Inference on the reliability of Weibull distribution by fusing expert judgements and multiply Type-I censored data

In this paper, considering that the multiple Type-I censoring is the general form of Type-I censoring and the expert judgements widely exist in engineering, we focus on the reliability of Weibull distribution by fusing them using Bayes theory. And the multiple Type-I censoring represents that all units in the life testing experiment are terminated at different times. First, the expert judgements are regarded as the prior information and how to determine the prior distribution of Weibull parameters is discussed. For completeness, the cases that there is only one and there are more than two expert judgements are both studied. Next, the posterior distribution of Weibull parameters is derived. As it is difficult to present the posterior distribution of reliability and closed-form for the Bayes estimation, an algorithm is proposed to generate the posterior samples of reliability based on the Monte Carlo Markov Chain (MCMC) method. And the Bayes estimation and credible interval for the reliability could be obtained according to these samples. Finally, an illustrative example is presented to show the application. It demonstrates that the proposed method is rather simple, satisfactory and robust.