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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 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.
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.
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 ...
The lower the accuracy and precision of an instrument, the larger the measurement uncertainty is. Precision is often determined as the standard deviation of the repeated measures of a given value, namely using the same method described above to assess measurement uncertainty. However, this method is correct only when the instrument is accurate.
where s is the estimated standard deviation of the n T T measurements. In Method 2, each individual T measurement is used to estimate g, so that n T = 1 for this approach. On the other hand, for Method 1, the T measurements are first averaged before using Eq(2), so that n T is greater than one. This means that
Measurement uncertainty is a value associated with a measurement which expresses the spread of possible values associated with the measurand—a quantitative expression of the doubt existing in the measurement. [36] There are two components to the uncertainty of a measurement: the width of the uncertainty interval and the confidence level. [37]
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.
The experimental uncertainty is inevitable and can be noticed by repeating a measurement for many times using exactly the same settings for all inputs/variables. Interpolation This comes from a lack of available data collected from computer model simulations and/or experimental measurements.