A Prior and Data Validation and Adjustment Scheme for Bayesian Reliability Analysis in Engineering Design

Bayesian reliability analysis (BRA) technique has been actively used in reliability assessment for engineered systems. However, there are two key controversies surrounding the BRA, that is, the reasonableness of the prior, and the consistency among all data sets. These issues have been debated in Bayesian analysis for many years, and as we observed, they have not been resolved satisfactorily. These controversies have seriously hindered the applications of BRA as a useful reliability analysis tool to support engineering design. In this paper, a Bayesian reliability analysis methodology with a prior and data validation and adjustment scheme (PDVAS) is developed to address these issues. In order to do that, a consistency measure is defined first that judges the level of consistency among all data sets including the prior. The consistency measure is then used to adjust either the prior or the data or both to the extent that the prior and the data are statistically consistent. This prior and data validation and adjustment scheme is developed for Binomial sampling with Beta prior, called Beta-Binomial Bayesian model. The properties of the scheme are presented and discussed. Various forms of the adjustment formulas are shown and a selection framework of a specific formula, based on engineering design and analysis knowledge, is established. Several illustrative examples are presented which show the reasonableness, effectiveness and usefulness of PDVAS. General discussion of the scheme is offered to enhance the Bayesian Reliability Analysis in engineering design for reliability assessment.