Measurement repeatability
Precision under defined short-term conditions, repeatability study design, standard-deviation estimation and uncertainty limits.
Tags: inspection, metrology, repeatability, measurement-systems
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Definition and conditions
Repeatability is precision under specified repeatability conditions. A system can repeat closely and still be biased. JCGM VIM3, 2.21
The five independent length readings in the example have mean 10.001 mm, sample SD 0.001581 mm and range 0.004 mm. The repetition contribution to uncertainty of their mean is 0.000707 mm. These are distinct results from the same observations.
The VIM's repeatability conditions include a common procedure, operator(s), measuring system, operating conditions and location, with repeated measurements on the same or similar objects over a short interval. State the conditions actually held fixed. “Ten repeat measurements” is incomplete if it does not say what was removed, reset, reloaded or independently prepared between trials. JCGM VIM3, 2.20
Name the precision statistic and units. SD, range, a multiple of SD and a manufacturer’s limit are different quantities. JCGM VIM3, 2.15
Decide which repetition is relevant
Define the measurand and intended procedure first. For a contact measurement, repeated placement and approach may matter; for a balance, unloading and reloading may matter; for a laboratory test, sample preparation may matter. If a study leaves these steps unchanged, its conclusion should be limited to that narrower condition.
The GUM asks whether observations are independent repetitions of the procedure. It specifically notes that when zeroing belongs to the procedure it should be included in each repetition, and that repeated observations on one sample do not characterize between-sample variation when sampling forms part of the measurement. JCGM GUM, Annex F.1.1
Choose stable specimens or reference artifacts appropriate to the working range, geometry and surface. Preserve observation order and relevant conditions. Do not confuse real changes in a specimen—warming, deformation, drying or wear—with instrument repeatability. If the method changes the specimen, use a study design that addresses specimen-to-specimen differences rather than assuming every replicate has an identical input.
A useful comparison is between indication noise with the setup undisturbed and procedure repeatability after normal repositioning. Both can inform diagnosis, but they answer different questions. Report which was studied instead of choosing the smaller spread as the system's general performance.
Estimate spread and retain its units
For n repeated values xᵢ, the ordinary sample estimates are:
x̄ = Σxᵢ / n
sᵣ = √[Σ(xᵢ − x̄)² / (n − 1)].
Here sᵣ is the estimated repeatability standard deviation for the stated conditions. Under an appropriate model of independent repetitions, the repeatability-related standard uncertainty of the mean is sᵣ/√n. NIST's Type A guidance uses independent observations and distinguishes their mean from the estimated standard deviation of that mean. NIST, Type A uncertainty evaluation
Original arithmetic example: five independent repetitions of a stated length procedure produce:
10.002, 10.000, 10.001, 9.999 and 10.003 mm.
| Quantity | Calculation/result |
|---|---|
| Mean | 10.001 mm |
| Deviations from mean | +0.001, −0.001, 0, −0.002, +0.002 mm |
| Sum of squared deviations | 0.000010 mm² |
| Sample variance | 0.000010 / 4 = 0.0000025 mm² |
| Repeatability standard deviation | 0.001581 mm, or 1.581 µm |
| Range | 10.003 − 9.999 = 0.004 mm |
| Standard uncertainty of the mean from repetition alone | 0.001581/√5 = 0.000707 mm |
The range is not the standard deviation. The smaller final value applies to the mean under the stated independence assumptions; it is not the repeatability of one future reading. These five invented results demonstrate the arithmetic, not a sufficient qualification study or a complete uncertainty budget. No reference value was supplied, so they do not establish bias.
More repetitions are not the whole study
Inspect the sequence for drift, warm-up, alternating behaviour or changes in technique. A standard deviation can be calculated even when one stationary short-term model does not adequately describe the data. Determine whether the statistic represents the operation being assessed before treating it as reusable performance evidence.
NIST recommends investigating whether repeatability differs with check standard, operator or gauge. It describes pooling weighted variances, when appropriate, to improve a repeatability estimate. Do not simply average standard deviations, or pool markedly different precision conditions without examining the differences. A pooled within-run estimate can remain a short-term quantity even when many runs contribute to it. NIST/SEMATECH, analysis of repeatability
No universal repetition count makes every study adequate. Select data quantity and coverage for the required precision of the estimate, relevant operating conditions and applicable customer or method requirements. Repeating one easy artifact many times does not establish performance over a whole measurement range.
Repeatability, intermediate precision and reproducibility
Intermediate precision keeps procedure and location common while allowing specified changes over an extended period, potentially including operators, calibrations or measuring systems. Identify which conditions changed and which remained fixed. This can better represent routine use than a single short run. JCGM VIM3, 2.22
Reproducibility conditions include differences in locations, operators and measuring systems, with the changed conditions stated. In industrial gauge R&R, the terminology and model may focus on operator effects within one facility, so name the study convention rather than assuming every use of “reproducibility” means the same design. JCGM VIM3, 2.24
ASQ describes gauge R&R as studying measurement variation, with repeatability and reproducibility separate from part-to-part variation. Use a suitable multi-part/multi-condition design when those effects matter. A one-operator repeatability run alone cannot estimate an operator-to-operator contribution. ASQ, gauge repeatability and reproducibility
Resolution and uncertainty boundaries
Identical digital readings do not establish perfect repeatability or zero uncertainty. Quantization can hide input changes. The GUM explains that a range of inputs may produce the same digital indication and treats finite indication resolution as a separate consideration. Check whether the system can distinguish variation relevant to the task before interpreting a zero calculated sample spread. JCGM GUM, Annex F.2.2.1
A repeatability study contributes to uncertainty assessment only when it represents the working measurement process. NIST warns that important effects may not appear in a short run and that later process changes can invalidate a study-based uncertainty estimate. Calibration-reference uncertainty, corrections, environmental effects and relevant longer-term variation still require consideration. NIST/SEMATECH, uncertainties from gauge studies
Report a bounded conclusion
Retain the measurand, specimen/artifact identity, procedure revision, instrument/configuration and resolution, operator, environment, times, repetition/reset method and unrounded observations. Report n, mean, standard deviation, relevant plots and the basis for any pooling or exclusions. State whether the result describes individual readings or an average.
Acceptance depends on the measurement need and governing rule. Small spread alone does not establish calibrated accuracy, negligible uncertainty, process capability or permission to release an out-of-tolerance item. Use the study to locate and reduce relevant variation, then confirm the improvement under the same defined conditions.