臺灣博碩士論文加值系統

在很多實際情形, 製程或產品品質可以透過反應變數與一個以上解釋變數兩者間的關係來表現更為合適，而所蒐集的樣本資料點形成曲線形式，稱為剖面資料。本篇論文探討監控第一階段非線性剖面資料的管制圖方法。
我們對第一階段剖面資料建立非線性迴歸模型，且為了改善偵測離群點的能力，提出利用Minimum Covariance Determinant (MCD) 穩健估計量及結合近年來生物統計界盛行的False Discovery Rate (FDR)方法來改良 管制圖。
我們以大量模擬方法得到這兩種不同方法的製程偵測力，且將所提出的方法應用在Kang and Albin (2000)的人工蔗糖例子。結果顯示我們所提出的新方法表現得相當良好，且也給了一些針對製程的各種偏移情形應使用何種方法做監控的建議。相信未來許多產品考量的變數會越趨複雜，所以曲線型產品特性之評估也將受到重視，而我們所提出的管制方法相信在對於相關產品上的監控可以達到一定的效果。

In this paper, we propose a control chart for process monitoring when the quality of a product is characterized by a nonlinear function (or profile). In the Phase I analysis of historical data, in order to improve the ability of detecting multiple outliers, we propose using a Hotelling chart based on Minimum Covariance Determinant (MCD) estimators, which are robust estimators of multivariate location and scale, in conjugation with the False Discovery Rate (FDR), which is a relatively new statistical procedure that bounds the number of mistakes made when performing multiple hypothesis tests. We apply the proposed method to a nonlinear profile example presented in Kang and Albin (2000). Simulation studies show that our methods are effective in detecting any reasonable number of outliers.

1 Introduction 1
2 Literature Review 4
2.1 Linear Profile. . . . . . . . . . . . . . . . . . . . . . 4
2.2 Nonlinear Profiles . . . . . . . . . . . . . . . . . . . . 6
2.3 Robust Estimation in Multivariate Control Chart . . . . . . . . . . . . . .. . . . . .. . . 9
3 Modeling Nonlinear Pro‾les 13
3.1
Nonlinear Regression Model . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Constructing the T2
mcd Statistic . . .. . . . . . . . . . . . . . . . . . 16
3.3 Aspartame Example . . .. . . . . . . . . . . . . . . . . . . . . 17
4 Methodologies 18
4.1 The T2 mcd Control Chart . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2 The FDR Procedure. . . . . .. . . . . . . . . . . . . . . . . . 20
5 Monitoring Schemes 23
5.1 Control Limit . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 Data Generation .. . . . . . . . . . . . . . . . . . . . . . 25
5.3 P-value of the Sample . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.4 The Signal Probability . . . .. . . . . . . . . . . . . . . . . . . 26
5.5 False-Rejection Rate and Correct-Rejection Rate . . . . . . . . . . . . . . . . 26
5.6 Results . . . . . . . . . . . . . . . . . . . . 27
6 Pro‾le Monitoring { Aspartame Example 29
6.1 A Simulation Study . . . . . . . . . . . . . . . . . . . . . 29
6.2 Results . . . . . . . . . . . . . . . . . . . . . . 30
7 Conclusions 31

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