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Phase-I robust parameter estimation of simple linear profiles in multistage processes

Abstract This paper addresses the problem of robust parameter estimation of simple linear profiles in multistage processes in the presence of outliers in Phase I. In this regard, two robust approaches, namely the Huber’s M-estimator and the MM estimator, are proposed to estimate the parameters of the process in Phase I in the presence of outliers in historical data. In addition, the U statistic is applied to the robust parameter estimates to remove the effect of the cascade property in multistage processes and as a result, to obtain adjusted robust estimates of the parameters of simple linear profiles. The performance of the proposed methods is evaluated under weak and strong autocorrelations involved in some numerical experimentation. The results show that the proposed robust methods perform efficiently to eliminate the effects of the outliers and the cascade property and demonstrate a better performance compared to the one of the classical approach under both weak and strong autocorrelations. Moreover, based on the results, the proposed MM estimator provides much better estimates of the parameters compared to the M estimator.