The article is devoted to the development of the main sections of the failures equipment prediction method by the example of the JSC «Transneft» conformity assessment system. The main position of the conducted researches is the admission, that the main argument of the developed forecasting method is the equipment initial operating time, characteristic for a zone of stable breakdown rate. Using this argument allows modeling the change of research objective function, changing its trajectory and as a result determining the number of equipment failures with the least response time of mathematical operations and the greatest accuracy of calculation. In this paper, the development of a mathematical model for determining the prelusory equipment running time is highlighted by a statistical approach based on the use of the Weibull distribution. The Weibull distribution is considered as the base one and is investigated at the extremum points, taking into account the condition for the maximum dynamics of the change in their limited state. The results of the work make it possible to establish a regularity that determines the prelusory equipment running time as a part of the Weibull distribution that has the minimum value of the derivative of the function, which appoints the allocation of equipment failure rates for the case under consideration. The results of research is the analytical dependence, which allow to determine the basic argument of the equipment failures prediction method, based on the following reliability indicators: the sum of the maximum and minimum number of intact equipment, average value of failure rate of equipment and total number of equipment failures.
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