Probabilistic risk assessments are increasingly being used to quantify the public risks of operating potentially hazardous systems such as nuclear power reactors. Such assessments require the quantification of the frequencies of various low-probability events. In performing these analyses, the risk analyst is often confronted with the dual problem of the appropriate data to be used to estimate the required frequencies and the development of the corresponding estimates. Often the problem reduces to one of how to combine (or pool) a variety of more or less applicable existing data sources. A Bayes/empirical-Bayes procedure is developed for combining as many as five different types of pertinent data. The five data types can be grouped under 1. analysis data, 2. similar operating data, 3. expert opinions, 4. historical operating data, 5. generic data. Example illustrations of each of these data types are given. The procedure is used to estimate the combined hourly failure rate of small manually operated sodium valves, such as those typically found in liquid-metal fast breeder reactor shutdown heat removal systems. Pertinent data sources include operating data from sodium test loops (similar operating data), expert opinion, operating data from the Experimental Breeder Reactor-II, and seven generic failure rate estimates for similar valves in both U.K. and U.S. operating light water power reactors. A final posterior distribution is produced that reflects the combined influence of all of these data. This distribution provides the required estimates and corresponding uncertainty bounds.