As presented at earlier INMM conferences, one can extract the singles, doubles and triples detection rates of multiplicity counting from certain moments (mean value, covariance function and bicovariance function) of the continuous voltage signals of fission chambers. The advantage of the proposed method over the traditional approach based on pulse counting is that it is inherently free from dead time arising in counting electronics. To investigate the performance of the new method, a computational study has been performed. Measurements were simulated and analysed to assess the impact of various parameters (measurement time, detection efficiency, electronic noise, non-neutron pulses) on the recovered detection rates. It was found that while the measurement time and the detection efficiency have a strong impact on the accuracy of estimated rates, the effect of electronic noise and non-neutron pulses is either negligible or can easily be corrected for. To compare the sensitivity of the traditional and the new methods, the detection rates were estimated for a wide range of count rates with both pulse counting and using the moments of the continuous signals. While the traditional approach underestimates the reference analytic values at large count rates due to dead time losses, the new method yields correct results. Further simulations investigating other parameters relevant in practice are currently in progress. To demonstrate the use of the proposed method, an experiment was performed at the KUCA facility of the Kyoto University. Although results from the preliminary analysis of this measurement have been presented before, a new and more complete analysis is reported in this paper. Four fission chambers were used to detect neutrons emitted from a combination of Cf-252 and U-235 samples. An FPGA based data acquisition system was assembled to record the voltage signals. The moments of the signals were estimated, from which the singles and doubles rates were calculated. To serve as a reference, the detection rates were determined by the traditional pulse counting approach as well. The two results show a good agreement which indicates that the newly proposed method of multiplicity counting is a viable alternative of the traditional one.