Probability Model of Strength Estimation of Articles by Results of Testing of Their Fragments

The probability model to calculate and predict the basic strength characteristics such as probability to withstand a specific load, mathematical expectation of strength, etc. is offered. The approximated asymptotic expressions for a case of high strength, when a probability of failure (rupture) is fairly small, as well as the general conditions, under which the relative variance (variation coefficient) of strength ξ_L increases (decreases) as the specimen length L increases, are obtained. A theorem is proven in which a general multi-parameter model of the stochastic distribution of strength is given at which an increase of the above relative variance takes place. Within the framework of this model, the problem is reduced to the point and confidence estimation of strength factors as functions of a vector of unknown parameters by results of stochastic tests. Inequalities are obtained which give estimations of a trend of the strength expectancy Mξ_Las the specimen length L increases. Analogous results are obtained for an expectancy of life of the successive system of n elements when the system "length" (number of elements) increases, which, in particular, allows the improvement of the known inequalities by Barlow and Proshan for such systems. The lower confidence bound is constructed for the reliability (probability to withstand a specific load) of the specimen with a length L.