Minimization of Risk of the Erroneous Decision in the Assessment of the Importance of Statistical Relations of Technical and Economic Indicators of the Objects of Electric Power Systems

Abstract

Improving the reliability of decisions taken in the organization of maintenance and repair of electric power systems is one of the most important and difficult problems. It is important because erroneous solutions lead, first of all, to an increase in operating costs. The difficulty in solving this problem is associated with the lack of appropriate methods to reduce the risk of erroneous decisions. The article presents one of the aspects of this problem, i.e. improving the reliability of the decision on the nature of the relationship of technical and economic indicators of electric power systems. Traditionally, increase of reliability of the decision is reached by reduction of a Type I error. Usually it is accepted to be equal to 5%, occasionally – to 1%, and at researches – even to 0.5 %. The corresponding critical values of correlation coefficients are given in mathematics reference books. This method implicitly assumes that the consequences of a Type I error significantly exceed the consequences of Type II errors, and the distribution of correlation coefficients corresponds to the normal law. Therefore, the risk of an erroneous decision concerning the absence of a significant statistical relation is not controlled. But even if there is a wish to estimate the Type II error, it is almost impossible to fulfill it, because there are no critical values for correlation coefficients of dependent samples. No less relevant is the problem of deciding on the statistical relationship between technical and economic indicators in conditions of equality of consequences of erroneous decisions, i.e. it is necessary to take into account both a Type I error and a Type II error. To overcome the mentioned difficulties a new method for estimating the critical values of correlation coefficients has been developed. The novelty consists in the application of fiducial approach; the calculation of critical values are fulfilled with the aid of computer technologies of simulation of possible realizations of the correlation coefficients for the two assumptions, viz. technical and economic indicators of the independent and dependent; simulation is fulfilled with the method of solving the “inverse problem”, which enables the possible implementation of the correlation coefficients for the really dependent and independent samples of random variables at a given sample size; the developed algorithms and programs for calculation made it possible to obtain the critical values of correlation coefficients for independent and dependent samples; in conditions of the sameness of the consequences of erroneous decisions it is proposed to make a decision not based on critical value but based on the boundary values of the correlation coefficients that correspond to the minimum total risk of erroneous decisions; the exemplification of the recommendations application was made on example of technical and economic parameters of boilers of power units of 300 MWt. The significant impact of the availability of interrelated technical and economic indicators on the result of the ranking of boiler plants by the reliability and efficiency of their work is demonstrated.