Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Measurement Uncertainty and Probability
  • Cited by 44
Publisher:
Cambridge University Press
Online publication date:
March 2013
Print publication year:
2013
Online ISBN:
9781139135085
DOI:
https://doi.org/10.1017/CBO9781139135085
Subjects:
Physics and Astronomy, Engineering, General and Classical Physics, Engineering: General Interest
Information

Book description

A measurement result is incomplete without a statement of its 'uncertainty' or 'margin of error'. But what does this statement actually tell us? By examining the practical meaning of probability, this book discusses what is meant by a '95 percent interval of measurement uncertainty', and how such an interval can be calculated. The book argues that the concept of an unknown 'target value' is essential if probability is to be used as a tool for evaluating measurement uncertainty. It uses statistical concepts, such as a conditional confidence interval, to present 'extended' classical methods for evaluating measurement uncertainty. The use of the Monte Carlo principle for the simulation of experiments is described. Useful for researchers and graduate students, the book also discusses other philosophies relating to the evaluation of measurement uncertainty. It employs clear notation and language to avoid the confusion that exists in this controversial field of science.

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Page 1 of 2

Contents

Page 1 of 2

References

References

Acton, F. S. 1959. Analysis of Straight-Line Data. Wiley.
Alfassi, Z. B., Boger, Z., and Ronen, Y. 2005. Statistical Treatment of Analytical Data. Blackwell.
Barnett, V. 1973. Comparative Statistical Inference. Wiley.
Bayarri, M. J., and Berger, J. O. 2004. The interplay of Bayesian and frequentist analysis. Statistical Science, 19, 58–80.
Beers, Y. 1957. Introduction to the Theory of Error, 2nd edn. Addison Wesley.
Bernardo, J. M. 2005a. An integrated mathematical statistics primer: Objective Bayesian construction, frequentist evaluation. In: Proceedings of the 55th International Statistical Institute Session, Sydney, 2005. ISI.
Bernardo, J. M. 2005b. Reference analysis. Pages 17–90 of: Dey, D. K., and Rao, C. R. (eds.), Handbook of Statistics, vol. 25: Bayesian Thinking: Modeling and Computation. Elsevier.
Bevington, P. R. 1969. Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill.
Bhattacharjee, G. P., Pandit, S. N. N., and Mohan, R. 1963. Dimensional chains involving rectangular and normal error-distributions. Technometrics, 5, 404–406.
Bich, W. 2008. How to revise the GUM. Accreditation and Quality Assurance, 13, 271– 275.
BIPM, IEC, IFCCet al. 1995. Guide to the Expression of Uncertainty in Measurement.
Box, G. E. P., and Draper, N. R. 1987. Empirical Model-building and Response Surfaces. Wiley.
Chatfield, C., and Collins, A. J. 1980. Introduction to Multivariate Analysis. Chapman and Hall.
Colclough, A. R. 1987. Two theories of experimental error. Journal of Research of the National Bureau of Standards, 92, 167–185.
Coleman, H. W., and Steele, Jr.,W. G.. 1999. Experimentation and Uncertainty Analysis for Engineers, 2nd edn. Wiley.
Croarkin, C. 1989. An extended error model for comparison calibration. Metrologia, 26, 107–113.
David, H. A. 1970. Order Statistics. Wiley.
Dieck, R. H. 2007. Measurement Uncertainty: Methods and Applications, 4th edn. The Instrumentation, Systems and Automation Society.
Dietrich, C. F. 1973. Uncertainty, Calibration and Probability. Adam Hilger.
Dunn, O. J. 1968. A note on confidence bands for a regression line over a finite range. Journal of the American Statistical Association, 63, 1028–1033.
Dunn, P. F. 2005. Measurement and Data Analysis for Engineering and Science. McGraw- Hill.
Edwards, A. W. F. 1976. Fiducial probability. The Statistician, 25, 15–35.
Edwards, A. W. F. 1983. Fiducial distributions. Pages 70–76 of: Kotz, S., Johnson, N. L., and Read, C. B. (eds.), Encyclopedia of Statistical Sciences, vol. 3. Wiley.
Eisenhart, C. 1963. Realistic evaluation of the precision and accuracy of instrument calibration systems. Journal of Research of the National Bureau of Standards –C. Engineering and Instrumentation, 67C, 161–187.
Elster, C. 2000. Evaluation of measurement uncertainty in the presence of combined random and analogue-to-digital conversion errors. Measurement Science and Technology, 11, 1359–1363.
Elster, C., and Toman, B. 2010. Analysis of key comparisons: estimating laboratories’ biases by a fixed effects model using Bayesian model averaging. Metrologia, 47, 113–119.
Elster, C., Chunovkina, A. G., and Wöger, W. 2010. Linking of a RMO key comparison to a related CIPM key comparison using the degrees of equivalence of the linking laboratories. Metrologia, 47, 96–102.
Feldman, G. J., and Cousins, R. D. 1998. Unified approach to the classical statistical analysis of small signals. Physical Review D, 57, 3873–3889.
Feller, W. 1968. An Introduction to Probability Theory and Its Applications, 3rd edn, vol. 1. Wiley.
Fisher, R. A. 1930. Inverse probability. Proceedings of the Cambridge Philosophical Society, 26, 528–535.
Fishman, G. S. 1996. Monte Carlo: Concepts, Algorithms, and Applications. Springer.
Fisz, M. 1963. Probability Theory and Mathematical Statistics, 3rd edn. Wiley.
Fotowicz, P. 2006. An analytical method for calculating a coverage interval. Metrologia, 43, 42–45.
Fraser, D. A. S., Reid, N., and Wong, A. C. M. 2004. Inference for bounded parameters. Physical Review D, 69, 033002.
Frenkel, R. B. 2009. Fiducial inference applied to uncertainty estimation when identical readings are obtained under low instrument resolution. Metrologia, 46, 661–667.
Fuller, W. A. 1987. Measurement Error Models. Wiley.
Geisser, S., and Cornfield, J. 1963. Posterior distributions for multivariate normal parameters. Journal of the Royal Statistical Society, Series B, 25, 368–376.
Gleser, L. J. 2002. Comment. Statistical Science, 17, 161–163.
Grabe, M. 2005. Measurement Uncertainties in Science and Technology. Springer.
Graybill, F. A., and Bowden, D. C. 1967. Linear segment confidence bands for simple linear models. Journal of the American Statistical Association, 62, 403–408.
Guthrie, W. F., Liu, H., Rukhin, A. L., Toman, B., Wang, J. C. M., and Zhang, N. 2009. Three statistical paradigms for the assessment and interpretation of measurement uncertainty. Pages 71–115 of: Pavese, F., and Forbes, A. B. (eds.), Data Modeling for Metrology and Testing in Measurement Science. Birkhäuser.
Hall, B. D. 2006. Computing uncertainty with uncertain numbers. Metrologia, 43, L56–L61.
Hall, B. D. 2008. Evaluating methods of calculating measurement uncertainty. Metrologia, 45, L5–L8.
Hannig, J., Iyer, H. K., and Wang, C. M. 2007. Fiducial approach to uncertainty assessment accounting for error due to instrument resolution. Metrologia, 44, 476–483.
Hodges, Jr., J. L., and Lehmann, E. L. 1964. Basic Concepts of Probability and Statistics. Holden-Day.
Hoeffding, W. 1982. Asymptotic normality. Pages 139–147 of: Kotz, S., Johnson, N. L., and Read, C. B. (eds), Encyclopedia of Statistical Sciences, vol. 1. Wiley.
Howe, W. G. 1969. Two-sided tolerance limits for normal populations – some improvements. Journal of the American Statistical Association, 64, 610–620.
Hughes, I. G., and Hase, T. P. A. 2010. Measurements and their Uncertainties: A Practical Guide to Modern Error Analysis. Oxford University Press.
IPCC. 2000. IPCC Good Practice Guidance and Uncertainty Management in National Greenhouse Gas Inventories. Annex 1: Conceptual Basis for Uncertainty Analysis, http://www.ipcc-nggip.iges.or.jp/public/gp/english/A1_Conceptual.pdf (accessed 27 January 2012).
ISO. 1998. SS-EN ISO 14253–1 Geometrical Product Specifications (GPS) – Inspection by Measurement of Workpieces and Measuring Equipment - Part 1: Decision Rules for Proving Conformance or Non-conformance with Specifications.
ISO. 2004. ISO/IEC 17000: 2004 Conformity Assessment – Vocabulary and General Principles.
Jaynes, E. T. 1957. Information theory and statistical mechanics. Physical Review, 106, 620–630.
Jaynes, E. T. 1968. Prior probabilities. IEEE Transactions on Systems Science and Cybernetics, SSC-4, 227–241.
Jaynes, E. T. 1982. On the rationale of maximum-entropy methods. Proceedings of the IEEE, 70, 939–952.
JCGM. 2008a. JCGM 100:2008 Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement, http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf.
JCGM. 2008b. JCGM 101:2008 Evaluation of Measurement Data – Supplement 1 to the “Guide to the Expression of Uncertainty in Measurement” – Propagation of Distributions Using a Monte Carlo Method, http://www.bipm.org/utils/common/documents/jcgm/JCGM_101_2008_E.pdf.
JCGM. 2011. JCGM 102:2011 Evaluation of Measurement Data – Supplement 2 to the “Guide to the Expression of Uncertainty in Measurement” – Extension to Any Number of Output Quantities, http://www.bipm.org/utils/common/documents/jcgm/JCGM_102_2011_E.pdf.
JCGM. 2012. Motivation and Scope for the Revision of the GUM. (Letter sent to National Metrology Institutes, January 2012).
Johnson, N. L., Kotz, S., and Kemp, A. W. 1993. Univariate Discrete Distributions, 2nd edn. Wiley.
Johnson, N. L., Kotz, S., and Balakrishnan, N. 1994. Continuous Univariate Distributions vol. 1, 2nd edn. Wiley.
Johnson, N. L., Kotz, S., and Balakrishnan, N. 1995. Continuous Univariate Distributions, vol. 2, 2nd edn. Wiley.
Johnson, R. A., and Wichern, D. W. 1998. Applied Multivariate Statistical Analysis. Prentice Hall.
Kaarls, R. 1980. Report of the BIPM Working Group on the Statement of Uncertainties (1st meeting 21 to 23 October 1980) to the Comité International des Poids et Mesures.
Kacker, R., Sommer, K.-D., and Kessel, R. 2007. Evolution of modern approaches to express uncertainty in measurement. Metrologia, 44, 513–529.
Kåhre, J. 2002. The Mathematical Theory of Information. Kluwer.
Kiefer, J. 1982. Conditional inference. Pages 103–109 of: Kotz, S., Johnson, N. L., and Read, C. B. (eds.), Encyclopedia of Statistical Sciences, vol. 2. Wiley.
Kirkup, L., and Frenkel, R. B. 2006. An Introduction to Uncertainty in Measurement. Cambridge University Press.
Larson, H. J. 1982. Introduction to Probability Theory and Statistical Inference, 3rd edn. Wiley.
Ledermann, W., and Lloyd, E. (eds). 1984. Handbook of Applicable Mathematics, vol. 6, Part B, Statistics. Wiley.
Lindgren, B. W. 1968. Statistical Theory. Macmillan. Lira, I. 2002. Evaluating the Measurement Uncertainty: Fundamentals and Practical Guidance. Institute of Physics.
Magee, B. 1973. Popper. Fontana/Collins.
Mandel, J. 1964. The Statistical Analysis of Experimental Data. Dover.
Mandelkern, M. 2002. Setting confidence intervals for bounded parameters. Statistical Science, 17, 149–159.
Marriott, F. H. C. 1990. A Dictionary of Statistical Terms, 5th edn. Longman.
Miller, Jr., R. G. 1980. Simultaneous Statistical Inference, 2nd edn. Springer-Verlag.
Miller, Jr., R. G. 1986. Beyond ANOVA, Basics of Applied Statistics. Wiley.
Murphy, R. B. 1961. On the meaning of precision and accuracy. Materials Research and Standards, 4, 264–267.
Neyman, J. 1937. Outline of a theory of statistical estimation based on the classical theory of probability. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 236, 333–380.
NIST. 2012. NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2 March 2012.
O’Hagan, A. 1994. Kendall’s Advanced Theory of Statistics, vol. 2B, Bayesian Inference. Edward Arnold.
Pedersen, J. G. 1978. Fiducial inference. International Statistical Review, 46, 147–170.
Popper, K. R. 1968. The Logic of Scientific Discovery, 2nd edn. Hutchinson & Co.
Rabinovich, S. 1995. Measurement Errors: Theory and Practice. American Institute of Physics.
Rabinovich, S. 2007. Towards a new edition of the “Guide to the expression of uncertainty in measurement”. Accreditation and Quality Assurance, 12, 603–608.
Shannon, C. E. 1948. A mathematical theory of communication. Bell System Technical Journal, 27, 379–423, 623–656.
Shirono, K., Tanaka, H., and Ehara, K. 2010. Bayesian statistics for determination of the reference value and degree of equivalence of inconsistent comparison data. Metrologia, 47, 444–452.
Sivia, D. S. 1996. Data Analysis: A Bayesian Tutorial. Clarendon Press.
Stevens, S. S. 1946. On the theory of scales of measurement. Science, 103, 677–680.
Stuart, A., and Ord, J. K. 1987. Kendall’s Advanced Theory of Statistics, 5th edn, vol. 1. Griffin.
van Dyk, D. A. 2002. Comment. Statistical Science, 17, 164–168.
VIM. 2012. JCGM 200:2012 International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM), http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf.
Wang, C. M., and Iyer, H. K. 2005. Propagation of uncertainties in measurements using generalized inference. Metrologia, 42, 145–153.
Wang, C. M., and Iyer, H. K. 2006. Uncertainty analysis for vector measurands using fiducial inference. Metrologia, 43, 486–494.
Wang, C. M., and Iyer, H. K. 2008. Fiducial approach for assessing agreement between two instruments. Metrologia, 45, 415–421.
Wang, C. M., and Iyer, H. K. 2009. Fiducial intervals for the magnitude of a complexvalued quantity. Metrologia, 46, 81–86.
Wang, C. M., and Iyer, H. K. 2010. On interchangeability of two laboratories. Metrologia, 47, 435–443.
Wasserman, L. 2002. Comment. Statistical Science, 17, 163–163.
Wilks, S. S. 1962. Mathematical Statistics. Wiley.
Willink, R. 2005. A procedure for the evaluation of measurement uncertainty based on moments. Metrologia, 42, 329–343.
Willink, R. 2006a. An approach to uncertainty analysis emphasizing a natural expectation of a client. Pages 344–349 of: Ciarlini, P.et al. (eds.), Advanced Mathematical and Computational Tools in Metrology VII. World Scientific.
Willink, R. 2006b. Uncertainty analysis by moments for asymmetric variables. Metrologia, 43, 522–530.
Willink, R. 2007a. A generalization of the Welch–Satterthwaite formula for use with correlated uncertainty components. Metrologia, 44, 340–349.
Willink, R. 2007b. On the uncertainty of the mean of digitized measurements. Metrologia, 44, 73–81.
Willink, R. 2007c. Uncertainty of functionals of calibration curves. Metrologia, 44, 182–186.
Willink, R. 2008. Estimation and uncertainty in fitting straight lines to data: different techniques. Metrologia, 45, 290–298.
Willink, R. 2009. A formulation of the law of propagation of uncertainty to facilitate the treatment of shared influences. Metrologia, 46, 145–153.
Willink, R. 2010a. Difficulties arising from the representation of the measurand by a probability distribution. Measurement Science and Technology, 21, 015110.
Willink, R. 2010b. Measurement of small quantities: further observations on Bayesian methodology. Accreditation and Quality Assurance, 15, 521–527.
Willink, R. 2010c. Probability, belief and success rate: comments on ‘On the meaning of coverage probabilities’. Metrologia, 47, 343–346.
Willink, R. 2012a. Measurement uncertainty and procedures of conformity assessment. Pages 426–433 of: Pavese, F.et al. (eds.), Advanced Mathematical and Computational Tools in Metrology and Testing, vol. 9. World Scientific.
Willink, R. 2012b. Interlaboratory comparisons and the estimation of biases. Metrologia (submitted).
Wolfson, D. 1985a. Lindeberg-Feller theorem. Pages 1–2 of: Kotz, S., Johnson, N. L., and Read, C. B.. (eds.), Encyclopedia of Statistical Sciences, vol. 5. Wiley.
Wolfson, D. 1985b. Lindeberg-Lévy theorem. Pages 2–3 of: Kotz, S., Johnson, N. L., and Read, C. B. (eds.), Encyclopedia of Statistical Sciences, vol. 5. Wiley.
Woodroofe, M., and Zhang, T. 2002. Comment. Statistical Science, 17, 168–171.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.