In the Monte Carlo method for criticality calculation, the convergence-in-distribution check of the sample mean of tallies can be approached in terms of the influence range of autocorrelation compared to the total number of generations iterated. In this context, it is necessary to evaluate the attenuation of autocorrelation coefficients (ACCs) over lags. However, in just one replica of calculation, it is difficult to accurately estimate small ACCs at large lags because of the comparability with statistical uncertainty. This paper proposes a method to overcome such an issue. Its essential component is the transformation of a standardized time series of tallies so that the resulting series asymptotically converges in distribution to Brownian motion. The convergence-in-distribution check is then constructed based on the independent increment property of Brownian motion. The judgment criterion is set by way of the spectral analysis of fractional Brownian motion. Numerical results are demonstrated for extreme and standard types of criticality calculation and different numbers of histories per generation. Excellent performance is observed for most replicas of calculation. An issue related to small numbers of generations is addressed for strongly autocorrelated tallies in the extreme type.