Bayesian method in statistics is very widely used in solving variety of complex problem. Bayesian method provides an important computational and methodological advantage over classical technique. The Markov Chain Monte Carlo (MCMC) method provides an alternative method for parameter estimation of the model. The book extensively uses Markov Chain Monte Carlo (MCMC) simulation method in Open BUGS to estimate the parameters of the model. A procedure is developed to estimate the scale and shape parameter of the model on a complete sample in Open BUGS. A module (Code) is incorporated in an Open BUGS. R-Functions are developed to study the statistical properties of the model. One real data set is analyzed for illustration in the book. Two distributions viz. Generalized Exponential and Inverse Weibull have been used for analyzing the reliability of the distribution .The MCMC methods in Open BUGS were found to be more simple and reliable as compared to tradition method like Maximum Likelihood Method.