Monitoring univariate and multivariate profiles using the triple exponentially weighted moving average scheme with fixed and random explanatory variables

Abstract

In many real-world applications, there is a functional relationship between a response variable and one or more explanatory variables. In such situations, classical quality monitoring schemes will not be able to provide accurate information about the process. To solve this problem, the literature recommends the use of regression monitoring tools known as profile monitoring schemes. In this paper, we use the recently proposed triple exponentially weighted moving average (TEWMA) scheme to develop new monitoring schemes for univariate and multivariate linear profiles to monitor the model parameters in conjunction with the error variance of the process with fixed and random explanatory variables. These are denoted as TEWMA3 and MTEWMA schemes, respectively. The performances of the new schemes are investigated in terms of the mean, median and standard deviation of their respective run-length distributions using both asymptotic and time-varying control limits. A numerical example is provided to facilitate the design and implementation of the proposed schemes.