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Decision designs that are insensitive to modeling uncertainty are developed for the Chernoff bounds on the performance of binary hypothesis testing problems. These designs are based on observations with statistical uncertainty modeled by using general classes generated by 2-alternating capacities. The results are illustrated for the two cases of independent identically distributed observations with uncertainty in the probability distribution and discrete-time stationary Gaussian observations with spectral uncertainty, and they are applicable to several other cases as well. For the Chernoff upper bounds on the error probabilities, a "robust" decision design based on the I/kel/hood-ratio test between a least-favorable pair of probability distributions or spectral measures, respectively, is derived. It is then shown that for all elements in the uncertainty class this choice of likelihood ratio guarantees the exponential convergence of the aforementioned Chernoff bounds to zero as the number of observations or the length of the observation interval increases.