A new method for monitoring Multivariate Simple Linear Profile

In some statistical process monitoring applications, the quality of a product or process can be determined by a linear or nonlinear regression relationship between a response variable and one or more explanatory variables called "profile". Sometimes, it is possible to describe the quality of a process or product by several simultaneous profiles in which the response variables are interdependent and are modeled as a set of linear functions of one explanatory variable, that is referred to as multivariate simple linear profile structure. In this paper, we propose a new method for monitoring phase II of multivariate simple linear profile. In this method, namely MHWMA/EWMA, a MHWMA control chart and an EWMA control chart based on generalized variance are used for monitoring the differences between the reference profile and the sample profile. Using the Mont-Carlo simulation, the statistical performance of the proposed method is evaluated in terms of the average run length criterion. The obtained results showed that the method effectively detects shifts in the profile parameters. The proposed MHWMA/EWMA method is compared with an existing method, and the results showed that this method has a good performance in detecting different types of shifts in profiles' parameters. In addition, the applicability of the proposed methods is illustrated using a real case of calibration application.