Introduction. Structural reliability is one of the key parameters of a building at all stages of its life cycle. An effective approach to reliability analysis is the use of probabilistic methods of structural mechanics. The actual problem of their application in practice is incomplete statistical information about the design parameters.

Aim. The research is aimed at developing a probabilistic approach to analyzing the reliability of structural elements in conditions of incomplete statistical information on random variables using methods for probability distribution function recovery.

Materials and methods. Nonparametric methods are used to recover an unknown probability distribution density of random variables based on data from a sample. Due to the fact that the reconstructed probability densities function has a complex analytical form for generating data using the N.V. Smirnov’s inverse transform sampling, the study uses the method of acceptance-rejection sampling (A/R sampling) for further use of the Monte Carlo Simulation (MCS) in the problem of probabilistic reliability analysis.

Results. The proposed algorithm is demonstrated by the example of a probabilistic calculation of the reliability of an element of a rod system. In case of incomplete statistical information, individual design parameters are estimated as confidence intervals, which leads to an interval estimate of the failure probability for a structural element. The estimated reliability is taken at the upper limit of the failure probability interval within the safety level.

Conclusions. The numerical approach to assessing the reliability of a structural object or its individual element is presented for cases of incomplete statistical information, in which reliability is expressed as an interval of failure probability. If the failure probability interval turns out to be too wide to make a decision on the reliability level, it can be narrowed by additional collection of statistical data on random parameters, or the cross-section can be increased (at the design stage) or reinforcement (at the operational stage) of the structural element can be performed. 

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.  

The article describes the experimental-theoretic method for the estimation of relative deformation of reinforced concrete column on the operation stage. The article also proposes methods for the calculation of reinforced concrete columns reliability on the strength criteria in condition of the single type of the stress plot of concrete column (compression). The offered methods take into account the incompleteness of statistical information. The article is intended for specialists in inspection and testing of reinforced concrete structures.

The article describes new methods of calculation of soil bases reliability (probability of non-failure) according to the load-bearing capacity criterion at the operation stage. The reliability of soil bases is considered as an integral part for assessing the overall operational reliability of buildings and structures, as well as for making a decision on the possibility and feasibility of reconstruction with increasing load. The proposed method of reliability calculation can be used to assess the reliability of load-bearing elements of the overhaul with replacement of parts of the building. The algorithm of the method of reliability calculation is presented in the numerical example of reliability calculation. 

The article discusses the problem of evaluation of safety of structures after seismic impacts. For the safety adopted the ultimate load and reliability of structures. The new methods proposed for evaluation of the ultimate loads and reliability for the main load-bearing elements of structures.

The article presents an approach to evaluation the reliability index of steel truss bars with the uncertainty of random variables expressed in the presence of information only about the bounds of variability. Different methods of estimating the bounds of variability for random variables are presented. The new approach is also developed using the provisions of the theory of possibility and the Dvoretzky–Kiefer–Wolfowitz inequality (DKW). The reliability index allows to compare various design solutions by the safety criterion, identify structural elements with the highest failure probability for monitoring the technical state and to quantify the increase in the safety level with strengthening of structural elements. The Monte Carlo statistical simulation data reflect the analogy of the non-probabilistic reliability index in the considered approach with the non-failure probability of the truss bar.