Algorithm for monitoring the power of criteria for testing the exponentivity of neutron flux density in the shelter object
Abstract
Nuclear safety monitoring of the "New Safe Confinement – Shelter Object" system requires constant monitoring of the dynamics of neutron flux density from clusters of nuclear fuel-containing materials at sub-reactor premises at the Shelter object. The paper proposes an algorithm for identifying transitions of neutron flux time series trends from lineal into exponential dependence. The monitoring of the powers of statistical criteria that can be used in determining the moments of transition of dynamic series to the law of exponential distribution has been carried out. The criteria are classified according to the "power - sample size" parameters. A set of criteria, which is most expedient to use when checking the laws of exponential distribution, is offered. The power of statistical criteria is estimated at different sample sizes, without taking into account competing hypotheses. Powers of three groups of exponentiality testing criteria for different data sets have been established. Motivated use of criteria for different sample sizes is recommended. The obtained results are the basis for the construction of algorithms for automated monitoring systems for assessing the state of fuel-containing materials in the complex "New Safe Confinement – Shelter Object". The scientific novelty of the obtained results consists in clarifying the list of exponentiality testing criteria for discretized time series, specifying the limits of their use, determining optimal sets of monitoring criteria for new classes of objects. The practical significance lies in the use of the results as a basis for designing a subsystem for exponentiality testing and monitoring in an automated control system and decision support system on the research object. The direction of further research is the use of the obtained results to construct algorithms for automated monitoring and decision support systems to assess the state of the New Safe Confinement – Shelter Object system
Keywords
"New Safe Confinement – Shelter Object"; nuclear-hazardous clusters; simulation modeling; time series analysis; operational diagnostics; hypothesis testing; statistical tests; decision support
References
[1] I. G. Sharaevskiy, T. S. Vlasenko, L. B. Zimin, A. V. Nosovskiy, N. M. Fialko, and G. I. Sharaevskiy, "Perspective directions of increase of operational reliability and maintenance of operative management by a resource of the main equipment", Yaderna energetyka ta dovkillya, vol. 3, no. 22, pp. 313, 2021 [in Ukrainian].
[2] I. S. Skiter, and M. V. Saveliev, "Simulation of neutron flux density anomalies in the automated nuclear safety control system of the Shelter's object", Мatematychni mashyny i systemy, no. 4, pp.70-77, 2021 [in Ukrainian].
[3] A. I. Kobzar, Applied Mathematical Statistics. For engineers and researchers. FIZMATLIT [in Ukrainian].
[4] B. V. Frozini, On the Distribution and Power of a Goodness-of-fit Statistic with Parametric and Nonparametric Applications, "Goodness-of-fit". North-Holland, 1987.
[5] A. Vahideh, and H. Arezou, "Test based on progressively type-II censored data via extension of cumulative Tsallis divergence", Revista Colombiana de Estadística - Applied Statistics, vol. 44, pp. 97-312, 2021.
[6] M. Mansour, "Non-parametric statistical test for testing exponentiality with applications in medical research", Statistical Methods in Medical Research, vol. 29, no. 2, pp. 413420, 2020.
[7] A. Adhikari, and J. Schaffer, "Modified Lilliefors test", Journal of Modern Applied Statistical Methods, vol. 14, no. 1, pp. 5369, 2015.
[8] E. O. Ossai, M. S. Madukaife, and A. V. Oladugba, "A review of tests for exponentiality with Monte Carlo comparisons", Journal of Applied Statistics, no. 2, pp. 345-420, 2020.
[9] S. S. Shapiro, and M. B. Wilk, "An analysis of variance test for the exponential distribution (complete samples)", Technometrics, vol. 14, no. 1, pp. 355-370, 1972.
[10] T. W. Anderson, and D. A. Darling, "Asymptotic theory of certain "goodness-of-fit" criteria based on stochastic processes", Annals of Mathematical Statistics, vol. 23, pp. 193212, 1952.
[11] T. W. Anderson, "On the distribution of the two-sample Cramer-von Mises criterion", Annals of Mathematical Statistics. Institute of Mathematical Statistics, vol. 33, no. 3, pp. 1148-1159, 1962.
[12] J. D. Spurrier, "An overview of tests for exponentiality", Communications in Statistics - Theory and Methods, vol. 13, pp. 56-69, 1984.
[13] D. A. Darling, "The Kolmogorov-Smirnov, Cramer-von Mises tests", The Annals of Mathematical Statistics, vol. 28, no. 4, pp. 823-838, 1957.
[14] R. Mezbahur, and W. Han, "Tests for exponentiality: A comparative study, American Journal of Applied Mathematics and Statistics, vol. 5, no. 4, pp. 125-135, 2017.
[15] M. S. Barlett, "Properties of sufficiency and statistical tests", Proceedings of the Royal Statistical Society, vol. 160, pp. 268-282, 1937.
[16] H. O. Hartley, "The maximum F-ratio as a short cut test for homogeneity of variance", Biometrika, vol. 37, pp. 308-312, 1950.
[17] M. A. Stephens, EDF-Tests of Fit for the Logistic Distribution: Technical report. Department of Statistics, Stanford University (Prepared under Grant DAAG29-77-G-0031 for the U.S. Army Research Office), no. 36, 1979.
[18] L. A. Klimko, C. E. Antle, A. W. Rademaker, and H. E. Rockette, "Upper bounds for the power of invariant tests for the exponential distribution with Weibull alternatives", Technometrics, vol. 17, no. 3, pp. 357-360, 1975.
[19] J. F. Lawless, Statistical Models and Methods for Lifetime Data (2-nd ed.). Hoboken, N.-J., USA: John Wiley & Sons, Inc., 2003.