Comparison of Generalized Poisson Regression and Negative Binomial Regression Models in Handling Overdispersion in Downtime Cases

Abstract

Downtime in industrial machinery has a significant impact on efficiency and operational costs. To model the number of downtime events, Poisson regression is used, which has several assumptions, including that the response variable must be Poisson distributed, there is no linear relationship between predictor variables (multicollinearity), and the variance is equal to the mean (equidispersion). However, in practice, violations of these assumptions are often encountered, where the variance of the response variable exceeds its mean, known as overdispersion. This issue can be addressed using approaches such as Generalized Poisson Regression (GPR) and Negative Binomial Regression (NBR). In this study, a comparison of the GPR and NBR models will be conducted using secondary data from the cement manufacturing industry in Indonesia, consisting of downtime as the response variable and five predictors: duration of disruptions, number of mechanical and electrical disruptions, raw material availability, and production output. Assumption tests showed no multicollinearity and that the response distribution followed a Poisson distribution, but overdispersion was present. The results show that all predictor variables in the GPR and NBR models are significant except for the duration variable, which does not significantly affect the amount of downtime. The best model is determined based on the smallest Akaike Information Criterion. (AIC) and Root Mean Square Error (RMSE) values. The results show that GPR has an AIC of 148.3074 and an RMSE of 3.608414, while NBR has an AIC of 48.3083 and an RMSE of 3.608534. Based on these criteria, GPR was selected as the superior model.