Abstract:
The problem of determining the properties of the object by analyzing the numerical and qualitative
characteristics of a discrete sample is considered. A method has been developed to determine the probability
of trouble-free operation of electronic systems for the case if the interpolation fields are different between
several interpolation nodes. A method has been developed to determine the probability of trouble-free
operation if the interpolation polynomial is the same for the entire interpolation domain. It is shown that
local interpolation methods give more accurate results, in contrast to global interpolation methods. It is
shown that in the case of global interpolation it is possible to determine the value of the function outside
the given values by extrapolation methods, which makes it possible to predict the probability of failure.
It is shown that the use of approximation methods to determine the probability of trouble-free operation
reduces the error of the second kind. A method for analyzing the qualitative characteristics of functional
dependences has been developed, which allows us to choose the optimal interpolation polynomial. With
sufficient statistics, using the criteria of consent, it is possible to build mathematical models for the analysis
of failure statistics of electronic equipment. Provided that the volume of statistics is not large, such statistics
may not be sufficient and the application of consent criteria will lead to unsatisfactory results. Another
approach is to use an approximation method that is applied to statistical material that was collected
during testing or controlled operation. In this regard, it is extremely important to develop a method for
determining the reliability of electronic systems in case of insufficiency of the collected statistics of failures
of electronic equipment.
