Modeling quality control data using mixture of parametrical distributions

In this paper, we present a Bayesian analysis of a data set selected from a Brazilian food company. This data set represents the times taken for different quality control analysts to test manufactured products arriving at the company’s quality control department. The samples selected from each batch contain mixtures of different products, which may be submitted to quality testing taking different times. From preliminary analysis of the data, it was observed that the histograms presented two clusters, indicating a mixture of distributions. A mixture of parametrical distributions was thus assumed in the presence of a covariate in order to analyze the data set and to establish standards to be used by the company for the times taken by the analysts. Inferences and predictions are obtained using a Bayesian approach with standard existing Markov Chain Monte Carlo (MCMC) methods.