In the context of bounded-error estimation, it is customary to assume that the error between the model output and output data should lie between some known prior bounds. In this paper, it is also assumed that the factors characterizing the experiments that have been carried out (e.g., measurement times) are uncertain, with known prior bounds. An algorithm based on interval analysis is used to characterize the set of all values of the parameter vector to be estimated that are consistent with these hypotheses. This is performed in a guaranteed way, even when the model output is a nonlinear function of the parameters and factors characterizing the experiments.