MONITORING OF CORRELATED LINEAR PROFILES USING GENERALIZED ESTIMATING EQUATIONS

Abstract

The quality characteristics of a process or product may sometimes be expressed as a functional relationship between a response variable and one or more explanatory variables typically referred to as a profile. Profile monitoring is a recent field of research in quality control, which involves monitoring the parameters of a profile model as against the quality characteristics. A general linear profile that can be represented by a simple linear regression model is considered in this research work and the Generalized Estimating Equation (GEE) procedure is used to estimate the parameters of the fitted linear profile and monitor the correlation structure within the linear profile. Three ‘working correlation structure’ (exchangeable, unstructured, and independent) are used to fit three different models using R programming language and the best fitted model is obtained using the Correlation Information Criterion (CIC). All three models gave the same CIC value, and hence, any of the correlation structure can be selected to fit the linear profile. Real life agricultural data of Schabenberger and Pierce (2002), consisting of 10 apple trees in which 25 apples are randomly selected on each tree and the diameters of the apples recorded in every 2 weeks during 12 weeks are then used to illustrate the study. Three selected multivariate controls charts (Hotelling T2, Multivariate Exponentially Weighted Moving Average (MEWMA) and Multivariate Cummulative Sum (MCUSUM)) are used to monitor the process over time and determine the changes in the profile parameters at weak, intermediate and strong correlation levels. The performances of these charts are compared using the Average Run Length (ARL) criterion in Phase II monitoring. The result of study shows that the Hotelling T2 control charts has the best performance in detecting large shifts in process parameters when compared with the MEWMA and MCUSUM control charts