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Intermediate measurement precision is measurement precision under declared intermediate precision conditions of measurement. The measurement procedure and location remain the same, measurements extend over a longer period, and specified changes can include operators, measuring systems or measurement calibration. It lies between a tightly restricted measurement repeatability study and a comparison across locations for measurement reproducibility.^[ref]

For a concrete study, one laboratory could measure the same stable reference block each working day with a differential length comparator, taking four complete placements per day. Keep the procedure fixed, record temperature and operator, and retain the day labels. The labels let the study distinguish variation between days from rapid reading-to-reading variation.

An original measurement model makes that distinction explicit:Here $D_d$ is a shared daily offset, while ${\epsilon }_{dj}$ varies between placements. Assume zero-mean independent random variables, independent also between days. A single measurement then has standard deviation $\sqrt{{\tau }^2+{\sigma }^2}$. For stipulated $\tau =0.30\mu \mathrm{m}$ and $\sigma =0.10\mu \mathrm{m}$, this is $0.316\mu \mathrm{m}$, even though within-day scatter reflects only $0.10\mu \mathrm{m}$.

For four readings from one day, the daily arithmetic mean hasAveraging four such means from independent days reduces that modelled standard deviation to $0.152\mu \mathrm{m}$. Four same-day readings do not average away their shared daily offset. The numbers illustrate the model, not measured comparator performance. A real study must estimate its components from enough days and investigate trends: deterministic instrumental drift is not automatically an independent daily offset.

An intermediate precision condition of measurement is part of the specified conditions used to assess intermediate measurement precision. The measurement procedure and location remain common, while replicate measurements extend over a longer period. Declared changes can include operators, measuring systems, reference devices used for measurement calibration, or new calibrations.^[ref] The record should state what changed as well as what was held fixed.

For an original length study, use the same laboratory, reference block and written comparator procedure in two sessions three weeks apart. Two operators each perform the complete remove-and-replace measurement cycle in both sessions. Record instrument identity, measurement calibration, temperature and settling conditions rather than treating “same laboratory” as a complete description.

Consider the following stipulated session means in millimetres:The operator difference is $6\mu \mathrm{m}$ within either session, and the session difference is $10\mu \mathrm{m}$ for either operator. In an additive model, those two comparisons distinguish the respective contributions because both operators appear in both sessions.

If operator A had measured only in session 1 and operator B only in session 2, the observed $16\mu \mathrm{m}$ difference would combine the two changes. It could not be uniquely attributed to operator or elapsed time from that design alone. Repeated complete trials within each operator-session combination are still needed to assess random scatter; four chosen means do not establish a general precision value.

A measurement repeatability study keeps more conditions fixed over a short interval. Changing locations and measuring systems leads toward reproducibility conditions of measurement. The intermediate specification identifies the particular longer-term changes included in the precision study, rather than promising that every source of variation has been sampled.

John S. Beers is a NIST dimensional metrology researcher and coauthor, with Ted Doiron, of The Gauge Block Handbook by Ted Doiron and John S. Beers. Its preface explicitly attributes the handbook's single-wavelength interferometry discussion to Beers's work. The official publication record retains the name John S. Beers.^[ref]

A gauge block provides a physical length standard, but its calibrated length depends on a stated convention. The handbook defines length using a wrung auxiliary plane and discusses mechanical comparison as well as interferometry.^[ref] This makes contact geometry and gauge block wringing part of the measurement, rather than treating the artifact as an abstract number printed on a block.

An original comparison example uses a reference and unknown of nominal length $50\mathrm{mm}$. Let the reference's certified deviation from nominal be $+0.120\mu \mathrm{m}$, and let the corrected unknown-minus-reference difference be $-0.035\mu \mathrm{m}$. The inferred unknown deviation is then $+0.085\mu \mathrm{m}$.

For independent reference and comparison standard uncertainties $u_r=0.025\mu \mathrm{m}$ and $u_d=0.015\mu \mathrm{m}$,If five independent repeat comparisons reduce only the second contribution, the result becomesThe common reference contribution does not disappear by repeating the comparison. This gauge-block reference uncertainty floor illustrates why high measurement repeatability alone cannot establish the same numerical measurement uncertainty as a reference-free measurement. Correlated inputs require the corresponding covariance terms.^[ref]

These chosen numbers explain a calibration principle; they are not reported performance values for Beers's apparatus. His documented contribution concerns the measurement methods and their controlled realization, including the link between an optical observation and a defined physical length.

Measurement precision describes agreement among repeated indications or measured values obtained under stated conditions. It is commonly characterized using a standard deviation, variance or coefficient of variation, which describe the observed spread. Measurement repeatability is precision under a particular restricted set of conditions; intermediate measurement precision and measurement reproducibility concern other specified conditions.^[ref]

For an original balance example, take three repeat readings of a reference object: $100.100$, $100.080$ and $100.120\mathrm{g}$. Their arithmetic mean and sample standard deviation areSuppose the reference object's assigned mass is $100.000\mathrm{g}$ with standard uncertainty $0.002\mathrm{g}$. The observed mean differs from that reference by $0.100\mathrm{g}$, much more than the within-series scatter. These chosen readings therefore illustrate why close repeat readings do not establish agreement with a reference. They do not determine the true systematic offset from only three trials.

Measurement accuracy and measurement trueness answer different questions from precision. A common additive offset leaves the deviations $x_j-\bar{x}$, and hence $s$, unchanged. Averaging more independent readings can reduce random uncertainty in the mean but does not by itself remove that common offset.^[ref]

A useful physical study repeatedly removes and replaces the reference object while recording load procedure, environmental conditions and elapsed time. Specify which parts of the measurement were repeated: repeated display readings alone may omit placement variation or instrumental drift. The statistic describes the stated experiment, not an unconditional property of the instrument.

Measurement repeatability is measurement precision under a declared set of repeatability conditions. The VIM's repeatability condition of measurement includes the same procedure, operators, measuring system, operating conditions and location, with repeated measurements over a short time.^[ref] The complete measurement cycle must be specified before its repeatability can be assessed.

For an original length-comparator study, one operator measures the same reference block using the same differential length comparator over a short session. Three readings without disturbing the setup happen to be $20.000,20.000,20.000\mathrm{mm}$. Their sample spread is zero. In a separate series, the operator removes and reseats the block for every trial, obtaining $19.980,20.000,20.020\mathrm{mm}$. That series givesThe two procedures repeat different parts of the experiment. The first data cannot establish the repeatability of the full remove-and-reseat procedure, nor does its zero observed spread prove an absence of readout noise or finite measurement resolution.

A repeatability experiment keeps the declared conditions stable and records each completed trial, including placement and settling when those belong to the procedure. Positioning repeatability applies this reasoning to repeated returns of a moving stage. Repeating a study over longer periods with selected changes can instead assess intermediate measurement precision; studies changing locations, operators and measuring systems concern measurement reproducibility.^[ref] Report those changes rather than describing every repeated experiment as the same repeatability test.

Michael H. Ramsey is a researcher credited as chair of the working group and co-editor of the 2019 guide to measurement uncertainty arising from analytical sampling. The editorial page gives his affiliation as the University of Sussex and names fellow editors Stephen L. R. Ellison and Peter Rostron.^[ref]

The scientific problem is the difference between the collected material and the material about which a conclusion is wanted. For a measurand defined over a larger target, excellent measurement repeatability on one extract does not establish small analytical sampling uncertainty. The guide treats collection and analysis as stages of the measurement process.^[ref]

An original measurement model illustrates why replication at the right level matters:Here $\mu$ is the target mean, $S_i$ is the zero-mean deviation associated with independently collected sample $i$, and $A_{ij}$ is zero-mean analytical variation in repeat $j$. Suppose all these effects are mutually independent, with variances ${\sigma }_S^2$ and ${\sigma }_A^2$. Averaging $m$ analyses on each of $n$ collected samples givesFor stipulated variance components ${\sigma }_S^2=9$ and ${\sigma }_A^2=4$ in squared concentration units, three collections analysed twice give variance $9/3+4/6=11/3$, or standard uncertainty about $1.915$ concentration units. Six analyses of only one collection instead give variance $9+4/6=29/3$, or about $3.109$ units. Both plans use six analyses; only the first averages over independently collected material.

The calculation assumes independent collections and an appropriate model for the target; a shared systematic collection error is not removed by increasing $n$. It explains the measurement-design issue addressed by the guide without presenting these invented numbers as Ramsey's experimental observations.

Paul Willetts is an analytical chemistry researcher associated with studies of laboratory performance and analytical sampling. The recovery-information report lists him at the MAFF Food Science Laboratory in Norwich, establishing the identity independently of unrelated authors with the same name.^[ref]

With Michael Thompson, Sharron Anderson, Paul Brereton and Roger Wood, Paul Willetts studied collaborative sampling of wheat and green coffee from bulk lots. Multiple samplers allowed the study to distinguish variation under different sampling conditions. Between-sampler variation contributed significantly for two wheat analytes; the coffee results showed significant sampling-repeatability variation without a detected significant sampling-reproducibility contribution.^[ref]

The measurement begins before material reaches the instrument. For an original illustration, two perfectly repeatable preparations might contain $10$ and $14\mathrm{mg}\mathrm{k}{\mathrm{g}}^{-1}$ because the collected portions differ. Repeating each instrument reading a hundred times would not make those portions identical. Measurement repeatability within a portion and measurement reproducibility across the relevant procedures therefore cannot be inferred from the same replication design.

Paul Willetts also coauthored the recovery-information guidance. Together these contributions emphasize that sample matrix, material selection, preparation loss and stated measurement uncertainty belong in the interpretation of an analytical result. They cannot all be assessed by repeatedly reading a single prepared solution.

Positioning repeatability describes the scatter of positions reached when a motion system repeatedly returns to the same commanded position under specified conditions. It is an application of measurement repeatability, a form of measurement precision. A system may return to almost the same wrong position each time, so small scatter does not establish measurement accuracy.^[ref]

The approach direction belongs in the test description. Unidirectional positioning repeatability keeps it fixed; bidirectional positioning repeatability includes returns from both directions. To measure the assembled stage, independently observe its final position rather than only the motor's rotary encoder count. Physik Instrumente describes a static test that lets the platform stop before reading it, using an interferometer for displacement and an autocollimator for angular error, with two reflecting mirrors on the stage.^[ref]

For an original numerical example, repeatedly command $x_{\ast }=10.000\mathrm{mm}$. Suppose an independent position readout with known measurement calibration gives the errors $e_j=x_j-x_{\ast }$, in micrometres,Each direction has the same sample standard deviation,Yet their arithmetic means are 0 and $2.0\mu \mathrm{m}$. The magnitude of their mean difference, a positioning reversal error at this target, is 2.0 micrometres, far larger than the within-direction scatter. Pooling all eight values gives a sample standard deviation of $\sqrt{8.04/7}\approx 1.149\mu \mathrm{m}$; that statistic mixes the directional shift with the smaller return-to-return variation.

The calculation uses a declared sample standard deviation, not an unspecified manufacturer's tolerance or a universal repeatability convention. A positioning specification must state its approach directions, target positions, settling/readout procedure, load, environmental conditions, statistic and measurement uncertainty. A single target does not establish performance over the travel range. The manufacturer's method explicitly separates directional means from scatter and combines information from multiple targets when forming axis-level specifications.^[ref]

Backlash is one possible cause of direction-dependent behavior, while thermal expansion and instrumental drift can move the apparent target over time. A repeatability experiment must distinguish those effects from random scatter. Measuring small returns to one target also answers a different question from minimum incremental motion, which asks whether a small commanded change can actually be executed.

Reference material homogeneity concerns whether variation of specified properties within or between usable portions is small enough for the intended measurement purpose. Homogeneity is property-specific and depends on the portion taken: uniform colour need not establish uniform refractive index, composition or another measured property. Sufficient homogeneity is part of the definition of a reference material.^[ref]

An original study takes several bottles from a batch and measures multiple portions from each, with the measurement order varied to avoid confusing bottle order with instrumental drift. A simple measurement model iswhere $b_i$ describes bottle-to-bottle variation and $e_{ij}$ includes variation among sampled portions and measurement noise. For independent zero-mean contributions, the variance of a single observation isRepeatedly reading one portion mainly probes repeat measurement scatter. It does not replace sampling different portions or bottles. Separating material variation from measurement repeatability requires a sampling and replication design appropriate to both.

Suppose an original fitted model gives a between-bottle standard deviation $3\times 10^{-6}$ in refractive index and within-bottle measurement scatter $4\times 10^{-6}$. Their combined standard deviation for one observation is $5\times 10^{-6}$ under the independence assumption. Averaging more readings from the same bottle can reduce the second contribution, but does not average away that bottle's common $b_i$ contribution. These are illustrative model values, not certificate data.

NIST's archived SRM1922 characterization tested multiple oil portions using minimum-deviation measurements and an Abbé-type refractometer.^[ref] Sampling different portions answers the homogeneity question directly; reference material stability separately addresses changes over time. A report should retain the sampled portion size and conditions so that a user can judge whether the evidence applies to their own use.

A repeatability condition of measurement belongs to a specified set of conditions used to assess measurement repeatability. The VIM set includes a common measurement procedure, operator, measuring system, operating conditions and location, with repeated measurements of the same or similar objects over a short period.^[ref] A condition is therefore meaningful relative to the whole declared set, rather than being a property supplied by the word repeat alone.

For a physical length experiment, specify one operator, one differential length comparator, a reference block, the contact orientation, the remove-and-replace cycle, the settling rule and a short session after thermal equilibration. Keep the measurement calibration fixed during that series. Record every completed measurement, including the elapsed time and block temperature. Reading the unchanged display repeatedly and replacing the block between readings are different measurement procedures, even if the displayed numbers happen to coincide.

An original thermal calculation explains why the operating conditions matter. Suppose a metal reference block has length $L_0=100\mathrm{mm}$ at $T_0$, with stipulated constant linear thermal expansion coefficient $\alpha =12\times 10^{-6}{\mathrm{K}}^{-1}$. In the small-expansion model,A temperature rise of $2\mathrm{K}$ changes its length by $0.0024\mathrm{mm}=2.4\mu \mathrm{m}$. If the intended measurand is length at $T_0$, that change requires an appropriate correction; it should not be silently interpreted as random comparator scatter. This calculation holds other thermal effects fixed and does not model expansion of the comparator itself.

The same room and a short elapsed time do not prove that the relevant conditions were stable. Record observed deviations and assess their effect. Deliberately varying operators over several days at the same location leads to a study of intermediate measurement precision; varying locations and measuring systems leads toward measurement reproducibility.