利用主成份分析監控剖面資料之研究

Abstract

在多數的品質監控應用上，我們使用一個或多個品質特性 (一個變數或多個變數) 來測量製程的品質。然而，在許多情況下，有興趣的反應變數不是一個變數，而是一個函數。這個函數稱為剖面 (profile)。本研究中我們採用無母數的模型去監控剖面資料而不是用有母數的模型。 對於剖面資料間可允許的變化，我們利用主成份分析分析剖面資料變異的結構。我們利用剖面資料所包含的主成份分數(Score)的資訊監控剖面資料。傳統的 統計量視每一個主成份同等重要。然而，對於貢獻解釋剖面的變異較少的主成份而言，當他們的分數與製程在控制中的值有顯著不同時，在實務上我們未必希望因此而發出失控警訊。換句話說，這些主成份的影響在統計上是顯著的，而在實際上卻並不重要。因此我們提出一個新的監控方法，其只對於重要的主成份改變時是敏感的。我們用模擬來檢驗此方法的效能。

In most of quality control applications, we use one or multiple quality characteristics (a single univariate or multivariate variable) to measure the process quality. However, in many situations, the response of interest is not a single variable but a function of one or more explanatory variables. This functional response is called a profile. We adopt nonparametric models to monitor profiles rather than parametric models. For profiles with allowable profile-to-profile variation, we utilize the technique of principal components analysis to analyze the covariance structure in profiles. We consider monitoring profile by using the information contained in the principal component scores. Classical T2 statistics treat each principal component equally important. However, for some principal components with little contribution in explaining the variability of profiles, it may not be desirable to signal out-of-control alarms when their scores are significantly different from the in-control values. In other words, effects of these components are statistically significant but not practically significant. Thus, we propose a new monitoring scheme that is only sensitive to shifts on “important” components. Simulation studies demonstrate the efficacy of the method.