Evaluation of reliability of axisymmetric stochastic elements of constructions under creepage on the basis of theory of runs

Probabilistic methods of evaluating of strength reliability of construction axisymmetric elements of working in creep conditions were considered. Rheological properties of the material were described by the random function of one variable (of radius $r$). Evaluation of reliability of stochastically inhomogeneous axisymmetric structural elements was considered by deformation criterion. The restriction was imposed on random displacement, which depends on the time and spatial coordinates. It was assumed that the random field of function $w(r,t)$ has Gaussian distribution, for which some simplifications were made. Maximum valid value of displacement was deterministic (value was taken from the model problems). The calculation of probability of failure-free operation of microinhomogeneous thick-walled cylinder with given parameters under internal pressure $q$ was considered as an example. The probability of failure-free operation and service life of thick-walled cylinder obtained in this work by the deformation criterion and the results obtained by other authors was compared. It was shown that this approach can be used for fail-safe constructions, which critical level of runs is a rare event.