Analysis of Pham(Loglog) Reliability Model using Bayesian Approach

In this paper, the two-parameter Pham(Loglog) model is considered to analyze the software reliability data. The Markov Chain Monte Carlo (MCMC) method is used to compute the Bayes estimates of the model parameters. It has been assumed that the parameters have gamma priors and they are independently distributed. Under the above priors, Gibbs algorithm in OpenBUGS has been applied to generate MCMC samples from the posterior density function. Based on the generated samples, the Bayes estimates and highest posterior density credible intervals of the unknown parameters have been computed. The maximum likelihood estimate and associated confidence intervals have been constructed to compare the performances of the Bayes estimators with the classical estimators. One real software reliability data set has been analyzed to demonstrate how the proposed method can be used in practice.