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Indirect Measurements

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Part of the book series: Springer Series in Measurement Science and Technology ((SSMST))

Abstract

As introduced in Chap. 1, indirect measurement is a measurement in which the value of the unknown quantity sought is calculated using measurements of other quantities related to the measurand by some known relation. These other quantities are called measurement arguments or, briefly, arguments. Among examples of indirect measurements, we can list measurement of the area of a plot of land presumed to have a rectangular shape (obtained from length measurements of the sides of the plot), measurement of wattage dissipated by a resistor under high-frequency current (obtained, e.g., by measurement of the voltage and current), measurement of temperature using a separately calibrated thermocouple and millivoltmeter and so on.

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Notes

  1. 1.

    As a historical note, when I originally proposed this method long time ago, I missed this subtlety, and we computed the uncertainty of the result based on the number of virtual realizations. This led to an apparent paradox of obtaining confidence interval of the result that was 2–3 times narrower than that of the arguments. This problem forced me to reject this method until recently, when I finally resolved this issue and arrived at the solution described here. This solution first appeared in [56].

References

Standards and Recommendations

  1. International vocabulary of metrology – Basic and general concepts and associated terms (VIM), ISO/IEC Guide 99 (2007)

    Google Scholar 

  2. Guide to the expression of uncertainty in measurement, ISO (1995)

    Google Scholar 

  3. Standard Practice for Use of the International System of units (SI), American Society for Testing and Materials E 380–91 (1991)

    Google Scholar 

  4. Standard Practice for Dealing with Outlying Observations, American Society for Testing and Materials, E 178–02 (Reapproved 2002)

    Google Scholar 

  5. National Measurement Accreditation Service, B 3003, English National Physical Laboratory, Teddington (1986)

    Google Scholar 

  6. Measurement Uncertainty, American National Standard ANSI/ASME РТС 19.1–1985 (1985)

    Google Scholar 

  7. Standard Practice for the Evaluation of Single-Pan Mechanical Balances, American Society for Testing and Materials, E 319–85 (1985)

    Google Scholar 

  8. Publication 51, PT 1–84, Direct Acting Indicating Analogue Electrical Measuring Instruments and Their Accessories, 4th ed., Bureau Central de la Comission Electrotechnique Internationale, Geneva (1984)

    Google Scholar 

  9. Recommandation Internationale 34, Classes de precision des Instruments de Mesurage, Organisation International de Metrologie Legale, Paris (1974)

    Google Scholar 

  10. Process Instrumentation Terminology, American National Standard ANSI/ISA-51.1-1979 (R 1993) (1993)

    Google Scholar 

  11. Direct Measurements with Multiple Observations, Methods of Processing the Results of Observations: Basic principles, State Standard of the Soviet Union, GOST 8.207–76, Moscow (1976)

    Google Scholar 

  12. Metrology. Basic terms and definitions. Recommendation 29–99 [In Russian]. Interstate Council for Standardization, Metrology, and Certification (Izdatel'stvo Standartov, Minsk, 2000)

    Google Scholar 

  13. Propagation of Distributions Using a Monte Carlo Method. ISO/IEC Guide 98–3:2008/Supplement 1 to the “Guide to the expression of uncertainty in measurement”, ISO (2008)

    Google Scholar 

  14. Russian Standard R 8.764–11, State verification scheme for means of measuring electrical resistance (Standardinform, Moskow, 2013)

    Google Scholar 

Books and Articles

  1. V. Ya. Alekseev, F.M. Karavaev, Zn. F. Kudryshova, S.G. Rabinovich, Estimate of the measured quantity from results of measurements with different systematic errors. Metrologia (Supplement to the journal Izmeritel’naya Technika (The journal Izmeritel’naya Technika was published for many years in the United States in English under the title Measurement Techniques.)) 1, 18–24 (1978)

    Google Scholar 

  2. W. Bich, “How to revise the GUM ?”, Accred. Qual. Assur. 13, 271–275 (2008)

    Google Scholar 

  3. H. Bäckström, Uber die dezimalgleichung beim ablesen von scalen. Zeitschrift fur Instrumentenkunde (1930–32)

    Google Scholar 

  4. J. L. Bucher (ed.), Metrology Handbook (ASQ Quality Press, Wilwaukee, 2004)

    Google Scholar 

  5. I.E. Burns, P.J. Campion, A. Williams, Error and uncertainty. Metrologia 9, 101–104 (1975)

    Article  ADS  Google Scholar 

  6. H. Cramer, Mathematical Methods of Statistics (Princeton University Press, Princeton, 1946)

    MATH  Google Scholar 

  7. C. Croarkin, Measurement Assurance Programs, Part II: Development and Implementation, NBS Special Publication 676–11 (U.S. GPO, Washington, DC, 1985)

    Google Scholar 

  8. G. D’Agostini, Bayesian Reasoning in Data Analysis. A Critical Introduction (World Scientific Publishing Co, River Edge, 2003)

    Book  MATH  Google Scholar 

  9. B. Efron, R. J. Tibshirani, An Introduction to the Bootstrap (Chapman & Hall/CRC Press, 1998)

    Google Scholar 

  10. B.D. Ellis, Basic Concepts of Measurement (Cambridge University Press, Cambridge, 1966)

    Google Scholar 

  11. C. Eisenhart, Realistic evaluation of the precision and accuracy of instrument calibration systems. J. Res. Natl. Bur. Stand. 67C, 161–187 (1963)

    Google Scholar 

  12. Fluke, Calibration: Philosophy in Practice, Fluke Corporation, 2nd ed. Everett, P.O. Box 9090, WA 98206, (1994)

    Google Scholar 

  13. I.A. Grachev, S.G. Rabinovich, Approximate method for constructing the distribution function of the composite of several distributions. Ismeritel’naya Technika 1, 8–11 (1968)

    Google Scholar 

  14. V.A. Granovskii, Dynamic Measurements, Principles of Metrological Support [in Russian] (Energoatomizdat, Leningrad, 1984)

    Google Scholar 

  15. V.A. Granovskii, T.N. Siraya, Methods of Processing of the Measurements of Experimental Data [in Russian] (Energoatomizdat, Leningrad division, Leningrad, 1990)

    Google Scholar 

  16. R.V. Hogg, Some observations on robust estimation. J. Am. Stat. Assoc. 62(320), 1179–1186 (1967)

    Article  MathSciNet  Google Scholar 

  17. R. Kaarls, Metrology, essential to trade, industry and society. Accred. Qual. Assur. 12(8), 435–437 (2007)

    Article  Google Scholar 

  18. R. Kacker, A. Jones, On use of Bayesian statistics to make the “Guide to the expression of uncertainty in measurement” consistent. Metrologia 40, 235–248 (2003)

    Article  ADS  Google Scholar 

  19. A.M. Kagan, Yu.V. Linnik, On some problems of mathematical statistics in metrology, in Fifty Years of Metric Reform in the USSR, Proceedings of the Metrological Institute of the USSR [in Russian], D.I. Mendeleev All-Union Scientific-Research Institutes of Metrology, No. 123 (183) (Leningrad, 1970), pp. 39–47

    Google Scholar 

  20. F.M. Karavaev, Measurements of the Activity of Nuclides [in Russian] (Izd. standartov, Moscow, 1972)

    Google Scholar 

  21. Zn.F. Kudryshova, S.G. Rabinovich, Methods of experimental data processing in indirect measurements, in Methods of Experimental Data Processing in Measurements, Proceedings of the Metrological Institutes of the USSR [in Russian], D.I. Mendeleev All-Union Scientific Institute of Metrology, No. 172 (232), (Energia, Leningrad, 1975)

    Google Scholar 

  22. I. Lira, Evaluating the Measurement Uncertainty. Fundaments and Practical Guidance. With an introductory chapter by T.J. Quinn, Director of the BIPM (Institute of Physics Publishing, Bristol, 2002)

    Google Scholar 

  23. M.F. Malikov, Foundations of Metrology [in Russian] (Committee on Measures and Measuring Devices at the Council of Ministers of the USSR, Moscow, 1949)

    Google Scholar 

  24. B.S. Massey, Measures in Science and Engineering, Their Expression, Relation and Interpretation (Wiley, New York, 1986)

    MATH  Google Scholar 

  25. A.I. Mechanikov, Methods for immediate processing of the results of observations with the help of ordering statistics. Metrologia (Supplement to Izmeritel’naya Technika) 4, 47–58 (1972)

    Google Scholar 

  26. P.J. Mohr, B.N. Taylor, D.B. Newell, CODATA recommended values of the fundamental physical constants: 2010. Rev. Mod. Phys. 84, 1527–1605 (2012)

    Google Scholar 

  27. J.G. Nee, Fundaments of tool design, 4th ed. (Society of manufacturing engineers, Dearborn, 1998)

    Google Scholar 

  28. S. Rabinovich, Towards a new edition of the “Guide to the expression of uncertainty in measurement”. Accred. Qual. Assur. 12(11), 603–608 (2007)

    Article  Google Scholar 

  29. S. Rabinovich, Accuracy of single measurements. Accred. Qual. Assur. 12(8), 419–424 (2007)

    Article  Google Scholar 

  30. S. Rabinovich, Measurement Errors and Uncertainties: Theory and Practice, 3rd edn. (Springer, New York, 2005)

    MATH  Google Scholar 

  31. S.G. Rabinovich, An efficient calculation for indirect measurements and a new approach to the theory of indirect measurements, Proceedings of the Measurement Science Conference, Anaheim, California, January 25 and 26, 1996

    Google Scholar 

  32. S.G. Rabinovich, Measurement Errors [in Russian] (Energia, Leningrad, 1978)

    Google Scholar 

  33. S.G. Rabinovich, T.L. Yakovleva, Analysis of the temporal stability of the distributions of the errors of measuring instruments. Metrologia (Supplement to Izmeritel’naya Technika) 7, 8–15 (1977)

    Google Scholar 

  34. S.G. Rabinovich, Method for calculating the measurement errors. Metrologia (Supplement to Izmeritel’naya Technika) 1, 3–12 (1970)

    Google Scholar 

  35. L. Sachs, Applied Statistics: A Handbook of Techniques (Springer, New York, 1984)

    Book  MATH  Google Scholar 

  36. K.P. Shirokov, Basic Concepts of Metrology, Proceedings of the Metrological Institutes of the USSR [in Russian], D.I. Mendeleev All-Union Scientific-Research Institute of Metrology No. 130 (190) (Izd. standartov, M.-L., 1972)

    Google Scholar 

  37. K.P. Shirokov, V.O. Arutyunov, E.M. Aristov, V.A. Granovskii, W.S. Pellinez, S.G. Rabinovich, D.F. Tartakovskii, Basic concepts of the theory of dynamic measurements, Proceedings of the 8th IMEKO Congress (Akademiai Kiado, Budapest, 1980)

    Google Scholar 

  38. V.M. Sviridenko, Logical-gnoseological aspect of the problem of the accuracy of measurements. Izmeritel’naya Technika1 5, 6–8 (1971)

    Google Scholar 

  39. B.L. van der Waerden, Mathematical Statistics (Springer, New York, 1969)

    Book  MATH  Google Scholar 

  40. R. Willink, Measurement Uncertainty and Probability (Cambridge University Press, Cambridge, UK/New York 2013)

    Google Scholar 

  41. T.L. Yakovleva, About statistical homogeneity of the samples of measuring instrument errors. Metrologiya (Supplement to Izmeritel’naya Technika1) 2, 19–23 (1979)

    Google Scholar 

  42. I.P. Zakharov, S.G. Rabinovich, “A comparative analysis of methods of experimental data processing in uncorrelated indirect measurements” [In Russian]. Sistemy Obrobki Informatsii 1(91), 33–37., Kharkiv (2011)

    Google Scholar 

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Rabinovich, S.G. (2017). Indirect Measurements. In: Evaluating Measurement Accuracy. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-60125-0_5

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