Paper Title
The Analysis of Defective Products in Auto Parts Factories with Generalized Linear Mixed Models

The objectives of this research are to propose a proper model for defective products in an autoparts manufacturing industry, to apply the proposed model to the defective products data, to investigate the factors related to the machines producing defective products, and to compare the proposed model with the generalized estimating equations model (GEE). The proposed model is a generalized linear mixed model (GLMM) in which the dependent variables have a Poisson distribution. The parameter are estimated using a Bayesian method. The data were collected from 12 machines, 15 days for each machine, from an autoparts manufacturing factory. The data collection dates vary depending on the working steps and the product types. The results show that the proposed model fits the data. The factors related to the machines producing defective products are working steps, workers, and product types. According to the estimates of the factors effects, the working step producing the largest number of defective products is the working step 2 followed by the working steps 3, 1 and 4, respectively. The worker producing the largest of defective products is the worker 4, followed by the workers 10, 5, 8, 6, 2, 3, 1, 7 and 9, respectively. The product type 3 has the largest number of defective products, followed by the product types 2 and 1, respectively. If the population-averaged effects are focused, the GEE is applied. However, the subject-specific is focused, the GLMM is applied. Keywords- Generalized linear mixed model (GLMM), Bayesian estimation, Autoparts manufacturing factory, Defective products