Modeling of the uncertainty of statistical data by p-boxes in the analysis of the reliability of building roof structures

The article describes a problem of uncertainty modeling of statistical data in the problems of structural reliability analysis. There are elements of subjectivity in decisions making about the type of distribution of a random variable and its parameters on the analysis of the results of numerical experiments and real tests of control samples of steel on yield strength. As an alternative to the cumulative distribution function it is proposed to use p-box as a model of a random variable. The new type of a p-box is proposed on the basis of the Dvoretzky–Kiefer–Wolfowitz inequality, which allows to form the area of possible cumulative distribution functions without base on classical probability distributions. By the example of reliability analysis of a steel structural element, the variants of using different p-boxes are shown depending on the available statistical data. The probability of no-failure is presented in interval form based on p-boxes. If the result of reliability analysis by the lower boundary does not allow to make a decision about the safety level of a structural element, two options are possible: to reduce the uncertainty of the data by conducting additional statistical researches or to increase the cross-sectional area of the structural element.