[en] The rapid measurement of anti-reactivities, in particular very low ones (i.e. a few tens of β) appears to be an interesting method for the automatic start-up a reactor and its optimisation. With this in view, the present report explores the various methods studied essentially from the point of view of the time required for making the measurement with a given statistical accuracy, especially as far as very low activities are concerned. The statistical analysis is applied in turn to: the methods for the natural background noise (auto-correlation and spectral density); the sinusoidal excitation methods for the reactivity or the source, with synchronous detection ; the periodic source excitation method using pulsed neutrons. Finally, the statistical analysis leads to the suggestion of a new method of source excitation using neutronic random square waves combined with an intercorrelation between the random excitation and the resulting output. (authors)