This paper deals with the problem of set-membership identification and fault detection using a Bayesian framework. The paper presents how the set-membership model estimation problem can be reformulated from the Bayesian viewpoint in order to, first, determine the feasible parameter set in the identification stage and, second, check the consistency between the measurement data and the model in the fault-detection stage. The paper shows that, assuming uniform distributed measurement noise and uniform model prior probability distributions, the Bayesian approach leads to the same feasible parameter set than the well-known set-membership technique based on approximating the feasible parameter set using sets. Additionally, it can deal with models that are nonlinear in the parameters. The single-output and multiple-output cases are addressed as well. The procedure and results are illustrated by means of the application to a quadruple-tank process.

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