The generalized exponential distribution could be a good option to analyse lifetime data, as an alternative for the use of standard existing lifetime distributions as exponential, Weibull or gamma distributions. Assuming different non-informative prior distributions for the parameters of the model, we introduce a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. Some numerical illustrations considering simulated and real lifetime data are presented to illustrate the proposed methodology, especially the effects of different priors on the posterior summaries of interest.

The use of saturated two-level designs is very popular, especially in industrial applications where the cost of experiments is too high. Standard classical approaches are not appropriate to analyze data from saturated designs, since we could only get the estimates of the main factor effects and we would not have degrees of freedom to estimate the variance of the error. In this paper, we propose the use of empirical Bayesian procedures to get inferences for data obtained from saturated designs. The proposed methodology is illustrated assuming a simulated data set.

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.