在Lewis的ARMA模型下 校正器的設計方法運用在統計製程控制上

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葉哲宏(Jhe-hung Yeh) 查詢紙本館藏

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工業管理研究所

論文名稱

在Lewis的ARMA模型下校正器的設計方法運用在統計製程控制上
(Applying Filter design Approach to Statistical Process Control for Lewis’s ARMA Model)

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摘要(中)

這篇研究主要是探討將校正器的設計運用在統計製程的管制上，並且討論對於不同製程分配的影響。不同於傳統的自我迴歸移動平均過程，我們假設Lewis的自我迴歸移動平均過程為製程資料。在本篇論文我們使用指數加權移動平均的管制圖。我們將運用線性的校正器作用在由製程資料產生的觀測值，藉此得到我們管制圖的統計量。根據管制圖的統計量，我們可以運用馬可夫鏈的方法去計算超出管制界限的平均連串長度。在此，我們研究的目標是在預定管制界的平均連串長度中，縮小超出管制界限的平均連串長度。最後透過調整參數和轉換分配的方式去提出相對簡單的演算法。如此一來，我們可以避免複雜且費時的計算。

摘要(英)

In this study, we apply filter design to statistical process control (SPC) and discuss the impact of different process distributions. Instead of using conventional autoregressive moving-average processes, we assume Lewis’s autoregressive moving-average (ARMA) processes as data processes. The control chart we used in this study is the exponentially weighted moving average (EWMA) control chart. We will apply linear filter on the observations generated from our data process to obtain our control chart statistic. With the control chart statistic, we can calculate the out-of-control ARL by Markov chain method. And our research objective is to reduce the out-of-control ARL with a predetermined in-control ARL. In the final, we adjust parameter and transform distribution to propose a relatively simple algorithm. Therefore, we can avoid complex and time-consuming calculation.

關鍵字(中)

★ 自我相關
★ 指數加權移動平均管制圖

關鍵字(英)

★ EWMA control chart
★ autocorrelation

論文目次

中文摘要 I
Abstract II
Table of Content III
List of Tables IV
List of Figures V
1. Introduction 1
1.1 Background and motivation 1
1.2 Research objective 2
1.3 Research framework 3
2. Literature review 5
2.1 Filter design 5
2.2 EWMA control chart 6
2.3 Time series 7
3. The model 9
3.1 Model description 11
3.2 Applying the filter design 14
3.3 Proposed algorithm 16
4. Numerical Analysis 18
4.1 Distribution comparison 18
4.2 Sensitive analysis 21
4.3 Normal approximation method 23
5. Conclusion and future research 25
5.1 Conclusion 25
5.2 Future research 25
References 27

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指導教授

葉英傑(Ying-chieh Yeh)

審核日期

2011-7-18

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