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 a Bayesian viewpoint in order to determine the feasible parameter set and, in a posterior fault detection stage, to check the consistency between data and the model. The paper shows that, assuming uniform distributed measurement noise and flat model prior probability distribution, the Bayesian approach leads to the same feasible parameter set than the set-membership strips technique and, additionally, can deal with models nonlinear in the parameters. The procedure and results are illustrated by means of the application to a quadruple tank process.

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