Bayesian Inference for General Half-Normally Distributed Lifetime Products

Abstract

The generalized half-normal (GHN) distribution has earned widely concerned in reliability analysis. Type-I hybrid censoring (HC-I) is one efficient scheme for saving test time and cost to collect lifetime information of reliable products. However, the HC-I scheme also induces a complicated likelihood function and makes the searching of maximum likelihood estimates of the model parameters difficulty. In this study, the maximum likelihood estimation and Bayesian estimation procedure are studied for the GHN distribution based on HC-I samples. The Markov chain Monte Carlo approach using the Metropolis-Hastings algorithm via Gibbs sampling is proposed to implement the Bayesian estimation procedure for obtaining the Bayes estimators of the model parameters. The Bayesian estimation procedure is more reliable than the ML estimation method due to the Bayesian estimation procedure does not use gradient methods to search the estimates of model parameters. Simulation results show that the proposed Bayesian estimation procedure perform well in terms of the bias and mean square error.