Возможности применения порядковых статистик в задачах обеспечения надежности технических объектов

Abstract

The problems of analytical calculation of the technical objects reliability by the limit state method at all stages of the object's life cycle (design, creation, operation) are considered. The fundamental shortcomings of the statistical analysis traditional (parametric) methods are shown for the problems of estimating extremely high values of an external load random variable and small values of element resistance from the empirical data of small or extremely small volume samples. They come from the discrepancy between the random physical quantities empirical distributions and the generally accepted distribution models: the normal (Gaussian) and related (lognormal, Gumbel) ones. As an alternative, the use of order (non-parametric) statistics with the robustness property is proposed. Their use is known in the tasks of processing telemetry data or radio signals, for example, in navigation; however, the position and scale parameters of a random variable are usually estimated in terms of average values and standard deviations. However, for reliability problems, it is necessary to estimate the distribution quantiles of a very low or, conversely, high order, and for this, original procedures for data approximation and dependence extrapolation have been created. Examples of the order statistics effective usage are given as applied to problems of controlling the strength of building materials (concrete) and predicting climatic loads on buildings and structures.