J.K. Shultis, D.E. Johnson, G.A. Miliken, and N.D. Eckhoff, GAMMA: A Code for the Analysis of Component Failure Rates with a Compound Poison-Gamma Model, Report NUREG/CR-2373, US Nuclear Regulatory Commission,Washington, DC, Dec. 1981.

In this report the theory is summarized for the homogeneous Poisson and compound Poisson-gamma failure rate model. In the homogeneous model, failure events are assumed to follow a Poisson distribution, while in the compound model failure events follow a marginal distribution formed by integrating, over all failure rates, the product of the prior gamma distribution and the conditional Poisson distribution. A computer code, GAMMA, is presented which uses these models to analyze failure rate attribute data consisting of the number of observed failures in a given test time for a normally active component. Failure rate data for a group of similar components are used to estimate the gamma prior parameters for the compound model by three methods: (i) matching the moments of the prior gamma distribution to those of the data, (ii) matching the moments of the marginal distribution to those of the data, and (iii) maximizing the likelihood of the marginal distribution. Variance estimators for the gamma prior parameters are presented for all three estimation techniques. Also chi-squared and generalized discrete Kolmogorov-Smirnov goodness-of-fit tests are developed to test the estimated failure models against the failure data. Many other properties of the estimated failure rate models are computed by GAMMA; the computer code is described in detail in this report.