It has been shown that determination of the a-activity of the radon daughters nuclides in triple time intervals, which employs air sample deposition on the air filter, are independent on the degree of the radiation disequilibrium. To decrease random errors, some additional simulations and gauge model measurements have been carried out in the radon chamber. The simulations indicate that small random errors are achieved for the counting time intervals of 1-7 min, 8-20 min and 21-30 min, 5 min deposition time, at reasonably long measuring cycle of 30 min. The counting begins parallely with the start of air pump which forces the air flow through the air filter. The radon daughter concentrations measured in such a way correspond well to the real changes of activity against time. The root mean square error of the a potential energy of radon decay products does not exceed 7.5% at about 8 mJ/m³.