第一階段剖面資料之無分配假設監控方法

Abstract

在許多應用上，製程品質是由自變數和應變數之間的函數關係來界定；在本 篇論文中，我們稱此函數關係為剖面 (profile)。近年來以統計觀點來監控製程或產品剖面資料的研究已有廣泛的發展，其中，由無母數迴歸模型建構的管制圖時 常運用在剖面資料型態很複雜且難以估計出其母體分配的情況，在分析實際資料 時，真正的母體分配通常不可知，因此近年來無母數分配和無分配假設 (distribution-free) 理論運用在製程監控上的方法越來越被重視。本論文提供第一階段無分配假設的剖面監控方法，其中，在進行主成份分析 (principal component analysis) 時，使用Chen et al. (2011)提出的共變異矩陣估計法估計剖面資料的共變異數矩陣。此方法運用在資料的樣本數小於共變異數矩陣的維度時特別能顯示其好處。

In many applications, quality of a process is best characterized by a functional relationship between a response variable and one or more explanatory variables. This functional relationship is often referred to as a profile in the literature. In statistical process control (SPC), profile monitoring is used for checking the stability of this relationship over time. Control charts based on nonparametric regression are particularly useful when the functional form of the in-control or out-of-control profiles is too complicated to be specified parametrically. Nonparametric or distribution-free methodologies have become popular tools in SPC because process distributions are often unknown in real applications. The purpose of this thesis is to provide distribution-free monitoring schemes for profiles with random effects in Phase I applications. When applying principal component analysis to characterize in-control profiles during Phase I analysis, we use the covariance matrix estimation method given in Chen et al. (2011) to estimate the covariance matrix of the discretized profiles in constructing our distribution-free profile monitoring schemes, which is useful in particular when the dimension of the covariance matrix is larger than the sample size.