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The nuclear industry uses fuel performance codes to demonstrate integrity preservation of fuel rods. These codes include a complex system of models with empirical constants that one needs to calibrate for best estimates and uncertainties. However, deriving the appropriate level of uncertainty is often challenging due to model inadequacies. This paper presents a method to address model inadequacies by adapting the mean and covariance of the model parameters so that the propagated uncertainty conforms with the spread of the residuals rather than calibrating the model parameters directly. We demonstrate the method on synthetic data sets from an artificial test-bed containing a cladding oxidation and a hydrogen pick-up model. A repeated validation using many synthetic data sets shows that the method is robust and handles model inadequacies appropriately in most cases. Furthermore, we compare with traditional calibration and show model inadequacy leads to underestimation of uncertainties if not addressed. • A simplified model for hydrogen pick-up and oxidation is implemented. • Synthetic data with the desired level of model inadequacy is generated. • Model inadequacy harms calibration, leading to underestimated uncertainties. • An inflated uncertainty of model parameters can account for model inadequacy. • Repeated calibration shows a promising method for treating model inadequacies. [ABSTRACT FROM AUTHOR]