Expert systems that perform diagnosis are being used increasingly in medicine, aerospace, and other high-stakes domains. Research has recently shown that heuristic schemes widely used in such systems to encode uncertain knowledge - used in diagnosis and decision making - can produce faulty reasoning. Schemes based on probability and decision analysis have been proposed as sounder; however, they have often then been dismissed as intractable. The goal of this research is to develop and evaluate new probabilistic and decision-analytic schemes, that are both sound and tractable. The planned products comprise methods for encoding uncertain knowledge in probabilistic form; for encoding judgments on values, costs, and preferences; efficient algorithms for probabilistic inference and decision making; and methods to generate comprehensible explanations of systems conclusions. These techniques are demonstrated and evaluated by application to two large knowledge-based systems, including a reformulation of QMR (Quick Medical Reference), a system for diagnosis in internal medicine; and a system for fault diagnosis and repair of gas turbines for power generation. These techniques are expected to lead to diagnostic expert systems that are easier to build and modify, that are more reliable, and that generate diagnostic test strategies that minimize unnecessary and expensive testing.