This paper provides a new framework for modeling uncertainty in the input data for power system risk calculations, and the error bars that this places on the results. Differently from previous work, systematic error in unit availability probabilities is considered as well as random error, and a closed-form expression is supplied for the error bars on the results. This closed-form expression reveals the relative contribution of different sources of error much more transparently than iterative methods. The new approach is demonstrated using the thermal units connected to the Great Britain transmission system. The availability probabilities used are generic type availabilities, published rounded to the nearest 5% by the system operator. Very wide error bars on the results of risk calculations result from the use of these probabilities; however, this is only revealed by modeling of the systematic error caused by the rounding. The approach is also used to investigate quantitatively the widely acknowledged view that comparing relative risks is a more robust use of simulated risk indices than stating absolute risk levels.