Monitoring multivariate simple linear profiles using robust estimators

Brief Abstract

This article focuses on estimation of multivariate simple linear profiles. While outliers may hamper the expected performance of the ordinary regression estimators, this study resorts to robust estimators as the remedy of the estimation problem in presence of contaminated observations. More specifically, three robust estimators M, S and MM are employed. Extensive simulation runs show that in the absence of outliers or for small amount of contamination, the robust methods perform as well as the classical least square method, while for medium and large amounts of contamination the proposed estimators perform considerably better than classical method.

Abstract

In some quality control applications, quality of a product or process can be characterized by a relationship between two or more variables that is typically referred to as a profile. This article focuses on multivariate linear profiles in which several correlated quality characteristics are modeled as a set of linear functions of one or more explanatory variables. Since, for the sake of simplicity, the model structure of our study consists of only one predictor, this type of profile has been referred to as multivariate simple linear profile. While outliers may hamper the expected performance of the ordinary regression estimators, which may lead to erroneous interpretation of the process status, this study resorts to robust estimators as the remedy of the estimation problem in presence of contaminated observations. More specifically, three robust estimators M, S and MM are employed using two different procedures named “one-stage” and “two-stage”. Our study comprises both phases one and two of statistical process control. Extensive simulation runs are conducted to investigate and compare the performance of the proposed estimators in terms of robustness and efficiency. The results show that in the absence of outliers or for small amount of contamination, the robust methods perform as well as the classical least square method, while for medium and large amounts of contamination the proposed estimators perform considerably better than classical method. More interestingly, comparison among robust approaches reveals that two-stage estimators exhibit superior performance in contrast with one-stage estimators. Besides, results show that MM-estimator has superior performance compared to both M and S estimators, and S estimator performs better than M estimator.

Keywords:

• Multivariate simple linear profile
• outlier data
• robust estimators
• statistical process control