Measurement Uncertainty and Traceability CLEEN MMEA Certainty Seminar 6.11.2013 MIKES, Espoo Maija Ojanen Maija.Ojanen@mikes.fi

Introduction Why should we estimate measurement uncertainty? To estimate the reliability of the results To compare different results and measurement methods To see if the device meets its specifications To be cost efficient To know in which applications the results can be used !!! 6.11.2013 Maija Ojanen

Identification of uncertainty components Measurement device Stability Needs to be studied based on successive calibrations Linearity Hysteresis Resolution Drift… Deviation of the results, sampling Measurement procedure Environmental conditions Temperature, vibration, relative humidity, air pressure, gravitation, air flow, … Change in the above mentioned can result in significant effect in the measurement result Calibrations typically done in well-controlled laboratory conditions! 6.11.2013 Maija Ojanen

Uncertainty classification Type A uncertainty Can be evaluated by statistical methods Type B uncertainty Evaluated by other means: calibration certificate, specifications, literature, earlier experience etc. Cannot be improved by repeating the measurements! Standard uncertainty Combined standard uncertainty Expanded uncertainty 6.11.2013 Maija Ojanen

Uncertainty analysis Express in mathematical terms the dependence of the measurand (output quantity) on the input quantities. In the case of a direct comparison of two standards the equation may be very simple, e.g. Y = X1+X2. Identify and apply all significant corrections. List all sources of uncertainty in the form of an uncertainty analysis. Calculate the standard uncertainty for repeatedly measured quantities (type A uncertainty). Evaluate type B uncertainty by other means. Calculate for each input quantity the contribution to the uncertainty associated with the output estimate resulting from the input estimate and sum their squares to obtain the square of the combined standard uncertainty of the measurand. If input quantities are known to be correlated, the associated covariances must be included. Calculate the expanded uncertainty by multiplying the standard uncertainty associated with the output estimate by a coverage factor k (typically k = 2 -> 95 % confidence level). 6.11.2013 Maija Ojanen

Uncertainty distributions Gaussian distribution Uncertainty from calibration certificate Repeatability Standard uncertainty = standard deviation (1 σ) Rectangular distribution Resolution of digital display Manufacturer specifications Triangular distribution Difference of two rounded values ±1 σ ±2 σ 6.11.2013 Maija Ojanen

Calculation example The measurand Y depends on input quantities Xi Using relative uncertainties (xi /Xi) multiplied and divided input quantities produce an equal relative uncertainty in the measurand If the input quantity is raised to nth power , the resulting relative uncertainty in the measurand is n-tuple 6.11.2013 Maija Ojanen

Calculation example Combined standard uncertainty is calculated as a square sum of the uncertainty components Expanded uncertainty is calculated by multiplying the combined standard uncertainty by a chosen coverage factor k (typically k = 2) Note: in this example all the input quantities are non-correlated! 6.11.2013 Maija Ojanen

Correlation Two input quantities dependent on each other Common calibration reference E.g. measurement of a 5-m distance with a 1-m ruler: measured distance is a sum of five separate measurements with same error/uncertainty Effect of correlation must be studied case by case; no general model Can either increase or decrease the combined standard uncertainty 6.11.2013 Maija Ojanen

Example of an uncertainty budget “Any detailed report of the uncertainty should consist of a complete list of the components, specifying for each the method used to obtain its numerical value” P. Kärhä, P. Toivanen, F. Manoochehri, and E. Ikonen, “Development of a detector-based absolute spectral irradiance scale in the 380-900-nm spectral range,” Appl. Opt. 36, 8909 - 8918(1997). 6.11.2013 Maija Ojanen

Precision vs. accuracy 6.11.2013 Maija Ojanen

Traceability 6.11.2013 Maija Ojanen

Literature BIPM, IEC, IFCC, ISO, IUPAC, UIPAP, OIML. JCGM 100:2008 Evaluation of measurement data - Guide to the Expression of Uncertainty in Measurement. (GUM 1995 with minor corrections), 2008 European cooperation for Accreditation, EA-4/02 Expression of the Uncertainty of Measurement in Calibration, December 1999. 6.11.2013 Maija Ojanen