A Copula Model For Accident Precursor Analysis. W. Yi and V. M. Bier, University of Wisconsin-Madison, 1513 University Avenue, Madison, WI 53706
Past Bayesian methods for analyzing precursor data have either rested on unreasonable simplifying assumptions (in particular, the assumption that successive system failures in an accident sequence are independent), or have been computationally difficult to use. This paper proposes a Bayesian copula model that discards the assumption of intersystem independence. Copulas are a way of representing arbitrary joint distributions that eliminates some of the difficulties usually involved in multivariate Bayesian analysis. In particular, the use of copulas makes it possible to specify joint distributions with arbitrary marginals and rank correlation coefficients. Thus, the failure rate of a particular system under normal and accident conditions, for example, may be correlated. Updating of these joint distributions with precursor data provides a theoretically rigorous way to estimate not only the accident frequency, but also the extent of intersystem dependence represented by the data. An application of this model demonstrates the feasibility of the approach, and shows that the assumption of independence can yield misleading results.
Work Supported by U.S. Nuclear Regulatory Commission under Grant No. NRC-04-94-098.