Bayesian analysis of constant stress AFT for Weibull distribution using Gibbs sampling

To mitigate the limitations of the traditional methods for reliability analysis such as BLUE, the model of Weibull constant-stress accelerated failure test (AFT) is considered here. Based on the theory of Bayesian survival analysis and informative prior hypothesis for model's parameters, Markov chain Monte Carlo (MCMC) method based on Gibbs sampling is used to dynamically simulate the Markov chain of the parameters' posterior distribution, under the condition that the lifetime's distribution is Weibull. Through that, the parameters' Bayesian estimations in the constant-stress AFT model were given. BUGS package is used here as an example. The example data is first used by Shisong Mao (2003). And, two result sets are presented based on two assumptions, one of which is that the truncated data in the AFT is viewed as the right censored data in survival analysis. The other assumption is that the truncated data in the AFT is viewed as just failure data but not truncated. The two data sets are used to be compared with the results provided by Mao using BLUE method. The results indicate that, the estimation given by BLUE is close to the results given under the assumption that the truncated data is just failure data. However, when we consider the truncated data, the results far differ from the former. The limitations of BLUE will be presented once more, and the significance and the effectiveness of the model will be illustrated.