A measurement is used to determine the actual value of a characteristic that is usually called measurand. A measurement is possible only if the measurand had been quantified prior to measurement by means of a suitable unit so that each value of the measurand is represented by a unique real number. For example, the characteristic "length" of a material object is quantified by the unit "meter", or the characteristic "(time) duration" of a development is quantified by the unit "second". Any measurement assumes a measurement process which is subject to randomness resulting in uncertainty about its indeterminate future outcome. Because of this uncertainty with respect to the future outcome of the measurement process, it is generally impossible to determine the true value of the measurand.
Contents
- Measurement procedure
- Reliability of a measurement procedure
- Accuracy of a measurement procedure
- Measurement procedure and prediction procedure
- References
The related problems are addressed in the ISO Guide to the Expression of Uncertainty in Measurement (GUM) which was first published in 1993. However, since the GUM was published, complaints and critiques about it did not cease. The weaknesses of the GUM were one reason that stochastic measurement procedures were introduced in 2001. They are based on a rigorous introduction of the concepts of randomness and uncertainty
Measurement procedure
The measurand is given by a variable with fixed, i.e., determinate, but unknown value, and it is therefore called deterministic variable. A measurement itself is performed by a measurement device that defines a measurement process. In contrast to the measurand the measurement process is subject to randomness and its future outcome is therefore indeterminate. Consequently, the measurement process is represented by a variable X which is called a random variable.
The task is to conclude the unknown value of the measurand from the observed outcome of the measurement process. It is impossible to determine the true value of the measurand by means of the measurement process because of randomness. It is only possible to specify a set of values that includes the true value. Such a set constitutes the measurement result and it is called "correct" if it contains the true value of the measurand and wrong if not.
A measurement procedure is specified by the measurand given by the deterministic variable D, a measurement device that defines the admitted measurement range denoted
Reliability of a measurement procedure
The symbol
How to select the reliability level
Accuracy of a measurement procedure
In traditional metrology, "measurement precision" and "measurement accuracy" are distinguished, this somewhat confusing differentiation is not necessary for stochastic measurement procedures, since they distinguish between correct and wrong measurement results and meet a reliability specification given by the reliability level
Measurement procedure and prediction procedure
Any stochastic measurement procedure is based on a stochastic model of the measurement process. This stochastic model is called Bernoulli space and enables the development of reliable and accurate stochastic prediction procedures given by the function
The measurement function
From this relation it is seen, that the measurement result
The prediction procedure to be derived based on the Bernoulli space
- The prediction procedure
A X ( β ) β . - The predictions
A X ( β ) ( { d } ) ford ϵ D must cover all possible observations{ x } . - The predictions
A X ( β ) ( { d } ) must be determined in a way that on average the measurement results have a minimum size.