Adaptive Diagnosis of Faulty Systems

A model is developed for diagnosis of faulty systems when symptoms are observable. The model considers the probabilities of various malfunctions conditioned on the observable symptom, p_ij (the probability of having the ith malfunction when observing the jth symptom), and the costs of testing various malfunctions. In practice, the exact values of these parameters are very difficult to obtain; under this condition, adaptive techniques can be used to improve our knowledge of these unknown parameters from results of past diagnoses (leaning observations). When the learning observations used to improve the knowledge of p_ij are from the successful diagnosis (in which the malfunction was found), then the optimal adaptive diagnostic procedure is defined as the one that yields minimum expected mean diagnostic cost based on the present state of knowledge of p_ij. The necessary and sufficient conditions satisfied by such a procedure are derived. The value of learning observations is the difference in the expected cost of the diagnostic procedure with and without learning observation data. A method for computing this value is presented.