Abstract
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.
Highlights
The times taken in carrying out quality control tests can often vary greatly, influenced by a range of factors, including the experience and skill of the quality control analysts, and the presence of different products being analyzed
We present a Bayesian analysis of a data set selected from a Brazilian food company
To analyze the times taken for quality control tests by the two analysts at the food company using a Bayesian approach, we first assume a mixture of two normal distributions defined by Eq (2) and Eq (3) with priors Eq (4) with a 8
Summary
The times taken in carrying out quality control tests can often vary greatly, influenced by a range of factors, including the experience and skill of the quality control analysts, and the presence of different products being analyzed It is, of interest to industrial managers to model these data sets, from which they can make inferences and predictions and identify important factors that could affect these times. We consider a data set from a food company in São Paulo state, Brazil This data set comprises quality control times for two different analysts observed on different days. As the two competing methodologies showed to be appropriated to analyze this data set, this article aims to explore in more detail the use of mixtures of Weibull distributions, as a good alternative for quality engineers, introducing a comparative study with the use of other mixture models like the mixture of normal distributions.
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