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
