Monitoring profiles in multistage processes using the multivariate multiple regression model

Abstract

Most recent production processes comprise multiple stages, where the final quality of products is determined by the upstream effects of output quality at each stage. Moreover, the quality of each stage is characterized by a functional relationship, referred to as a profile, between input variables and output quality variables. Therefore, the effective profile monitoring of the multiple stages is crucial in maintaining and improving the final output quality. A multistage process is separated into a series of single-stage processes, and each single-stage process is treated as a profile structure. In each stage, we implement the multivariate multiple linear regression (MMLR) model using the orthogonal design coding. The coefficient estimators of the MMLR are obtained as a matrix, whose column vectors indicate the coefficient vectors for given output quality variables and row vectors indicate the coefficients of output quality variables for given regression coefficients. Since the use of orthogonal design coding makes the regression coefficient estimator vectors for the intercept and the input variables mutually independent, it is possible to monitor the process using Hotelling's T2 charts separately. We explain the process of estimating and monitoring the regression coefficients from Phase I samples, and evaluate the performance of the proposed procedure in Phase II. © 2022 John Wiley & Sons Ltd.