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A probabilistic approach to reliability analysis for stability of an imperfect supporting shell has been elaborated. The nonlinear stability of the shell under combined loading conditions is analyzed taking into account the shell imperfection. A surface of critical load combinations has been constructed and a field of stability has been defined. The stability reliability has been determined allowing for various types of distribution in frequency of the shell imperfection and its maximum possible preset value through the use of reliability surface. The authors have derived allowable combinations of complex loadings that should be taken into consideration during the design and operation of a supporting shell.Introduction. The available analysis methods for three-dimensional structures along with present-day computing facilities make it possible to analyze complex structures that interact with the environment. However, there is still a great gap between the high theoretical and computational level at which the strength and stability problems for structures are tackled and the level of validity of conclusions about reliability and service life of such structures. It is the structural mechanics where the issue of the theory of reliability was first raised. The idea of applying statistical methods to strength analysis was pioneered by M. Maier and N. Khotsialov as early as 1926-1929 years. A special contribution to implementation of statistical methods in the structural mechanics was made by M. S. Streletskii who, starting from 1935, came up with a number of publications on that subject. For instance, in [1] he set out, in a systematic manner, a statistical concept of structure safety. This concept was implicitly represented in the procedure for structure analysis by the limit state. There were many relevant publications in the post-WW II period, such as those by O. R. Rzhanitsyn, A. Freidental, A. Ionson, and others. O. R. Rzhanitsyn was the first who found the answer to how the structure reliability could be analyzed in a form convenient for the use in engineering practice. Starting from 1940s he developed the theory of reliability for building structures [2]. In the same period the implementation of probabilistic methods in machine building, ship building, and other fields of engineering was started. From then on, owing to a deeper understanding of the reliability principles, there occurred a transition from elementary methods of the probability theory to the methods of random functions. Bolotin [3][4][5] was the first who generalized the theory of reliability of building structures from the standpoint of the theory of random processes and solved many problems of the theory of reliability of building structures.Nowadays, the probabilistic and statistic methods of strength and reliability analysis for building structures find the ever increasing application in structural mechanics and engineering. They have been used as a basis for many of the latest editions of building codes in various countries [6]. The probabilis...

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