Statistical inference of reliability distributions based on progressively hybrid censoring data

Abstract

This paper studies the statistical inferences of the unknown parameters of some reliability models using progressively hybrid censoring of type-I and type-II. We apply the maximum likelihood and Bayesian approaches to perform the statistical inferences of the parameters when the data follow Weibull, power Lindley, and Sarhan–Tadj–Hamilton distributions. Bayes method is implemented under the squared error loss function when the parameters are independent and follow gamma prior distributions with known hyperparameters. The maximum likelihood estimates cannot be obtained in an analytic form. Therefore we use the R function “optim” to find those estimates. Also, the joint posterior distribution of the unknown parameters cannot be obtained in closed form. Therefore, we will use the Markov Chain Monte Carlo method to approximate the Bayesian analysis. We constructed the highest posterior density intervals of the model parameters. We analyzed three real data sets for illustration and comparison purposes. We found out that Sarhan–Tadj–Hamilton distribution fits those three real data sets better than Weibull and Power Lindley distribution using both complete and progressively hybrid censored samples. We used expected experimentation time to discuss the optimal test plans. Simulation studies are performed to investigate the proposed methods. Based on the simulation results, we could conclude that Bayesian method does not provide better estimations than the maximum likelihood method.

Keywords

• Maximum likelihood
• Bayesian
• MCMC
• Sarhan–Tadj–Hamilton