Recently, the transport problem is acute to minimize accidents and disasters, caused by the failure of the functional elements. Today it is still not a fully developed theory of the solution of such problems. The authors propose an approach to perform this task, based on the methodology of extreme statistics and information Janes principle. Example given in the article and the calculations prove this possibility, up to an extreme level of statistical sampling, when it reaches capacity. The method allows for a decision on a sample survey, when the nature of the distribution is not known anything other than the expectation of a random variable.