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Hanoi University of Science & Technology Department of Precision Mechanical & Optical Engineering Measurements and Uncertainty of Measurements D.Eng. Vu Thanh Tung tung.vuthanh@hust.edu.vn 1
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Metrology & Key Organizations Metrology: “the science of measurement, embracing both experimental and theoretical determinations at any level of uncertainty in any field of science and technology” Metrology is defined by the International Bureau of Weight and Measures (BIPM) [1]. Key Organizations ✓ The International System of Units (SI) ✓ General Conference on Weights and Measures (CGPM) ✓ International Committee for Weights and Measures (CIPM) Figure 1: NMIs of different countries. [1] URL: http://www.bipm.org/en/convention/wmd/2004/ 2
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True value and Accuracy The true value is the actual value of the property being measured. Since the true value cannot be absolutely determined, in practice an accepted reference value is used. The accepted reference value is usually established by repeatedly measuring some NIST or ISO traceable reference standard. Accuracy is the closeness of agreement Figure 2: True value and measured value. between a measured value and the true value. 3
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Error Error is the difference between a measurement and the true value of the measurand (the quantity being measured). ➢ Systematic error: tends to shift all measurements in a systematic way so that in the course of a number of measurements the mean value is constantly displaced or varies in a predictable way. The causes may be known or unknown but should always be corrected for when present. Systematic error can be corrected for only when the "true value" (such as the value assigned to a calibration or reference specimen) is known. ➢ Random error is a component of the total error which, in the course of a number of measurements, varies in an unpredictable way. It is not possible to correct for random error. Random errors can occur for a variety of reasons such as: lack of equipment sensitivity, noise in the measurement, imprecise definition 4
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Precision Precision: “Degree to which further measurements will show the same or similar results”. In metrology, precision refers to the dispersion of measurements. In the details, precision is: closeness of agreement between indications or measured quantity values obtained by replicate measurements on the same or similar objects and under specified conditions. Figure 3: Accuracy, Precision, Error, and Trueness. 5
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Repeatability and Reproductibility Repeatability closeness of the agreement between the results of successive measurements of the same measurand carried out under the same conditions of measurement. This represents precision under a set of identical conditions of measurement: ✓ Same operators ✓ Same measuring system ✓ Same measurement procedure ✓ Same operating conditions ✓ Same site ✓ Same or similar objects ✓ Short time period 6
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Repeatability and Reproductibility Reproducibility is closeness of the agreement between the results of measurements of the same measurand carried out under changed conditions of measurement. This represents the precision under a set of variable conditions of measurement: ✓ Different operators ✓ Different measuring system ✓ May use different measurement procedure ✓ Same or similar objects 7
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Resolution Resolution of a sensor is the smallest change in a measurement that causes a perceptible change in the corresponding indication. In general, instruments change their output in a stepwise fashion, and the relationship between the minimum step size and the full scale output is referred to as resolution. 8
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Standards and Traceability The National Institute of Standards and Technology (NIST) defines traceability as an “establishment of an unbroken chain of comparisons to stated references each with a stated uncertainty [3]. Figure 3: Representation of the traceability chain. [2] URL: http://www.nist.gov/pml/mercury_traceability.cfm 9
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Units of Measurements [3] [3]The International System of Units (SI). B.N. Taylor, ed., NIST Special Publication 330, 200110
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Measurement Uncertainty Uncertainty of Measurement is a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand [4]. Uncertainty is described as the doubt about the validity of a measurement result. A measurement never gives the true value; however, it is the best estimation of it. This way, a measurement is only complete if it is accompanied by a statement of the associated uncertainty. [4] https://www.bipm.org/en/publications/guides/gum.html 11
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Sources of Uncertainty of a Measuarement a) incomplete definition of the measurand; b) imperfect reaIization of the definition of the measurand; c) nonrepresentative sampling, the sample measured may not represent the defined measurand; d) inadequate knowledge of the effects of environmental conditions on the measurement or imperfect measurement of environmental conditions; e) personal bias in reading analogue instruments; f) finite instrument resolution or discrimination threshold; g) inexact values of measurement standards and reference materials; h) inexact values of constants and other parameters obtained from external sources and used in the data-reduction algorithm; i) approximations and assumptions incorporated in the measurement method and procedure; j) variations in repeated observations of the measurand under apparently identical conditions. 12
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