無母數剖面資料製程之監控與診斷

Abstract

在品管上，一般而言，製程或產品之品質特性都是一個變數。然而對某些製程而言， 品質特性是由反應變數和一或多個解釋變數間之關係來界定。因此一個品質特性乃以一 個函數、一條曲線或是一個曲面之資料型式來呈現，稱之為profile (縱斷面或剖面)。本 計劃主旨在於研究探討如何有效地監控製程profiles。文獻上大都假設固定效應或採用參 數迴歸模型。本計畫採用隨機效應無母數迴歸模型讓profiles 的函數形式更具彈性，可 應用的範圍更廣。在此模型下，Shiau et al. (2009) 利用主成份分析(principal component analysis, PCA)來剖析profiles 的特性，然後由此提出監控方法。不過，此作法要有其效 用，卻隱藏著一個不太明顯的假設：無論是in-control 還是out-of-control profiles，其主 要的特性都要能被此K 個有效主成份所描述。因此當一個形式與in-control 的形式大不 相同的out-of-control profile 產生時，就不一定能被由in-control 資料建構出來的管制圖 所偵測到。第一年之研究計畫中，將對Shiau et al. (2009) 所提監控方法提出修正方法使 之得以適用所有的情形。第二年之研究計畫將想發展一個類似failure modes analysis 的 診斷工具。當一個線上監控的profile 被第一年計畫所提之監控方法判定為out-of-control 時，系統可自動執行此診斷工具，提供製程工程師那一種out-of-control condition 最有可 能，如此可減少偵錯時間，提高效率。本計畫所提之研究在學術上和實際應用上都有相 當的貢獻。

In many practical situations, the quality of a process or product is characterized by a relationship (or profile) between a response variable and one or more independent variables instead of by the distribution of a single quality characteristic. Most research works in the literature assumed fixed-effect and/or parametric regression models to model profiles. The main objective of this project is to develop tools for profile monitoring and diagnosis for profiles of more flexible shapes and under more general and practical situations. Under a random-effect model and adopting nonparametric regression approach, Shiau et al. (2009) proposed some profile monitoring schemes. They proposed to first characterize the process via functional principal component analysis and then construct control charts accordingly. However, this method works only when all profiles, including out-of-control profiles, all can be well characterized by the functional space spanned by the chosen effective principal components. Thus when out-of-control profiles have quite different features from in-control profile, the method might fail. This is a two-year project. In the first year, we will study and propose a new profile monitoring scheme that can fix the above problem. In the second year, assuming profiles for some frequent out-of-control conditions are available, we propose to develop a diagnostic tool to provide practitioners a ranking of these likely-occurred out-of-control conditions, when a profile signals out-of-control. These tools would save practitioners much time in finding assignable causes and hence bring up quality and productivity. Results and products of this project will definitely make contributions in both academia and industries.