilities of EWMAZx-bar-EWMAZlnSx^2 and EWMAZe-bar-EWMAZlnSe^2 control charts ..........................................74
    Appendix 2: The calculation of all transition probabilities of EWMAUx-bar-EWMAVx-bar control charts .................81
    Appendix 3: The calculation of all transition probabilities of EWMAMx-bar and EWMAMe-bar control charts .............88

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