Principal component regression-based control charts for monitoring count data

Control charts based on regression models are appropriate for monitoring in which the quality characteristics of products vary depending on the behavior of predecessor variables. Its use enables monitoring the correlation structure between input variables and the response variable through residuals from the fitted model according to historical process data. However, such strategy is restricted to data from input variables which are not significantly correlated. Otherwise, colinear variables that hold substantial information on the variability of the response variable might be absent in the regression model adjustment. This paper proposes a strategy for monitoring count data combining Poisson regression and principal component analysis. In such strategy, colinear variables are turned into uncorrelated variables by principal component analysis and a Poisson regression is performed on principal component scores. A deviance residual control chart from the fitted model is then used to evaluate the process. The performance of that new approach is illustrated through a case study in a plastic plywood process with real and simulated data.