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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.
Essentially, the mean is the location of the PDF on the real number line, and the variance is a description of the scatter or dispersion or width of the PDF. To illustrate, Figure 1 shows the so-called Normal PDF , which will be assumed to be the distribution of the observed time periods in the pendulum experiment.
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.
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 ...
Uncertainty is involved in every measurement, such as measuring a distance, a temperature, etc., the degree depending upon the instrument or technique used to make the measurement. Similarly, uncertainty is propagated through calculations so that the calculated value has some degree of uncertainty depending upon the uncertainties of the ...
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.
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. [35] There are two components to the uncertainty of a measurement: the width of the uncertainty interval and the confidence level. [36]
Indeterminacy in measurement was not an innovation of quantum mechanics, since it had been established early on by experimentalists that errors in measurement may lead to indeterminate outcomes. By the later half of the 18th century, measurement errors were well understood, and it was known that they could either be reduced by better equipment ...