A new uncertainty analysis method based on the generalized bias operator method is presented. The new method can be used for those cases in which the other uncertainty analysis methods cannot be applied, due to the lack of or the incomplete knowledge about the input parameter's uncertainties, or due to an inadequate model. The method presented can be applied in those cases in which at least one of the system's responses is measured and the accuracy of the measurements is better than the deviation between the measured and the calculated value obtained. The theory of the method is presented, as well as methods to obtain the special sensitivity matrices associated with the method.