Methods for Classifying Mixtures of Exponential Distributions Based on Either Exponential or Poisson Data.

摘要

It is common in treating reactor reliability data for probabilistic risk assessment to have data on either the time to failure of certain components or data on the number of component failures in a given test time. In many cases, it is assumed that the time to failure data follow exponential distributions with unknown constant failure rates lambda, while equivalently the number of failures in test time T are assumed to follow Poisson distributions with parameter lambda T. Often, however, there is not a single underlying failure rate lambda for all of the data. The purpose of this report is to examine several techniques which allow the investigator to classify data as coming from distributions with similar failure rates. Three schemes are presented for the classification of exponential and Poisson failure data. These are the classical scheme, the maximum posterior probability scheme, and classification by minimum expected loss. Each scheme is investigated using both the correct and incorrect prior.