# Fundamentals of Reliability Theory

## Abstract

The previous chapters were devoted to the theoretical fundamentals of statistical mechanics and the theory of random vibrations. The readers attention was focused on mathematical methods of solving problems of the dynamics of mechanical systems loaded with random forces and the determination of the probability characteristics of the vector of the system state, or, what is the same, to the determination of the probability characteristics of the “output” given that the probability characteristics of the “input” are known. Mechanical systems with a finite number of degrees of freedom and systems with distributed parameters (structures or elements of structures reduced to a mathematical model of a rod) were considered. Methods making it possible to determine the probability characteristics of the stress-strain state of the structural members at non-stationary and stationary random forces were presented. It has been shown that methods of statistical dynamics allow the solution of many applied problems when the random components of loads cannot be ignored. However, questions of the “strength” of a structure at random loads were, in fact, not considered.

## Keywords

Safety Factor Equivalent Stress Random Quantity Probability Characteristic Reliability Theory## Preview

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