Comparison of deviance and ridge deviance residual-based control charts for monitoring Poisson profiles

Abstract

Ridge estimator is one of the solutions for the multicollinearity problem caused by the absence of independency among predictors. Since the ridge estimator depends on the ridge biasing constant, a large number of techniques were studied in the literature to find a better way of calculating the ridge biasing constant. In this paper, we compare deviance residual-based control charts to ridge deviance residual-based control charts where Shewhart, EWMA, and CUSUM type control charts are constructed. We also compare several existing techniques used to calculate the ridge biasing constant and obtain the iterative ridge estimator for monitoring Poisson profiles under multicollinearity. The performance of each control chart is evaluated by using the average run length criterion and compared through a simulation study and a real data.

Keywords:

• Poisson regression
• Profile monitoring
• Residual control charts
• Ridge biasing constant
• Ridge estimator