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8 Measurement Uncertainty
8.17 Calculating the Combined Uncertainty
(for the Selected Coverage Factor k)
The concept of expanded uncertainty, noted as U has been introduced to determine
the range that encompasses a sufficient probability of the spread of values that can be
assigned to the measured quantity in a justified way. The expanded uncertainty U is
obtained through the multiplication of the value of the combined standard uncertainty
u c (y) by the coverage factor k.
The coverage factor k can have different values, depending on the required confidence (probability) level. The k value in the range of 2–3 is the one used most
often, which with the assumption of a normal distribution, means a trust range of
approximately 95% or 99%, respectively. The measurement result is provided as
Y y ± U
(8.20)
which means that the best approximation of the measured quantity Y is y and that a
majority of the value spread of the measured quantity is in the range from y– U to
y + U.
Selected terms used for expanded uncertainty are listed below.
Expanded measurement uncertainty: the product of a combined standard measurement uncertainty and a factor larger than the number one.
*
Clause 2.35; ISO/IEC Guide 99
Coverage interval: the interval containing the set of true quantity values of a
measurand with a stated probability, based on the information available.
Clause 2.36; ISO/IEC Guide 99
Coverage probability: the probability that the set of true quantity values of a
measurand is contained within a specified coverage interval.
Clause 2.37; ISO/IEC Guide 99
Coverage factor: the number larger than one by which a combined standard
measurement uncertainty is multiplied to obtain an expanded measurement
uncertainty.
**
Clause 2.38; ISO/IEC Guide 99
* The term ‘factor’ in this definition refers to a coverage factor.
** Coverage factor is usually symbolized by k
8 Measurement Uncertainty
8.17 Calculating the Combined Uncertainty
(for the Selected Coverage Factor k)
The concept of expanded uncertainty, noted as U has been introduced to determine
the range that encompasses a sufficient probability of the spread of values that can be
assigned to the measured quantity in a justified way. The expanded uncertainty U is
obtained through the multiplication of the value of the combined standard uncertainty
u c (y) by the coverage factor k.
The coverage factor k can have different values, depending on the required confidence (probability) level. The k value in the range of 2–3 is the one used most
often, which with the assumption of a normal distribution, means a trust range of
approximately 95% or 99%, respectively. The measurement result is provided as
Y y ± U
(8.20)
which means that the best approximation of the measured quantity Y is y and that a
majority of the value spread of the measured quantity is in the range from y– U to
y + U.
Selected terms used for expanded uncertainty are listed below.
Expanded measurement uncertainty: the product of a combined standard measurement uncertainty and a factor larger than the number one.
*
Clause 2.35; ISO/IEC Guide 99
Coverage interval: the interval containing the set of true quantity values of a
measurand with a stated probability, based on the information available.
Clause 2.36; ISO/IEC Guide 99
Coverage probability: the probability that the set of true quantity values of a
measurand is contained within a specified coverage interval.
Clause 2.37; ISO/IEC Guide 99
Coverage factor: the number larger than one by which a combined standard
measurement uncertainty is multiplied to obtain an expanded measurement
uncertainty.
**
Clause 2.38; ISO/IEC Guide 99
* The term ‘factor’ in this definition refers to a coverage factor.
** Coverage factor is usually symbolized by k