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Calibration concepts

Measurement uncertainty explained

Understand uncertainty, error, resolution, uncertainty budgets, CMCs and coverage factors with a simple example.

Calibration concepts For Owner, Administrator, Quality manager, Calibration manager, Calibration engineer

Measurement uncertainty explained

A measured value is an estimate. Measurement uncertainty describes the spread of values that could reasonably be attributed to the quantity being measured, using the available information. The **measurand** is that quantity: for example, the temperature of a particular bath under specified conditions. See the JCGM definition of measurement uncertainty.

Read an uncertainty statement

Consider this illustrative result:

Temperature: 100.00 °C; expanded uncertainty: 0.20 °C; coverage factor: k = 2.

The interval around the result runs from 99.80 to 100.20 °C. Its interpretation depends on the stated coverage probability and the measurement model. It is not a guarantee that every future reading will fall inside that interval, and it does not tell you whether the thermometer passes its specification.

Expanded uncertainty U is combined standard uncertainty multiplied by a coverage factor k. A factor of 2 often corresponds to approximately 95% coverage under suitable assumptions; it does not always do so. Read the actual statement rather than assuming a probability. The NPL beginner's guide, section 7.4 explains this relationship.

Terms that are easy to confuse

TermWhat it tells you
Measurement errorThe difference between a measured value and a reference value. It can have a positive or negative sign.
CorrectionA value, factor or other adjustment to the result that compensates for an estimated systematic effect.
UncertaintyHow much spread remains associated with the measurement result. It is non-negative.
ToleranceThe permitted limits defined for the intended use or specification.
ResolutionThe smallest change the instrument can distinguish; extra display digits do not by themselves prove a smaller uncertainty.

For error and correction, see the JCGM error definition and correction definition. Accuracy describes closeness to a true value; it is not another name for an uncertainty figure. See JCGM on measurement accuracy.

Standard uncertainty expresses uncertainty on a standard-deviation basis. Combined standard uncertainty brings the relevant contributions together using the measurement model. Expanded uncertainty then scales that combined result for reporting.

What is an uncertainty budget?

A budget records the contributions and assumptions used to evaluate uncertainty. Contributions may come from a reference standard, repeated readings, resolution, drift or environmental effects.

Type A evaluates uncertainty statistically from observations. Type B uses other information, such as a calibration certificate or specification. These describe ways of evaluating uncertainty, not quality grades. Components need a justified model and compatible units before they can be combined. See the NPL beginner's guide, sections 4 to 7.

How Metra uses uncertainty

An uncertainty budget revision defines a controlled calculation. An uncertainty evaluation retains the observations, sources and result for particular calibration work. Approving a budget is different from reviewing a completed calculation.

Metra's current calculation policy uses a fixed k = 2. It records the factor with the result; the setting alone does not establish a 95% coverage claim. Its current model combines independent components and does not support correlated components or arbitrary formulas. The technical guides describe these limits before you configure a budget.

An accreditation scope's CMC and a job's calculated uncertainty serve different purposes. Read Accreditation profiles and scopes explained before using schedule evidence.

Put it into practice