1. A method for monitoring a degradation in an on-board device of an aircraft, implemented by a computer, the method comprising: measuring physical parameters from a plurality of sensors on the on-board device of the aircraft; transforming, using the computer, the measured physical parameters to obtain an abnormality score for a given flight of the aircraft; comparing the abnormality score obtained for the given flight of the aircraft to a decision threshold; and transmitting an alert when the decision threshold is exceeded, wherein the decision threshold is automatically determined for a given probability of alert Pa, corresponding to a probability of an alert being transmitted during the monitoring method when the on-board device is undamaged, by: computing a plurality of abnormality scores for a plurality of flights of the aircraft without degradation; obtaining a distribution of a probability density of the plurality of abnormality scores, with the distribution being specific to a physical nature of the on-board device; obtaining a continuous adjusted distribution function by adjusting the distribution using a non-parametric estimator of the probability density; computing a continuous adjusted division function based on the continuous adjusted distribution function; and determining the decision threshold by reading an antecedent of the continuous adjusted division function for a given value, the antecedent corresponding to the decision threshold, wherein the given value is 1−Peac, where Peac is an elementary probability of exceeding the decision threshold for confirmation per k exceedances of the decision threshold during n consecutive flights and is 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 the probability of alert.