Measurement reproducibility

Reproducibility is precision under stated changes of location, operator or measuring system. Record what changed and what was held constant. JCGM VIM3, reproducibility conditions, measurement reproducibility

In the example, independent laboratory and repeatability SDs are 0.004 and 0.003 mm. One result has SD 0.005 mm. Averaging four independent repeats within one laboratory gives 0.00427 mm because only the repeatability variance is divided by four. This model excludes material heterogeneity and other effects.

Distinguish the precision conditions

A study within one laboratory over several days may characterize intermediate precision rather than interlaboratory reproducibility. Neither label automatically includes every possible change in use. VIM3, repeatability conditions, intermediate precision conditions, intermediate precision

Precision concerns dispersion, not agreement with a correct reference value. Several laboratories can agree closely while sharing the same offset. A reproducibility study and a bias evaluation answer different questions; reporting one does not eliminate the need for the other where the measurement decision requires it.

Identify the population and result being studied

Define the measurand, units, method, material or part family, measurement range and reported result. A single reading, mean of several readings and result after a specified calculation have different precision models. Specify whether specimen preparation is repeated for each test or whether laboratories receive already prepared specimens. Otherwise, important preparation variation may be omitted without being apparent from the final numbers.

ISO 5725-2:2025, third edition, dated December 2025, describes collaborative interlaboratory experiments for estimating precision of standard methods producing a continuous-scale result. Its basic design uses the same number of results at the same sample levels in participating laboratories. It assumes approximately normal results under its model and homogeneous materials, or treatment of heterogeneity within the precision assessment. This is a defined experimental framework, not a claim that any exchange of measurements between two sites is an ISO precision study. ISO 5725-2:2025

Choose material levels and participating conditions that represent the intended use. If each laboratory receives a different production batch, a laboratory difference may actually be a batch difference. If the same object changes during transport or testing, differences may reflect instability. Plan distribution, storage, conditioning and identification so these effects can be evaluated rather than silently assigned to the instruments.

Separate variation components

A useful model distinguishes within-condition scatter from differences among conditions. More replicate readings improve knowledge of within-condition variation, but they do not substitute for independent laboratories, operators or days when those are the population of interest. Plot individual results and condition means; retain the grouping and collection order required by the model.

NIST's reproducibility example analyzes day-to-day variability using repeated measurements of check standards and pools estimates across runs. It also illustrates that a small study can yield a zero estimated between-day component even when a larger database reveals a real effect. A zero component estimate is not proof that the physical influence is absent. NIST: analysis of reproducibility

Original simplified model: suppose a stable material is measured in a population of laboratories. Assume independent zero-mean laboratory effects with SD σL and independent repeatability errors with SD σr. Ignore material heterogeneity and other effects. A single result from a randomly selected laboratory has:

reproducibility SD = sqrt(σL² + σr²)

If estimated σL = 0.004 mm and σr = 0.003 mm, the combined SD is √(0.000016 + 0.000009) = 0.005 mm. For a mean of four independent repeats made in one laboratory, the model instead gives:

SD of laboratory mean = sqrt(σL² + σr² / 4)
                      = sqrt(0.000016 + 0.00000225)
                      ≈ 0.00427 mm

Averaging reduced repeatability's contribution; it did not divide the laboratory effect by four. These are assumed components illustrating a random-effects model, not estimates calculated from an actual dataset, an expanded uncertainty or a universal acceptance limit. Other designs, dependencies and corrections require their own model.

Understand the Gage R&R usage

In Minitab's crossed operator-by-part ANOVA, the full model divides its reproducibility component into operator and operator-by-part interaction. The interaction represents operator differences that depend on the part. A reduced model omits the interaction and assigns reproducibility to operator variation. This software usage can describe a study conducted with one gauge at one location; it does not by itself demonstrate the wider VIM condition set. State the factors, analysis and scope rather than treating the output label as evidence of interlaboratory coverage. Minitab: crossed-study analysis models

For practical diagnosis, distinguish a consistent operator shift from a part-specific interaction. The first may suggest a common setup or reading difference; the second may require investigation of access, alignment or feature interpretation. Those are hypotheses to investigate, not conclusions established by an ANOVA term alone.

Use reproducibility data in an uncertainty evaluation carefully

ISO 21748:2017, second edition, dated April 2017, gives guidance on evaluating uncertainty using ISO 5725-2 study data and comparing that approach with uncertainty propagation. It assumes recognized non-negligible systematic effects are corrected or their causes removed. It explicitly does not describe using repeatability data alone without reproducibility data. A published reproducibility SD is useful evidence, but applicability to the current laboratory, material, range and result still needs examination. ISO 21748:2017

Do not add components already included in a reproducibility estimate a second time. Conversely, do not assume it includes a new specimen type, extra preparation step, environmental range or known reference-value uncertainty that the study never addressed. Report whether the stated number is a standard deviation, relative standard deviation, variance, coverage interval or expanded uncertainty.

Decision and reporting boundaries

Set the required precision and acceptance basis for the actual inspection task. Agreement between sites does not establish that a part meets its tolerance, and a small study SD does not guarantee correct classification near a specification limit. Investigate unexplained differences before applying a pooled number to all sites. If the process changes, assess whether the earlier study still represents it.

Retain the procedure revision, participants, instruments, material levels, preparation and distribution, conditions changed and unchanged, raw results, grouping, exclusions, statistical model, variance estimates and confidence information. State the range and population to which the conclusion applies. “Reproducibility SD 0.005 mm under the listed conditions” is more useful than an unqualified claim of “excellent reproducibility.”

Sources were reviewed November 1, 2026. VIM3 terminology is used with the separately identified ISO 5725-2:2025 and ISO 21748:2017 editions; older standards cited in VIM notes are not treated as current editions. The NIST handbook and Minitab help pages did not display article revision dates.

Inspection and quality documents