Univariate and Multivariate Linear Profiles Using Max-Type Extended Exponentially Weighted Moving Average Schemes

Abstract

Many studies have shown that industrial as well as non-industrial business organisations present a growing need of robust and more efficient multivariate monitoring schemes in order to be able to monitor several quality characteristics simultaneous. To monitor two or more parameters simultaneously, several monitoring schemes are used concurrently in most of the cases instead of using a single scheme. Thus, in this paper, the exponentially weighted moving average (EWMA), double EWMA (DEWMA) and the recent triple EWMA (TEWMA) procedures are used to develop new single univariate and multivariate Max-type monitoring schemes for linear profiles under the assumptions of fixed and random linear models to monitor the regression parameters and variance error simultaneously. It is observed that the newly proposed schemes are better alternatives of the classical univariate and multivariate EWMA, DEWMA and TEWMA schemes for linear profiles in terms of the average run-length (<i>ARL</i>) and expected <i>ARL</i> profiles. Numerical examples are presented using simulated and real-life data.