Bayesian reliability modeling for pass/fail systems with sparse data

This paper proposes a Bayesian method to evaluate and predict reliability of a system when there are limited testing data and the development tests are composed of different mixtures of subsystems. Expert knowledge on subsystems is integrated by using appropriate prior distributions. The development tests provide information through the likelihood function. The effects of prior knowledge and available data on subsystems/components lead to a posterior distribution which can then be used as a prior distribution for a fully functional system. Complex likelihood functions based on developmental tests are demonstrated. Prior distributions selection and elicitation is investigated, and the Bayesian reliability approach is compared with the frequentist reliability estimation results. The proposed Bayesian reliability assessment and prediction method is demonstrated through numerical examples for a new product development.