Method for monitoring a degradation of an on-board device of an aircraft with automatic determination of a decision threshold

1. A method for monitoring a degradation of an on-board device of an aircraft, comprising:

measuring physical parameters of the on-board device of the aircraft;

determining, using a computer, an abnormality score of the on-board device for a given flight of the aircraft;

comparing the abnormality score obtained for the given flight of the aircraft to a decision threshold; and

emitting an alarm when the decision threshold is exceeded,

wherein the decision threshold is determined automatically for a given alarm probability Pa, corresponding to a probability of an alarm being emitted during the monitoring method when the on-board device is undamaged, by:

calculating 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, 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;

calculating a continuous adjusted allocation function from the continuous adjusted distribution function; and

determining the decision threshold by reading a precedent of the continuous adjusted allocation function for the value 1-Pa, the precedent corresponding to the decision threshold.

2. The method for monitoring according to claim 1 , wherein the non-parametric estimator of the probability density is a Parzen window estimator.

3. The method for monitoring according to claim 2 , wherein the distribution is formed from a number N of abnormality scores for a plurality of flights of the aircraft without degradation, the distribution having an estimated standard deviation {circumflex over (σ)}, the Parzen window has a width h defined according to formula:

h

=

σ

^

⁡

(

4

3

*

N

)

1

/

5

.

4. The method for monitoring according to claim 1 , wherein the alarm probability Pa is obtained using formula:

P

⁢

⁢

α

=

Pe

(

1

-

Pe

)

·

(

1

-

β

)

α

⁢

⁢

priori

·

Pd

(

1

-

Pd

)

in which:

Pe corresponds to the probability of the on-board device being undamaged when an alarm is emitted;

Pd corresponds to the probability of a degradation for a given flight; and

(1−β) a priori corresponds to the probability of detecting a degradation priori.

5. The method for monitoring according to claim 4 , further comprising:

implementing the method for monitoring a degradation of the on-board device, with the decision threshold determined in advance, for a plurality of abnormality scores formed for a plurality of flights of the aircraft with degradation to deduce therefrom a probability of detecting a degradation a posteriori (1−β) a posteriori ;

determining a new alarm probability Pa on the basis of the probability of detecting a degradation a posteriori (1−β) a posteriori ; and

determining a new, refined decision threshold from the new alarm probability Pa.

6. The method for monitoring according to claim 1 , wherein the on-board device is a fuel metering device.