具相關誤差之線性迴歸模型的剖面曲線監測

Abstract

Profile monitoring is a relatively new technique and becoming popular in the area of quality control, as it is used when the process is characterized by a profile at each time period. This project considers the situation where profiles are modeled parametrically using a multiple linear regression model with random errors following an autoregressive moving-average process. Diagnostic schemes to find out-of-control samples are developed for this purpose. A simulation study examines the performance of the proposed approach based on average run length criterion. A real data example is implemented to illustrate the results, in which both phase I and phase II schemes are considered.

剖面曲線監測（profile monitoring）在品質管制的領域中，是一相對新且漸為受到重視的方法；其應用於在給定的時間內，以一剖面曲線（profile）描繪該一製程。本研究計畫主要討論的剖面曲線為誤差具自我相關移動平均過程（autoregressive moving-average process）的複迴歸模型，將提出相關統計方法在此類剖面曲線的製程下，藉以發現失控樣本的診斷設計。研究以電腦模擬方式檢驗所提出的方法；同時，藉由一個實際的資料分析陳示此方法。