A Bayesian method for analyzing dependencies in precursor data

Past Bayesian methods for analyzing accident precursor data have rested on unreasonable simplifying assumptions; in particular, the assumption that successive stages of each accident sequence (e.g. successive system failures) are independent. However, obtaining information on intersystem dependencies is one of the greatest benefits of precursor analysis. With such dependencies, each system may have not one but several conditional failure probabilities; for example, one under normal or test conditions, and another during accident conditions (e.g. after other systems have already failed). These probabilities, while not identical, may be correlated, since the system will contain the same components (with the same inherent reliability levels) regardless of whether other systems have already failed. In this paper, extended natural conjugate distributions are used in a Bayesian method to analyze pairs of correlated probabilities. While motivated by applications to precursor analysis, the method is in fact quite general.