On the homogeneity grouping of same-type NPP equipment when aggregating statistical data using the Poisson model.

Aim. The paper uses the Poisson model to analyse failure flows of NPP systems’ elements and thus describes an approach to defining homogeneity groups, i.e., the broadest possible groups of same-type elements whose failure rates may be considered constant. Defining such groups allows aggregating operational data on equipment failures and times-to failure, which improves the quality of statistical estimates of failure rates as part of assessing the dependability of systems made up of highly dependable elements. Methods. For thepurpose of grouping, it is proposed to use the following methods: structural (based on the positional symmetry of the same-type elements in redundant system channels, which allows combining the elements within a system) and statistical (using the results of the statistical test of the homogeneity hypothesis of any combined groups of same-type elements). The structural method was substantiated. The author proposes a statistical test based on the correlation of the estimated variations in the failure rates with and without regard to the assumption of the homogeneity of the aggregated data. The properties of the test were examined; the correlations for the first two moments of its statistics were obtained. It was shown that a discrete distribution of statistics with a large number of groups to be combined can be described by a gamma distribution. A rule for identifying the main hypothesis acceptance and rejection regions was proposed. Results. The paper presents an example of the application of statistical analysis of aggregated data on 10 groups of motor-operated valves of various NPP systems. Based on the obtained assessment of the test statistics, it is concluded that a group with a sharply deviating partial assessment of the failure rate is to be excluded from the general population. For the remaining groups, the homogeneity test was repeated. A result was obtained that allows combining the data of the 9 groups. The paper also discusses potential ways of solving the problem of assessing the dependability parameters of new NPP equipment, when operational information is not sufficient for obtaining representative estimates of dependability indicators. For such purposes, it is proposed using the empirical Bayes method, whereas the a priori distribution is obtained by aggregating data on similar items taking into account their possible heterogeneity. It is shown that the method that is focused on the construction of a priori distributions based on a likelihood function maximum can also be used for solving the homogeneity verification problems examined in this paper. Based on the proposed methods, a general approach has been developed for assessing the dependability of highly dependable NPP systems using information obtained in the course of operation of both the object of analysis (a specific NPP) and similar facilities (reference NPPs, NPPs with the same type of nuclear reactor). The method is also effective as regards probabilistic safety analysis of NPPs at the stage of their design and initial operation.

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