Safety Margin Prediction Algorithms Based on Linear Regression Analysis Estimates

Abstract

In this paper, we consider the problem of approximating the safety margin of a single instance of a technical system based on inaccurate observations at specified time points. The solution to this problem is based on the selection of a certain set of reference points in time, in a small neighbourhood of which a sufficiently large number of inaccurate measurements are carried out. Analogously with the failure rate, it is assumed that the rate of decrease in the safety margin over time is represented by a polynomial of the fourth degree, and the safety margin itself is a polynomial of the fifth degree. A system of linear algebraic equations is constructed that determine the coefficients of this polynomial through its values and the values of its derivative at reference points in time. These values themselves are estimated by the method of linear regression analysis based on numerous observations in a small neighbourhood of reference points in time. A detailed computational experiment is carried out to verify the accuracy of the approximation of a fifth-degree polynomial and alternative ways of estimating it are constructed in the vicinity of points where the quality of approximation is insufficient.