Impact analysis of prior distributions on the ADT Bayesian optimal design based on relative entropy

Accelerated degradation testing (ADT) optimal design means the ADT plans are designed under the particular conditions, e.g. stress range, detection times, testing cost, etc., to obtain accurate estimates of the reliability indexes. The ADT optimal design has been developed to be one of the most important techniques in the field of accelerated testing. For ADT Bayesian optimal design method, prior information has a great influence on the results of optimal plan through the prior distributions of parameters. Therefore, the proper prior distributions would improve the accuracy of the ADT Bayesian optimal design method well. Hence, this article will do impact analysis of prior distributions on ADT Bayesian optimal design method. Firstly, the model and the prior parameters of ADT Bayesian optimal method are briefly introduced. Then, how to obtain the prior distributions through the prior information under the Bayesian theory framework is studied. Lastly, different prior distributions are treated as the input of the optimal design method to get the corresponding optimal testing plans and the maximum relative entropy, while the best prior distribution is obtained through comparing the maximum relative entropy of different prior distributions. Furthermore, this research can guide the ADT optimal plan design when facing the selection problem of prior distributions, and saving the test costs and resources.