Hurdle Modeling for Defect Data with Excess Zeros in Steel Manufacturing Process

Abstract

The modern steel industry aims to produce high-quality products with higher product yield, lower costs, and lower energy consumption to meet market demands. To accomplish these goals, it is necessary to reduce or eliminate product defects. However, the relationship of operating conditions to the defect formation is not fully understood. There is increasing interest in developing models to monitor the quality and predict the number of defects in real time. Modeling and analyzing the defect count data is a very challenging problem because the defect count data exhibit the unique characteristics of non-negative integers, overdispersion, high skewed distribution, and excess zeros. To explicitly account for these unique characteristics, the present work develops an on-line quality monitoring and prediction system based on the hurdle regression model. The basic idea of the hurdle model is that a binomial model governs the binary outcome of the dependent variable being zero or positive. If the dependent variable takes a positive value, ”hurdle is crossed”, and the conditional distribution of the positives can be modeled by a zero-truncated Poisson or negative binomial (NB) model. Compared to Poisson and NB models, the hurdle model is not only suitable for modeling discrete and non-negative integer data, but also sufficient for handling both overdispersion and excess zeros data. The effectiveness of the hurdle model was verified through its application to the real defect data of a steelmaking plant. The results have demonstrated that the hurdle NB model is superior to the Poisson, NB, hurdle Poisson, and PLS models in the prediction performance.