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In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a quantity measured on an interval or ratio scale.. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation.
Uncertainty quantification (UQ) is the science of quantitative characterization and estimation of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
that is, find (z − E[z] ) and do the necessary algebra to collect terms and simplify. 7. For most purposes, it is sufficient to keep only the first-order terms; square that quantity. 8. Find the expected value of that result. This will be the approximation for the variance of z.
Measurement errors can be divided into two components: random and systematic. [2] Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Random errors create measurement uncertainty.
In physical experiments uncertainty analysis, or experimental uncertainty assessment, deals with assessing the uncertainty in a measurement.An experiment designed to determine an effect, demonstrate a law, or estimate the numerical value of a physical variable will be affected by errors due to instrumentation, methodology, presence of confounding effects and so on.
In daily life, measurement uncertainty is often implicit ("He is 6 feet tall" give or take a few inches), while for any serious use an explicit statement of the measurement uncertainty is necessary. The expected measurement uncertainty of many measuring instruments (scales, oscilloscopes, force gages, rulers, thermometers, etc.) is often stated ...
JCGM 103. Evaluation of measurement data – Supplement 3 to the "Guide to the expression of uncertainty in measurement" – Developing and using measurement models. (Under development) JCGM 104:2009. Evaluation of measurement data – An introduction to the "Guide to the expression of uncertainty in measurement" and related documents. JCGM 105.