Mixture failure rate: A study based on cross-entropy and MCMC method

In this paper, the parameters and reliability characteristics of the mixture of the failure time distribution are estimated based on a complete sample using both Markov chain Monte Carlo (MCMC) method and maximum likelihood estimation via cross-entropy (CE) algorithm. While maximum likelihood estimation is the most frequently used method for parameter estimation, MCMC has recently emerged as a good alternative. The most popular MCMC method, called the Metropolis-Hastings algorithm, is used to provide a complete analysis of the concerned posterior distribution. A simulation study is provided to compare MCMC with CE, and differences between the estimates obtained by the two approaches are evaluated.