A practical method for obtaining prior distributions in reliability

In this paper, we propose a comprehensive methodology to specify prior distributions for commonly used models in reliability. The methodology is based on characteristics easy to communicate by the user in terms of time to failure. This information could be in the form of intervals for the mean and standard deviation, or quantiles for the failure-time distribution. The derivation of the prior distribution is done for two families of proper initial distributions, namely s-normal-gamma, and uniform distribution. We show the implementation of the proposed method to the parameters of the s-normal, lognormal, extreme value, Weibull, and exponential models. Then we show the application of the procedure to two examples appearing in the reliability literature, [26] and [28]. By estimating the prior predictive density, we find that the proposed method renders consistent distributions for the different models that fulfill the required characteristics for the time to failure. This feature is particularly important in the application of the Bayesian approach to different inference problems in reliability, model selection being an important example. The method is general, and hence it may be extended to other models not mentioned in this paper.