Preview

Izmeritel`naya Tekhnika

Advanced search
Open Access Open Access  Restricted Access Subscription Access

On the format of the representation for uncertainties in solving measurement problems

https://doi.org/10.32446/0368-1025it.2022-4-14-22

Abstract

Two formats for the representation of uncertainties in solving measurement problems are considered: the probability distribution and the scattering parameter of the distribution. Inconsistency of definitions of a number of terms GOST R ISO 3534-1-2019 “Statistical methods. Dictionary and symbols. Part 1. General statistical terms and terms used in probability theory” and the lack of definitions of important terms – composition, convolution, probability of agreement, mixture of distributions. It is shown that the convolution of probability distributions gives the most complete representation of the probabilistic properties of the uncertainty of results in metrology.

About the Author

S. F. Levin
Moscow Institute for expertise and tests
Russian Federation

Sergey F. Levin

Moscow



References

1. JCGM 200:2008. International Vocabulary of Metrology – Basic and General Concepts and Associated Terms, VIM, 3rd ed., 2007.

2. International Vocabulary of Metrology – Basic and General Concepts and Associated Terms, VIM, 2nd ed., 1993.

3. Rukovodstvo po vyrazheniyu neopredelyonnosti izmereniya, Ed. prof. V. A. Slaev, S. Petersburg, D. I. Mendeleev VNIIM Publ., 1999, 134 p. (In Russ.)

4. Guide to the Expression of Uncertainty in Measurement (GUM), First ed., ISO, Switzerland, 1993, 101 p.

5. Levin S. F., Chego na samom dele dolzhny opasat’sya vedushchie specialisty po vnedreniyu neopredelennosti v otechest- 22 Измерительная техника № 4, 2022 vennye izmereniya, Izmeritel’naya tekhnika, 2008, no. 12, pp. 61– 64. (In Russ.)

6. Matematicheskaya enciklopediya, in 5 volums, vol. 4, ed. I. M. Vinogradov, Moscow, Sovetskaya enciklopediya Publ., 1984, 1216 co. (In Russ.)

7. Matematicheskaya enciklopediya, in 5 volums, vol. 2, ed. I. M. Vinogradov, Moscow, Sovetskaya enciklopediya Publ., 1979, 1104 co. (In Russ.)

8. Levin S. F., Measurement Techniques, 2019, vol. 62, no. 11, pp. 933–944. https://doi.org/10.1007/s11018-020-01716-0

9. Veroyatnost’ i matematicheskaya statistika: Enciklopediya, ed. Yu. V. Prohorov, Moscow, Bol’shaya Rossijskaya enciklopediya Publ., 1999, 910 p. (In Russ.)

10. Matematicheskaya enciklopediya, in 5 volums, vol. 5, ed. I. M. Vinogradov, Moscow, Sovetskaya enciklopediya Publ., 1984, 1248 co. (In Russ.)

11. Wilks S. S., Statistical prediction with special reference to the problem of tolerance limits, Annals of Mathematical Statistics, 1942, vol. 13, pp. 400–409.

12. Robbins H., On distribution-free tolerance limits in random sampling, Annals of Mathematical Statistics, 1944, vol. 15, pp. 214–216.

13. Scheff é H., Tukey J. W., Nonparametric estimation. I. Validation of order statistics, Annals of Mathematical Statistics, 1945, vol. 16, pp. 187–192.

14. Levin S. F., Measurement Techniques, 2018, vol. 61, no. 2, pp. 91–97. https://doi.org/10.1007/s11018-018-1393-6

15. Levin S. F., Measurement Techniques, 2018, vol. 61, no. 4, pp. 327–334. https://doi.org/10.1007/s11018-018-1429-y

16. Levin S. F., Rukovodstvo po vyrazheniyu neopredelennosti izmereniya: problemy, nerealizovannye vozmozhnosti i reviziya. Chast’ 3. Privedenie k obshchemu terminologicheskomu znamenatelyu, Izmeritel’naya tekhnika, 2019, no. 7, pp. 14–22. (In Russ.) https://doi.org/10.32446/0368-1025it.2019-7-14-22

17. Jacobi C. G. J., De Determinantibus functionalibus, Journal für reine und angewandte Mathematik, 1841, Bd. 22, s. 319– 359. (In Lat.)

18. Fizicheskaya enciklopediya, in 5 volums, vol. 3, ed. A. M. Prohorov, Moscow, Bol’shaya Rossijskaya enciklopediya Publ., 1992, 672 р. (In Russ.)

19. Markov A. A. Izbrannye trudy po teorii nepreryvnyh drobej i teorii funkcij nai-menee uklonyayushchihsya ot nulya, Moscow– Leningrad, Gostekhizdat Publ., 1948, pp. 292–375. (In Russ.)

20. Levin S. F., Measurement Techniques, 2005, vol. 48, no. 2, рp. 101–111. https://doi.org/10.1007/s11018-005-0106-0

21. Levin S. F., Measurement Techniques, 2005, vol. 48, no. 8, рp. 754–759. https://doi.org/10.1007/s11018-005-0216-8

22. Lukacs E., Characteristics functions, 2nd ed., revised & enlarged, London, Griffi n, 1970, 350 p.

23. Levin S. F., Measurement Techniques, 2021, vol. 64, no. 4, рp. 273–281. https://doi.org/10.1007/s11018-021-01929-x

24. Levin S. F., Metrologiya. Matematicheskaya statistika. Legendy i mify 20-go veka: Legenda o neopredelennosti, Partnery i konkurenty, 2001, no. 1, pp. 13–25. (In Russ.)

25. Levin S. F., Measurement Techniques, 2020, vol. 63, no. 7, рр. 1–10. https://doi.org/10.1007/s11018-020-01819-8


Review

For citations:


Levin S.F. On the format of the representation for uncertainties in solving measurement problems. Izmeritel`naya Tekhnika. 2022;(4):14-22. (In Russ.) https://doi.org/10.32446/0368-1025it.2022-4-14-22

Views: 127


ISSN 0368-1025 (Print)
ISSN 2949-5237 (Online)