Lognormal and Gamma mixed negative binomial model for defects prediction in steel products

In steel industry, variations in the manufacturing process cause various defects in products. Thus, it is important to forecast the instance of defects in real time. However, ordinary probability models are not adequate enough to describe the observed defect count data due to the nonnegative integers characteristics, high imbalanced distribution, and overdispersion. To explicitly account for these distinctive characteristics, the present work proposes an online quality forecast system developed on the lognormal and Gamma mixed negative binomial (LGNB) model. LGNB incorporates the lognormal and Gamma distributions to account for the random effect and dispersion in the data. In addition, the drawbacks of the ordinary negative binomial (NB) model such as low robustness and biased parameter estimation against data with large dispersion are conquered by the LGNB model. The efficacy of the LGNB model was validated via its application to the defect data of an ironmaking plant. The results show that the LGNB model improves the forecast accuracy as compared to the PLS, Poisson, and NB models, respectively.