Volume 08,Issue 02

Robust Monitoring of Simple Linear Profiles Using M-estimators

Authors

Mohammad Mahdi Ahmadi, Hamid Shahriari

Abstract
In many applications of statistical process control, the quality of a product or a process is described by the relationship between the response variable and one or more independent variables which is called a profile. A profile could be either linear or nonlinear. The control limits of a chart, used to monitor a profile, are functions of model parameters. The classical estimators used to estimate the parameters, are defined under certain hypotheses such as the normality of the error terms. Deviation from any of these assumptions may cause contamination. Whenever contamination exists, the classical estimators are not robust, and the resulting control charts are not accurate when monitoring the profiles. In this research, a robust estimator of the model error term variance is introduced and evaluated using MSE. Then the robust estimators of the slope and the intercept along with the robust estimator of the error term variance are used to define the control limits for the process profile under consideration. Simulation results indicate that the out of control ARL of the proposed control charts is smaller than the ARL of the classical control charts in the presence of contamination.

Keyword: Linear Regression, Profile Monitoring, Robust Estimators, Statistical Process Control, Outliers.

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