| Criticality safety, the prevention of nuclear chain reactions, depends on Monte Carlo computer codes for most commercial applications. One major shortcoming of these codes is the limited accuracy of the atomic and nuclear data files they depend on. In order to apply a code and its data files to a given criticality safety problem, the code must first be benchmarked against similar problems for which the answer is known. The difference between a code prediction and the known solution is termed the “bias” of the code.; Traditional calculations of the bias for application to commercial criticality problems are generally full of assumptions and lead to large uncertainties which must be conservatively factored into the bias as statistical tolerances. Recent trends in storing commercial nuclear fuel—narrowed regulatory margins of safety, degradation of neutron absorbers, the desire to use higher enrichment fuel, etc.—push the envelope of criticality safety. They make it desirable to minimize uncertainty in the bias to accommodate these changes, and they make it vital to understand what assumptions are safe to make under what conditions.; A set of improved procedures is proposed for (1) developing multivariate regression bias models, and (2) applying multivariate regression bias models. These improved procedures lead to more accurate estimates of the bias and much smaller uncertainties about this estimate, while also generally providing more conservative results. The drawback is that the procedures are not trivial and are highly labor intensive to implement. The payback in savings in margin to criticality and conservatism for calculations near regulatory and safety limits may be worth this cost.; To develop these procedures, a bias model using the statistical technique of weighted least squares multivariate regression is developed in detail. Problems that can occur from a weak statistical analysis are highlighted, and a solid statistical method for developing the bias model is demonstrated. Simulations of the bias model development by a casual analyst are compared with the rigorously developed bias model. In particular, questions of benchmark critical experiment sample size and selection methods are examined. |
