Study of the reliability of an aircraft not leaving the tolerance zone in a certain period of time based on the spectral-finite method using a continuous Fourier basis

The article evaluates the reliability of a navigation parameter, in this case, altitude, not going beyond the tolerance zone at a certain time interval, and also carries out a comparative analysis of theoretical and statistical reliability. The problem posed is solved a priori on the basis of the spectral-finite method of assessing reliability and the continuous Fourier basis. To solve the problem, the Karhunen-Loeve expansion is used, which involves solving complex integral equations. After this, a statistical analysis is performed on a sample of 600 implementations, which is compared with theoretical data. Interference is not taken into account in this work.