A Hierarchial Bayes Approach to System Reliability Analysis

The Comprehensive Test Ban Treaty of 1996 banned any future nuclear explosions or testing of nuclear weapons and created the CTBTO in Vienna to implement the treaty. The U.S. response to this was the cessation of all above and below ground nuclear testing. As such, all stockpile reliability assessments are now based on periodic testing of subsystems being stored in a wide variety of environments. This data provides a wealth of information and feeds a growing web of deterministic, physics-based computer models for assessment of stockpile reliability. Unfortunately until 1996 it was difficult to relate the deterministic materials aging test data to component reliability. Since that time we have made great strides in mathematical techniques and computer tools that permit explicit relationships between materials degradation, e.g. corrosion, thermo-mechanical fatigue, and reliability. The resulting suite of tools is known as CRAX and the mathematical library supporting these tools is Cassandra. However, these techniques ignore the historical data that is also available on similar systems in the nuclear stockpile, the DoD weapons complex and even in commercial applications. Traditional statistical techniques commonly used in classical re liability assessment do not permit data from these sources to be easily included in the overall assessment of system reliability. An older, alternative approach based on Bayesian probability theory permits the inclusion of data from all applicable sources. Data from a variety of sources is brought together in a logical fashion through the repeated application of inductive mathematics. This research brings together existing mathematical methods, modifies and expands those techniques as required, permitting data from a wide variety of sources to be combined in a logical fashion to increase the confidence in the reliability assessment of the nuclear weapons stockpile. The application of this research is limited to those systems composed of discrete components, e.g. those that can be characterized as operating or not operating. However, there is nothing unique about the underlying principles and the extension to continuous subsystem/systems is straightforward. The framework is also laid for the consideration of systems with multiple correlated failure modes. While an important consideration, time and resources limited the specific demonstration of these methods.