Difficulties computing k in non-uniform, multi-region systems with loose, asymmetric coupling

Using the Monte Carlo method for k-eigenvalue calculations has several well-documented issues that can lead to incorrect answers should users not exercise caution. One such issue that has garnered little attention is the problem of under-sampling or statistical coverage, which is often confused with bias in k. Three problems are developed that specifically demonstrate this issue, often resulting in an incorrect calculation of k; all of these have features of containing multiple discrete fissile regions with loose, asymmetric coupling that is unfavorable toward the most reactive region in the problem. The three problems are: the 'Revised k-Effective of the World Problem', the 'Two-Room Vault Problem', and the 'Near-Infinite Plutonium Plane Problem'. The specifications of each problem and their specific features that make them pathological are discussed. Given these problems, the impacts of failure to provide adequate statistical coverage is discussed and advice to practitioners is provided. (authors)