Применение теории статистических гипотез в задачах автоматизации технологических процессов

Abstract

The paper substantiates the application of methods of the theory of statistical hypotheses for the tasks of automation of technological processes. The functioning of the process automation system is considered as the management of a complex technical system. The operation of the automation system belongs to the multi-alternative in terms of the theory of statistical hypotheses: two hypotheses of the correct mode and two hypotheses of the erroneous operation of the system. The article provides general expressions for calculating the probabilities of these modes for two statistical models of the controlled parameter of the technological process and standard models of the metrological spread of the measuring channel. In this case, the accuracy class of the measuring channel should be expressed as a reduced error. The simulation of the operating modes of the process automation system is carried out within the framework of the theory of statistical hypotheses. The results of modeling for the normal probability density of the statistical model of the controlled quantity, uniform and triangular statistical models of estimation of the controlled parameter are presented. A program of statistical evaluation of the modes of operation of the automation system has been developed for symmetric and asymmetric statistical models of the spread of the controlled parameter and several models of metrological spread of the evaluation of the technological parameter. The calculation of the a priori probability of the normal functioning of the automation system of the technological process and the calculation of the a priori probability of erroneous operation of the automation system is given. Expressions for calculating a posteriori probability of the results of verification of measuring instruments of automation systems are obtained.