利用單體資料縱深測度建構剖面資料之無母數監控方法

Abstract

在目前的統計製程管制中，當製程品質特性可以用剖面資料來作很好的描述時，對剖面資料的監控是一種新穎且有用的技術。這篇論文目的在於藉著無母數方法發展對於有隨機個體效應之剖面資料的監控方法。此處“個體效應”指製程在管制狀態下允許某種程度的剖面資料間之變異。我們利用主成分分析來分析參考剖面資料並且藉由主成分來降低資料的維度。資料縱深測度是無母數多變量資料分析方法中重要的一環。而單體資料縱深測度則是眾多計算資料縱深測度的方法之一。我們藉由每一筆剖面資料的主成分分數計算出相對於參考剖面資料的單體料縱深測度。在建構管制圖的過程中，主成分的選擇對於偵測製程改變的能力是有影響的。藉著單體資料縱深測度的概念所得出的由中心到外的順序，我們利用三種管制圖，包括了r-管制圖，Q-管制圖和DDMA-管制圖，來執行第二階段的製程管制。這些管制圖對於製程資料不需要作任何分配上的假設，基於這個無母數的優點，這些管制圖可以有更廣泛的應用。最後我們用Kang和Albin 在西元2000年所介紹的阿斯巴甜剖面資料來作方法說明並研究這些方法的有效性。

Profile monitoring is presently a new and useful technique in statistical process control best used in where the process data of an object follow a profile (or curve) of an independent variable. This study is aimed at developing monitoring schemes for profiles with random effects (or more precisely, subject effects) by nonparametric methods. The term "subject effects" here means a certain degree of profile-to-profile variation is allowable for an in-control process. We utilize the technique of principal components analysis to analyze the reference profiles and reduce each profile data to a principal component score vector of lower dimension. Data depth is one of the important notions of nonparametric multivariate analysis. Simplicial depth is one of the popular data depths. We convert the principal component score vector of each profile to a simplicial depth value with respect to the reference score vectors. The choice of principal component scores used in constructing a control chart has effects on the detecting power. With the center-outward ranking induced by the notion of simplicial depth, we construct three control charts, including r-chart, Q-chart, and DDMA-chart, to perform Phase II process monitoring. These control charts are completely nonparametric and have broader applicability than the usual multivariate control charts. These approaches are illustrated and studied using the aspartame example presented in Kang and Albin [7].