Detailed one-dimensional calculations have been performed to simulate reflected shock tube experiments in the weak and strong ignition regime in hydrogenoxygenargon mixtures. It is found that the experiments and simulations agree well in the strong ignition case studied. In the weak ignition case, the simulations show the same qualitative behavior as the experiments. Here ignition starts at a distance away from the reflecting wall at a time much earlier than the calculated chemical induction time. This latter effect is shown to arise because of the sensitivity of the chemical induction time to fluctuations in the calculation. In the calculations these fluctuations arise because of numerical inaccuracies. In experiments, they can arise from a number of sources including nonuniformities in the incident shock wave leading to nonuniform reflection, thermal conduction to the walls, and interactions with boundary layers.