1. Method for monitoring a degradation in an on-board device of an aircraft, implemented by a computer, with the degree of the degradation of said on-board device being defined by an abnormality score formed on the basis of measurements of physical parameters of said on-board device, said monitoring method comprising a step of comparing an abnormality score obtained for a given flight of said aircraft with a decision threshold and a step of transmitting an alert in the event of said decision threshold being exceeded, with said decision threshold being automatically determined for a given probability of alert Pa, which corresponds to the probability of an alert being transmitted during said monitoring method when said on-board device is healthy, by means of the following steps: a step of computing a plurality of abnormality scores for a plurality of flights of said aircraft without degradation so as to obtain a distribution of the probability density of the abnormality score, with the distribution being specific to the physical nature of the on-board device; a step of adjusting the distribution using a non-parametric estimator of the probability density so as to obtain a continuous adjusted distribution function; a step of computing a continuous adjusted division function on the basis of the continuous adjusted distribution function; and a step of reading the antecedent of the continuous adjusted division function for a given value, said antecedent corresponding to said decision threshold, wherein said given value is 1−Peac, with Peac being the elementary probability of exceeding the threshold for confirmation per k exceedances of threshold during n consecutive flights and being obtained by the following formula: 
 Peac= B −1 (k,n−k+1) ( Pa ) wherein B −1 (k,n−k+1) is an inverse Beta division function of parameters k and n−k+1 and Pa is said probability of alert.