Measurement uncertainty

In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty. By international agreement, this uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity value.

The measurement uncertainty is often taken as the standard deviation of a state-of-knowledge probability distribution over the possible values that could be attributed to a measured quantity. Relative uncertainty is the measurement uncertainty relative to the magnitude of a particular single choice for the value for the measured quantity, when this choice is nonzero. This particular single choice is usually called the measured value, which may be optimal in some well-defined sense (e.g., a mean, median, or mode). Thus, the relative measurement uncertainty is the measurement uncertainty divided by the absolute value of the measured value, when the measured value is not zero.

The purpose of measurement is to provide information about a quantity of interest – a . For example, the measurand might be the size of a cylindrical feature, the volume of a vessel, the potential difference between the terminals of a battery, or the mass concentration of lead in a flask of water.

No measurement is exact. When a quantity is measured, the outcome depends on the measuring system, the measurement procedure, the skill of the operator, the environment, and other effects. Even if the quantity were to be measured several times, in the same way and in the same circumstances, a different measured value would in general be obtained each time, assuming the measuring system has sufficient resolution to distinguish between the values.

The dispersion of the measured values would relate to how well the measurement is performed. Their average would provide an estimate of the true value of the quantity that generally would be more reliable than an individual measured value. The dispersion and the number of measured values would provide information relating to the average value as an estimate of the true value. However, this information would not generally be adequate.

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