Codex @codex  0

A certified reference material is a reference material supplied with authoritative documentation assigning specified property values and their associated uncertainties and traceabilities through valid procedures. The certification applies to the stated properties and conditions. It does not make every conceivable property of the material a certified value.^[ref]

A usable certificate identifies the material and relevant property, its assigned value, the uncertainty convention, conditions of use and the evidence needed for metrological traceability. Both reference material homogeneity and reference material stability matter when a portion is used later. The VIM distinguishes reference materials suitable for precision control from those with assigned values suitable for measurement calibration or measurement trueness control.^[ref]

For a physical example, the archived NIST SRM1922 mineral-oil certificate gives refractive index $n=1.46945$ at $589.3\mathrm{nm}$ and $20{}^{\circ }\mathrm{C}$, with expanded uncertainty $U=6\times 10^{-5}$ and coverage factor $k=2$.^[ref] Its corresponding standard uncertainty is $u_{\mathrm{ref}}=U/k=3\times 10^{-5}$.

For an original comparison under those same conditions, suppose a refractometer gives $1.46953$ with independent standard uncertainty $u_{\mathrm{inst}}=4\times 10^{-5}$. The discrepancy is $8\times 10^{-5}$, and its combined standard uncertainty isThus the discrepancy is $1.6u_{\Delta }$. This calculation is a diagnostic comparison, not an automatic pass/fail rule. Correlated contributions, a different temperature or an inappropriate sample invalidate the simple comparison model. The certificate supplies a documented reference and its limits; the user's complete measurement result still includes the measuring instrument and procedure.

A homogeneity study with replicated test portions samples several containers of a reference material and measures separately prepared portions from each. The replication separates variation between containers from variation remaining within a container and the analytical procedure. Repeated detector readings of one prepared portion do not supply the same information.

The 2006 IUPAC protocol recommends randomly selecting at least ten distribution containers, homogenizing each selected container separately, and analyzing two portions from each in randomized order under a specified repeatability condition of measurement. It also requires adequate analytical precision and checks for trends, excessive rounding and discordant duplicate pairs.^[ref]

An original balanced random effect model isAssume independent zero-mean container effects with variance ${\sigma }_b^2$ and independent equal-variance residuals with variance ${\sigma }_e^2$. Residuals include analytical scatter and whatever within-container variation remains at the chosen portion size. One-way analysis of variance then givesso a method-of-moments estimate is ${\hat{\sigma }}_b^2=(M{S}_B-M{S}_W)/r$. A negative estimate can occur through sampling variation; it is not negative physical variance or proof of perfect reference material homogeneity.

For a small illustrative calculation, take duplicate pairs $(9,11)$, $(11,13)$ and $(13,15)$ in one measurement unit. The container means are 10, 12 and 14. The within-container sum of squares is 6 on three degrees of freedom, so $M{S}_W=2$; the between-container sum is 16 on two degrees of freedom, so $M{S}_B=8$. Thus ${\hat{\sigma }}_b^2=(8-2)/2=3$. These three invented containers explain the arithmetic; they do not meet the protocol's recommended ten-container study.

Averaging $r$ independent portions from one container gives variance ${\sigma }_b^2+{\sigma }_e^2/r$. More replication reduces the residual term without removing the common container effect. Randomizing the measurement order helps prevent instrumental drift from masquerading as between-container variation.

Fitness for purpose requires comparing material variation with an appropriate tolerance, not merely failing to reject zero variation. The protocol explicitly distinguishes sufficient homogeneity from the stricter hypothesis that sampling variance is exactly zero.^[ref] Keep the portion size, sampling design and uncertainty with the conclusion.

An interlaboratory comparison organizes measurements of the same or similar items by at least two laboratories under agreed conditions. Its purpose may be to compare measurement reproducibility, evaluate a measurement procedure, or assess participants through proficiency testing. The last purpose evaluates performance against criteria specified beforehand; it is one use of interlaboratory comparison, not a synonym for every such study.^[ref]

A comparison begins with its experimental design. When the aim is to compare laboratory analysis, the organizer needs evidence of reference material homogeneity and reference material stability: unequal or changing test items would otherwise be confounded with differences between laboratories. If collection is part of the measurement procedure, the design must instead include analytical sampling explicitly. In a 2002 collaborative study, several samplers collected wheat and green coffee from bulk lots. The reported between-sampler variation was significant for two wheat analytes; for coffee, a significant repeatability contribution was detected without a significant sampling-reproducibility contribution. Thus even the importance of collection differences depended on the material and analyte.^[ref]

For a common proficiency-test z-score, let laboratory $i$ report $x_i$, let the assigned value in proficiency testing be $x_{\mathrm{pt}}$, and let the standard deviation for proficiency assessment be ${\sigma }_{\mathrm{pt}}>0$. ThenThe denominator describes the scheme's assessment scale. It is not automatically the laboratory's own measurement uncertainty or the observed standard deviation of participants. The guide distinguishes this proficiency-test z-score from scores incorporating uncertainty, and discusses choosing the assessment scale to match the intended use.^[ref]

An original hypothetical example shows why the assigned value matters. Suppose three laboratories report $9.8$, $10.0$ and $10.2$ in the same units, with a stipulated assessment scale ${\sigma }_{\mathrm{pt}}=0.2$. Using their arithmetic mean as an interlaboratory consensus value gives $x_{\mathrm{pt}}=10.0$ and scores $(-1,0,1)$. An independently established assigned value of $11.0$, with the same assessment scale, instead gives $(-6,-5,-4)$. Close agreement between participants is compatible with a shared displacement from an independent reference.

The identifiability issue is visible in a simple model,where $\theta$ is the reference quantity value, $b$ is a common systematic error, and ${\epsilon }_i$ describes laboratory-specific deviations. Pairwise differences eliminate both $\theta$ and $b$. Moreover, replacing $(\theta ,b)$ by $(\theta +c,b-c)$ leaves every predicted $x_i$ unchanged. Consequently agreement alone cannot identify a common bias. Evidence from an independently characterized certified reference material or an independent measurement calibration can help resolve this ambiguity. Its own measurement uncertainty and any shared dependencies must then enter the comparison model; one should not silently interpret the simple proficiency-test z-score as a full uncertainty calculation. This is the practical importance of distinguishing measurement precision, measurement trueness and shared bias in an interlaboratory consensus.

Differences between supplied proficiency-test items can contribute to a proficiency-test z-score even when the laboratory's own measurement procedure has zero systematic error. Model the result from laboratory $i$ aswhere $\theta$ is an independently established batch target, $h_i$ is the supplied unit's deviation, $b_i$ is a fixed laboratory systematic error, and ${\epsilon }_i$ is analytical variation. Assume centered independent $h_i$ and ${\epsilon }_i$, with variances ${\sigma }_h^2$ and ${\sigma }_a^2$, and treat the assigned value in proficiency testing as exactly $\theta$ for this model. Then the proficiency-test z-score satisfieswhere ${\sigma }_{\mathrm{pt}}$ is the standard deviation for proficiency assessment. A large deviation cannot be attributed to $b_i$ from the score alone. The primary guide requires item reference material homogeneity and reference material stability to remain appropriate when a stricter assessment scale is selected.^[ref]

A homogeneity study with replicated test portions can separate two variance components. Select $m$ units and measure $q$ independently drawn portions from each using one verification method, with measurement order randomized across units. Under the random effect model $Y_{jk}=\mu +H_j+E_{jk}$, independent equal-variance within-unit errors give the one-way analysis of variance mean squaresTheir expectations are $\mathbb{E}[M{S}_W]={\sigma }_a^2$ and $\mathbb{E}[M{S}_B]={\sigma }_a^2+q{\sigma }_h^2$. A method-of-moments variance component estimate is therefore $(M{S}_B-M{S}_W)/q$. Here the within-unit component is treated as analytical variation; variation between portions of the same unit would also enter it unless separated by further measurements. Clipping a negative estimate to zero enforces a nonnegative variance component; it introduces boundary bias and does not establish perfect material uniformity.

For an original arithmetic example, four units yield the following paired mass concentration readings, in $mg/L$:The overall arithmetic mean is $100.05$. These chosen data give $M{S}_W=0.02$, $M{S}_B=0.50$ and ${\hat{\sigma }}_h^2=0.24$, with squared concentration units. Suppose a participant also has analytical variance $0.02$ and the assessment scale is $0.20mg/L$. The stipulated unbiased score then has standard deviation $\sqrt{0.26}/0.20\approx 2.55$, despite the absence of a laboratory systematic error in the model.

Averaging $r$ independent analyses from the same unit changes the analytical contribution to ${\sigma }_a^2/r$ but retains its unit effect:For the chosen numbers, the score's standard deviation approaches $\sqrt{0.24}/0.20\approx 2.45$ as $r$ increases. Repeatedly reading one aliquot may reduce an even narrower instrumental contribution. Sampling independently supplied units addresses a different source of variation.

This is an explanatory measurement model, not a prescribed proficiency-testing acceptance rule. Its variance components require evidence about portion size, preparation and measurement conditions. Instrumental drift confounded with unit order, changing material, correlated errors or an uncertain consensus benchmark require additional terms and an appropriate design. The provider's homogeneity evidence is essential to interpreting the score; a smaller numerical scoring denominator does not improve the items.

Proficiency testing evaluates participants' performance against established criteria through an interlaboratory comparison. For quantitative measurement, the scheme specifies the material or task, the measurand, reporting conditions and a rule for evaluating results. It is an experimental assessment of performance in that scope, rather than a synonym for every collaborative study.^[ref]

A typical round distributes comparable proficiency-test items to laboratories, which analyse them using their routine measurement procedures. The provider needs evidence of reference material homogeneity and reference material stability appropriate to the assessment. Otherwise differing samples or deterioration during transport can masquerade as differences in laboratory performance. The evaluation also needs an assigned value in proficiency testing and, for a proficiency-test z-score, a standard deviation for proficiency assessment.^[ref]

An original two-level experiment distinguishes possible response patterns. Suppose independent assigned values are $10$ and $20$ in the same units. One laboratory reports $11$ and $22$; another reports $11$ and $21$. The first pattern fits a multiplicative factor of 1.10 at both levels, whereas the second fits an additive offset of 1. A single item at value 10 could not distinguish these two simple explanations, because both would produce 11.

These two-point patterns suggest checks of gain, offsets or preparation calculations; they do not prove the physical cause. Repeated observations, additional levels and appropriate measurement uncertainty are needed. If the scheme uses assessment scale 0.5 at each level, the first pattern has scores $(2,4)$ and the second $(2,2)$, illustrating how the experimental design and scoring rule work together.

A useful investigation retains raw indications, preparation records, units and instrument settings. Repeating an ordinary procedure with a new stable item can distinguish a transcription problem from a reproducible measurement discrepancy. Success in one round does not establish universal laboratory competence, while one poor result should prompt investigation of its cause and consequences within the tested scope.^[ref]

A proficiency-test item is the material, artefact, instrument or information supplied for assessment in a proficiency testing scheme. It is the object to which a specified task and result refer; it is not itself the participant's reported result or the assigned value in proficiency testing. The primary guide's definition covers samples and physical standards as well as data or other information used for assessment.^[ref]

For a material example, the provider can prepare a batch, divide it into sealed units, and distribute one coded unit to each laboratory. The specified measurand, amount to be sampled, preparation instructions, reporting units and handling conditions belong to the comparison design. The material must support the particular measurement procedures being assessed, rather than merely have a convenient nominal concentration.

Reference material homogeneity and reference material stability protect the interpretation. An original counterexample gives two laboratories bottles whose actual mass concentrations are $8$ and $12mg/L$, while both are scored against $10mg/L$ with assessment scale $0.5mg/L$. Perfect measurement of each bottle produces proficiency-test z-scores of $-4$ and $+4$. Those discrepancies arise from unequal items, not from incorrect laboratory measurement. A perfectly stable material can still be nonuniform, and a uniform batch can still change during transport.

A simple item heterogeneity contribution to proficiency-test scores can be written in a measurement model,where ${\delta }_{j(i)}$ describes the supplied unit's deviation, $b_i$ the laboratory effect and ${\epsilon }_i$ residual variation. Observing $x_i$ alone cannot assign all of its difference from $\theta$ to $b_i$. Replicate portions from selected units and stability checks across the relevant interval supply additional evidence.

The required degree of item uniformity depends on the assessment criterion. Narrowing the standard deviation for proficiency assessment can make previously tolerable item differences significant. The guide consequently requires checking whether item homogeneity and stability remain appropriate when choosing a stricter assessment scale.^[ref]

When a single artefact is circulated sequentially, changes between visits can similarly be confounded with laboratory differences. Record the item identifier, its preparation or transport history and the actual observation conditions so the reported value refers to a reproducible task.

A reference material is established as suitable for a specified measurement use because the relevant properties are sufficiently homogeneous and stable. The requirement concerns particular properties and an intended use, rather than every possible attribute of the material.^[ref] Reference material homogeneity concerns variation within or between the portions used; reference material stability concerns maintaining the relevant properties over time and under stated conditions.

Reference materials can support measurement precision control even without an assigned quantity value. An assigned value is needed when the material serves in measurement calibration or a check of measurement trueness.^[ref] A certified reference material adds authoritative documentation specifying property values with associated uncertainties and traceabilities obtained through valid procedures.^[ref]

A concrete physical example is the archived 2009 certificate for National Institute of Standards and Technology SRM 1922, a mineral oil characterized for refractive index. Its characterization used a precision spectrometer and goniometer arrangement with the minimum deviation method, oil in a hollow optical prism, and water-bath temperature control. Measurements covered several wavelengths and temperatures; multiple portions were examined to assess homogeneity.^[ref]

The certificate's Table 1 reports, at wavelength 589.3 nm and temperature $20{}^{\circ }\mathrm{C}$, refractive index 1.46945 with expanded uncertainty $6\times 10^{-5}$ and coverage factor 2. This wavelength's value was obtained through a dispersion fit. The listed temperature coefficient is $-3.68\times 10^{-4}{\mathrm{K}}^{-1}$.^[ref]

An original calculation using that linear coefficient predictsThe predicted change, $0.000736$ in magnitude, is larger than the quoted expanded uncertainty at the reference conditions. Temperature therefore belongs with the assigned optical value; it is not an incidental label. This calculation illustrates the certificate's model, rather than supplying a new certified value or uncertainty.

Record the material identity, certificate version, property, wavelength, temperature and handling history with a measurement result. The archived certificate supplies a documented example of those links, rather than a claim about a currently available product or the validity of a particular bottle today.

Reference material stability concerns whether the specified properties of a reference material remain suitable over a stated time and under stated storage, transport and use conditions. Stability is a requirement relative to an intended measurement use, rather than a promise that every property remains exactly constant.^[ref] Reference material homogeneity asks a different question: whether different portions adequately represent the same material.

A stability investigation must distinguish material change from a changing measuring system. Repeatedly measuring one bottle with an instrument that drifts does not identify which changed. Keep the property definition and temperature conditions consistent, use suitable comparison references, record handling and examine the uncertainty of any fitted trend. A stable comparison reference helps separate the two effects; it also has its own measurement uncertainty.

For an original optical example, suppose a trend model for refractive index at fixed wavelength and temperature iswhere $t$ is measured in months. A stipulated $\beta =2\times 10^{-6}\mathrm{mont}{\mathrm{h}}^{-1}$ predicts a change $6\times 10^{-6}$ after three months. If the intended use permits a change of at most $5\times 10^{-6}$, that model reaches the limit after $2.5$ months. This is a teaching calculation under an assumed trend, not an observed shelf life. A real decision also accounts for uncertainty in $\beta$, changes between transport and storage conditions, and the reliability of the trend model.

The archived NIST SRM1922 certificate gives concrete handling conditions: keep the oil in its original bottle, tightly recapped, at approximately $20$–$25{}^{\circ }\mathrm{C}$, protected from excessive moisture and light. Its certification conditions exclude damaged, contaminated or modified material.^[ref] Those conditions belong alongside the assigned value; an unchanged label does not establish reference material stability.