Criticality control of random media such as fuel debris is one of the most important safety issues in postaccident management. A 1/fβ spectrum randomizing model is expected to simulate such random media because it is well known that 1/fβ noise can describe a diverse range of random and disordered natural phenomena. In this paper, we focus on the relationship between the multiplication factor and moderation condition in the 1/fβ random media. A number of random media were realized with the 1/fβ spectrum randomizing model that is based on the randomized Weierstrass function (RWF). The volume ratio of concrete to fuel was adopted as an index for the moderation condition. The multiplication factors were calculated with a two-energy-group Monte Carlo calculation. The calculation results were analyzed by using standard deviation, skewness, and kurtosis. Those statistical parameters had an extreme value around the optimum moderation condition. This result suggested that it is possible to predict the rough trend of variation range, distortion, and outlier of multiplication factors in the 1/fβ random media.