用無母數迴歸方法監控隨機效應曲線型品質特性之製程

Abstract

監控製程與產品之曲線型資料在統計品質管制中是ㄧ個非常熱門且 有前景的研究領域。我們的研究將以對具有隨機效應之非線性曲線型資料的監控方法為主。

對隨機效應模式，我們利用主成分分析來分析曲線型資料的共變異 結構，並利用每個曲線型資料所得之主成分分量來做監控。在第二階段中，因為個別的主成分分量很難區別開變動的趨勢，所以我們建議利用combined chart，即合併主成分分量的方法來做監控。

在第一階段中，因為主成分分量的相依特性，我們採用T^2圖來檢測 穩定性。我們利用大量模擬的方法來說明，當outliers 出現的形式是短暫時，T1^2表現的較T2^2佳。

而且，我們也發現用來建造控制圖的主成分個數會影響偵測力。我 們採用交互驗證(cross-validation)的方法，來選擇主成分的個數。

The monitoring of process and product profiles is a very popular and promising area of research in statistical process control. This study is aimed at the monitoring scheme for nonlinear profiles with random effects.

For random effect models, we use the technique of principal component analysis to analyze the covariance structure of the profiles and use principal component scores of each profile to perform monitoring. In Phase II, since it is difficult for each principal component score to have identified direction of shifts, we recommend using a combined chart scheme that combines the principal component scores to perform monitoring.

In the historical analysis of Phase I data, due to the dependency of principal component scores, we adopt the T^2 chart to check for stability. We show by simulation that the sample-covariance-based T1^2 performs better than the successive-difference-based T2^2 for temporal shifts.

Also, the number of principal component scores used in constructing control charts has an effect on the detecting power. We adopt the cross-validation to choose the number of principal component scores.