This paper shows how to estimate the likely death and sickness rates caused by release of toxic material when the probability of a spill, the amount spilled, the amount transported by air or water away from the primary spill site, and the types of material spilled have uncertainties. In addition, using risk methods that include quantitative procedures for determining the relative contribution, relative importance, and relative sensitivity of the uncertainties, which of the uncertain parameters is causing the greatest degree of uncertainty in the death and sickness rates, can also be identified. This affords the reduction of uncertainty. In this way, focusing on limiting the parameters that are dominant without spending effort and money on parameters that contribute little to lessening of uncertainty of death and sickness rates is possible. In addition, synergistic effects are considered for two toxic materials combining to produce either a more virulent or benign toxic effect than the original materials. For such synergistic involvement, death and sickness rates are also quantitatively described with the dominance ordering of uncertain parameters involved in the synergism. The numerical illustrations exemplify the method for assessing the risk and uncertainty and also illustrate the use of uncertainty to more precisely determine what is necessary to ameliorate the risk to the maximum extent possible.

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