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The Quantifying of Uncertainty in Measurement

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Handbook of Metrology and Applications

Abstract

Despite the importance of measurement uncertainty, it is widely misunderstood, and it represents a vague subject for both industrial and scientific practitioners. In this chapter, it is aimed to introduce the subject of measurement uncertainty step-by-step starting from the basic principles to the actual uncertainty evaluation techniques. The text does not only present the theoretical aspects of uncertainty, but it also deals with its practical implementation. The chapter begins by introducing the concept of uncertainty and its importance, and then it discusses Type A and Type B uncertainty evaluation methods. After that, the GUM uncertainty framework is presented as well as the Monte Carlo simulation technique and its programming details. Throughout the chapter, several examples are demonstrated to put the discussed concepts into action. The chapter is very useful for anyone whether an industrial practitioner, scientist, or student.

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References

  • A. A. Hawam, A. M. El-Kassas, G. M. Mahmoud, E. H. Hasan, and M. Ahmadein, "The resolution of analogue measuring devices and its associated uncertainty: an investigation with practical recommendations," Precis Eng, vol. 71, pp. 57–62, 2021/09/01/ 2021, https://doi.org/10.1016/j.precisioneng.2021.02.012

  • ASME B89.7.3.1 (2001) Guidelines for decision rules: considering measurement uncertainty in determining conformance to specifications. The American Society of Mechanical Engineers, New York, p 2001

    Google Scholar 

  • ASME B89.7.3.2 (2007) Guidelines for the evaluation of dimensional measurement uncertainty (technical report). The American Society of Mechanical Engineers, New York, p 2007

    Google Scholar 

  • ASME B89.7.3.3 (2002) Guidelines for assessing the reliability of dimensional measurement uncertainty statements. The American Society of Mechanical Engineers, New York, p 2002

    Google Scholar 

  • ASME B89.7.4.1 (2005) Measurement uncertainty and conformance testing: risk analysis (an ASME technical report), the American Society of Mechanical Engineers, New York

    Google Scholar 

  • Bell S (2001) A Beginner's guide to uncertainty of measurement. National Physical Laboratory, United Kingdom

    Google Scholar 

  • Bich W, Cox MG, Harris PM (2006) Evolution of the ‘guide to the expression of uncertainty in measurement’. Metrologia 43(4):S161–S166. https://doi.org/10.1088/0026-1394/43/4/s01

    Article  ADS  Google Scholar 

  • Boumans M (2013) Model-based type B uncertainty evaluations of measurement towards more objective evaluation strategies. Measurement 46(9):3775–3777. https://doi.org/10.1016/j.measurement.2013.04.003

    Article  ADS  Google Scholar 

  • Cipra BA (2000) The best of the 20th century: editors name top 10 algorithms. SIAM news 33(4):1–2

    Google Scholar 

  • Coleman HW, Steele WG (2009) Experimentation, validation, and uncertainty analysis for engineers, 3rd edn. John Wiley & Sons

    Book  Google Scholar 

  • Evaluation of measurement data — Guide to the Expression of Uncertainty in Measurement JCGM 100:2008, BIPM et al., 2008a

    Google Scholar 

  • Evaluation of measurement data — Supplement 1 to the “Guide to the expression of uncertainty in measurement” — Propagation of distributions using a Monte Carlo method, JCGM 101:2008, BIPM et al., 2008b

    Google Scholar 

  • Evaluation of measurement data — An introduction to the “Guide to the expression of uncertainty in measurement” and related documents, JCGM 104:2009, BIPM et al., 2009

    Google Scholar 

  • EA-4/02 (2013) Evaluation of the uncertainty of measurement in calibration, EA

    Google Scholar 

  • EUROLAB (2006) Guide to the evaluation of measurement uncertainty for quantitative test results, France

    Google Scholar 

  • Fishman GS (1996) Monte Carlo: concepts, algorithms, and applications (springer series in operations research). Springer Science & Business Media New York

    Book  Google Scholar 

  • Guide to the expression of uncertainty in measurement — Part 6: Developing and using measurement models, JCGM GUM-6:2020, BIPM et al., 2020

    Google Scholar 

  • Gobet E (2016) Monte-Carlo methods and stochastic processes: from linear to non-linear. CRC Press

    Book  MATH  Google Scholar 

  • Hawam AA, Hasan EH, Mohamed G, Ahmadein M (2018) The resolution uncertainty associated with digital indications revisited: the inclusion of the quantization effect and the impact of noise presence in the estimation process. Metrologia 55(6):883–892. https://doi.org/10.1088/1681-7575/aaebb6

    Article  ADS  Google Scholar 

  • Ignacio HL, Wolfgang W (1997) The evaluation of standard uncertainty in the presence of limited resolution of indicating devices. Measure Sci Technol 8(4):441. [Online]. Available: http://stacks.iop.org/0957-0233/8/i=4/a=012

    Article  Google Scholar 

  • ILAC (2013) Policy for uncertainty in calibration ILAC-P14:01/2013. ILAC, Australia

    Google Scholar 

  • International vocabulary of metrology – Basic and general concepts and associated terms (VIM), JCGM 200:2012, BIPM et al., 2012

    Google Scholar 

  • ISO (2017) 14253–1:2017, geometrical product specifications (GPS) — inspection by measurement of workpieces and measuring equipment — part 1: decision rules for verifying conformity or nonconformity with specifications. The International Organization for Standardization

    Google Scholar 

  • Kacker R, Sommer K-D, Kessel R (2007) Evolution of modern approaches to express uncertainty in measurement. Metrologia 44(6):513–529. https://doi.org/10.1088/0026-1394/44/6/011

    Article  ADS  Google Scholar 

  • Kadis RL (2000) Correct evaluation of type-B standard uncertainty. Meas Tech 43(5):403–404. https://doi.org/10.1007/BF02503653

    Article  Google Scholar 

  • M3003 (2012) The expression of uncertainty and confidence in measurement M3003, UKAS. United Kingdom

    Google Scholar 

  • Martins MAF, Requião R, Kalid RA (2011) Generalized expressions of second and third order for the evaluation of standard measurement uncertainty. Measurement 44(9):1526–1530. https://doi.org/10.1016/j.measurement.2011.06.008

    Article  ADS  Google Scholar 

  • Raghu NK, James FL (2007) Trapezoidal and triangular distributions for Type B evaluation of standard uncertainty. Metrologia 44(2):117. [Online]. Available: http://stacks.iop.org/0026-1394/44/i=2/a=003

    Article  Google Scholar 

  • Ribeiro ÁS, Gölze M, Members EUROLABTCQA (2017) EUROLAB technical report no.1/2017 - decision rules applied to conformity assessment. EUROLAB BELGIUM

    Google Scholar 

  • Shonkwiler RW, Mendivil F (2009) Explorations in Monte Carlo methods. Springer, New York

    Book  MATH  Google Scholar 

  • Sommer KD, Siebert BRL (2006) Systematic approach to the modelling of measurements for uncertainty evaluation. Metrologia 43(4):S200–S210. https://doi.org/10.1088/0026-1394/43/4/s06

    Article  ADS  Google Scholar 

  • Sommer KD, Kochsiek M, Siebert B, Weckenmann A (2003) “A generalized procedure for modelling of measurements for evaluating the measurement uncertainty ” in XVII IMEKO world congress, Dubrovnik, Croatia, pp 1248–1253. ISBN: 953–7124-00-2

    Google Scholar 

  • Sommer KD, Weckenmann A, Siebert BRL (2005) A systematic approach to the modelling of measurements for uncertainty evaluation. J Phys Conf Ser 13:224–227. https://doi.org/10.1088/1742-6596/13/1/052

    Article  ADS  Google Scholar 

  • Thomopoulos NT (2013) Essentials of Monte Carlo simulation: statistical methods for building simulation models. Springer, New York

    Book  Google Scholar 

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Correspondence to Ahmed A. Hawam .

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Hawam, A.A. (2023). The Quantifying of Uncertainty in Measurement. In: Aswal, D.K., Yadav, S., Takatsuji, T., Rachakonda, P., Kumar, H. (eds) Handbook of Metrology and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-99-2074-7_126

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