Validation and Adjustment of Prior Distributions to Improve Bayesian Reliability Analysis for Beta-Binomial Data

This paper examines the Bayesian Reliability Analysis (BRA), and more generally, Bayesian Analysis (BA) methodology and implementation process, and identifies some issues and challenges in engineering applications including prior distributions and sampling data consistency validation, double counting, and data set combinability. Traditionally, the BRA or BA uses prior distributions without checking the consistency between prior and the sampling data. This paper improves the traditional BRA or BA by adding a step to address the issue of the prior and sampling data inconsistency. Some examples of prior and sampling data inconsistency are presented, and the inconsistency induced adverse effects on the validity and credibility of BRA results are discussed including misleading analysis results leading to inadequate engineering decision in product design, development and testing. The sources of the inconsistencies are identified under the reliability engineering context in the areas of design, operating environment, manufacturing, reliability and risk. A set of general guidance and recommendations are presented to minimize the inconsistency that can help applying BRA/BA for achieving more valid and more credible BRA/BA results. To further help addressing the prior and sampling data inconsistency, a statistical procedure that checks for inconsistency between prior and sampling data with a statistical confidence is proposed. A prior adjustment method for Beta- Binomial data, once the prior is found to be inconsistent with the sample data, is developed. The method brings the prior to be within the consistent region with the sampling data. The illustrative examples are presented with the use of the prior adjustment method that verifies the improvement of validity and credibility of the BRA results. With all above efforts, it is hoped that BRA/BA can be a more valid and credible analysis tool in practical engineering applications.