Estimation and Interpretation of k_eff Confidence Intervals in MCNP

Abstract

The Monte Carlo code MCNP has three different, but correlated, estimators for calculating k_eff in nuclear criticality calculations: collision, absorption, and track length estimators. The combination of these three estimators, the three-combined k_eff estimator, is shown to be the best k_eff estimator available in MCNP for estimating k_eff confidence intervals. Theoretically, the Gauss-Markov theorem provides a solid foundation for MCNP’s three-combined estimator. Analytically, a statistical study, where the estimates are drawn using a known covariance matrix, shows that the three-combined estimator is superior to the estimator with the smallest variance. Empirically, MCNP examples for several physical systems demonstrate the three-combined estimator’s superiority over each of the three individual estimators and its correct coverage rates. Additionally, the importance of MCNP’s statistical checks is demonstrated.