Mathematical Models of the Failure Flow of the Aircraft Electronic System Components

Abstract

Ab s t r a c t. The subject of the article is the process of functioning of the modern aircraft electronic system, its components and functional units as an object of mathematical model. The purpose is to analyze an existing mathematical apparatus, which is used to calculate the failure flow of the plane radio-electronic system and opportunities for its improvement. Tasks: to build mathematical models of the failure flow of components, functional units and the plane radioelectronic system as a whole with an unlimited number of recoveries with different depth of resource recovery. The analyzed methods are: parametric methods and probabilistic methods for assessment failureless. The results obtained: mathematical models of the failure flow of the circuit positions of the aircraft electronic system were developed. Conclusions. A generalization of the well-known mathematical models of the failure flow with an unlimited number of minimum restorations of finite duration is obtained as a result of consideration of mathematical models of the failure flow of the circuit positions of the plane radio-electronic system.

Mathematical Models for Calculating the Residual Life of the Recoverable Components of the Aircraft Electronic System

“…In the case of minimal recovery of the selected circuit position, the failure and recovery flow is described by the failure flow model with a finite number of minimum restorations. These models are considered in [11,12].…”

“…We reduce the calculation of the integral in expression (13) to the basic Owen integrals. From expressions (13) and 14we have In accordance with the recommendations of the method [11] we distinguish a set of AE, the technical condition of which is not controlled, and a set of controlled on the considered interval of operation of AE.…”

“…To perform calculations on the ratio (18) it is necessary to pre-calculate the coefficients of operational readiness of the elements of FD (FS), the resource of which is restored in full, incomplete or minimal. We use for this purpose the calculated relations for the failure flow parameter obtained in [11] for flows with FR, IR and MR with a limited number of recoveries. Thus, for the case of FR, the probability that the residual operating time before the failure of the element of a certain circuit position, FD, FS will be not less than a given value, we find the formula…”

“…or substituting in (19) we obtain We now write the corresponding formula for the case of the MR element. In [11] the basic relations for processes with instantaneous MR were considered. Then, conducting reasoning similar to the above in deriving formula (6), we obtain…”

“…The scheme of calculation of indicators of residual resource of radio electronic system (RES) of the plane offered in [11,12] provides division of all accessories (AS), functional devices (FD) and functional systems (FS) of RES of the plane into non-renewable or renewable with various depth of recovery, with continuous or periodic monitoring of the technical condition, with a finite or unlimited number of failures during the specified service life, and the calculation of residual life (RL) for selected types of AS, then for FD and FS.…”