Modeling quality control data using Weibull distributions in the presence of a change point

Abstract

In this paper, we introduce a Bayesian analysis of a data set selected at a Brazilian food company. This data set is related to the times for different quality control analysts to test samples of manufactured products that arrive at the company’s quality control department. A sample is selected from each batch of products arriving at the company’s quality control sector, and these samples have a mix of different products, which spend different times in quality control testing. From preliminary data analysis, the histograms for the data obtained are observed to have different clusters, with different parametrical distributions. Thus, we assumed two standard Weibull distributions in the presence of a covariate and a change point to analyze the data and to get standards to be used in the control of the analysts’ work. Inferences and predictions are obtained using a Bayesian approach with standard existing Markov Chain Monte Carlo methods. We also assumed a mixture of two Weibull distributions as an alternative model to be fitted to the data. The great advantage of the two models proposed under a Bayesian approach is related to better simulation procedures to be used by the quality control engineers, better predictions, and the possibility of including informative prior commonly available to industrial engineers in the choice of prior distributions.