Methods for classifying mixtures of exponential distributions based on either exponential or Poisson data

In conducting probabilistic risk analyses of nuclear power plants a suitable data base must be developed for use in estimating component unavailabilities which are required in quantification of accident sequences. Often data exists on either the time to failure of certain components or the number of component failures in a total operating or test time. Frequently there is not a single underlying failure rate lambda for all of these data and the data represent a mixture of different populations. Techniques are developed in this manuscript which allow the analyst to classify data as coming from populations with failure rates that either do or do not differ by a specified amount such as an order of magnitude. It is assumed that the failure data either follow an exponential (time to failure observed) or a Poisson (number of failures observed) distribution and that the true failure rate is itself a random variable with a specified prior distribution. Several different prior distributions are considered in examining the performance of the methods