Verifying a new design using Bayes' theorem

Abstract

This paper addresses how to verify the expected reliability of a missile system and its subsystems using Bayes' theorem. During the early development phase, a number of design engineering tests are performed to establish the operational characteristics and robustness of a new design. Actual test data is not used for reliability assessment purposes until the system is close to full-scale production. This approach adds a considerable amount of risk to the program, especially if the new design cannot meet the required specification. By using Bayes' theorem, we can verify the prediction of a new system reliability using all the test data and engineering information available. This technique enables us to verify the new design much earlier and improves our confidence in meeting or exceeding the reliability requirement. Using the MIL-HDBK and verifying the reliability prediction with Bayes' theorem is a far superior approach. The model can be structured to use all the known information about the system gathered during the design stage, development testing, and its periodically demonstrated performance. This information is then weighted and projected into probability density curves that demonstrate the systems' predicted failure rate for an assigned performance period. The Bayes' approach uses early design and test data, engineering judgment, and "Expert Opinion" to predict a realistic system failure rate. Using this methodology to verify the new prediction will give both customer and management a higher degree of confidence that the individual system reliability will be met.