以無母數方法提供二維剖面之第一階段監控方法

Abstract

一個成功的第一階段分析在第二階段分析當中佔了很重要的地位。雖然已經有許多針對多維度製程的第一階段監控方法被提了出來，但是在面對二維剖面這樣的多維度資料時，這些方法大多會因為資料的維度太高而無法使用。這份論文建立了一個針對這種二維剖面的第一階段管制圖方案。使用multilinear principal component analysis (MPCA) 來解決二維剖面維度過高的問題，並且搭配Cheng (2012)所提出的第一階段無母數監控方法score-based multivariate sign Shewhat (SMSS) chart，來構成一個以無母數方法所完成的第一階段管制圖方案。透過模擬研究，我們能夠對我們所提出的管制圖的 false alarm probability (FAP) 和偵測能力 (false positive rate、true positive rate)有清楚的了解。我們會使用多維度常態、多維度t和gamma分配以及不同的子群數目來做模擬研究。而我們的模擬研究結果顯示，我們所提出的兩種管制圖在各種分配之下都表現得很好，而在不同的偏移型態中兩種管制圖各有不同的優勢的地方。因此我們建議同時使用這兩個管制圖來做製成監控，以利偵測部的偏移情形。

A well-performed Phase I analysis plays an important role in the success of the Phase II monitoring. Although many Phase I methods have been provided for multivariate processes, most of them are not suitable for profiles of a surface because of the large dimensionality. This thesis develops a distribution-free Phase I control charting scheme for profiles of a surface by using score-based multivariate sign Shewhart (SMSS) chart proposed by Cheng (2012) to provide a distribution-free Phase I method, and by using multilinear principal component analysis (MPCA) to solve the large dimensionality problem of profiles of a surface. By conducting simulation studies to investigate the false alarm probability (FAP), false positive rate, and true positive rate of the chart, we provide several simulation results under multivariate normal, multivariate t, and gamma distributions under different numbers of subgroups. And from our simulation studies, the proposed charts perform very well under various distributions, but each perform better than another under different OC conditions. So we suggest that we should monitor the profiles of a surface by both of these two charts.