Phase I and phase II analysis of linear profile monitoring using robust estimators

Abstract

Performance of any control scheme in Phase II depends directly on the quality of estimators utilized in Phase I. In practice, outliers could be present in the data which would impact the performance of estimators adversely. This study deals with robust parameter estimation and monitoring linear profiles in the presence of outliers and compares the results with the least squares (LS) estimators. For this purpose, M-estimators are used as robust estimators and empirical distributions for related statistics are determined using Mont Carlo simulation to calculate control limits for two $T^2$ control charts and for codding independent variable method. Using a numerical example, profile parameters are estimated by ordinary least squares and M-estimators and the resulting statistics are monitored by two $T^2$ control schemes. Phase II control charts are determined based on the two types of estimators and compared for different out of control profiles. Empirical distributions did not follow their exact distributions obtained by least squares method. Simulation results confirm that M-estimators lead to better estimates in comparison to LS estimators and also improves classification performance. Robust estimators also lead to improvement in ARL performance in comparison to LS estimators.

Keywords:

• Profile monitoring
• linear profiles
• robust estimators
• M-estimators
• average run length