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.

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.

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 reproducibility is measurement precision under specified reproducibility conditions of measurement. These include changed locations, operators and measuring systems; the measurement procedures may also differ. The comparison must state what changed and what remained common.^[ref] This is a metrological use of reproducibility, concerned with agreement of measured values under declared conditions.

An original comparison sends a stable reference block to three laboratories. Each laboratory uses its own differential length comparator and operator, measures the same specified measurand, and reports three length errors relative to the common reference, in micrometres:Each laboratory has sample standard deviation $1\mu \mathrm{m}$, yet their arithmetic means differ by as much as $6\mu \mathrm{m}$. Relative to the grand mean $2/3\mu \mathrm{m}$, the total squared deviation separates into within-laboratory and between-laboratory terms:Consequently the nine chosen values have pooled sample standard deviation $\sqrt{62/8}\approx 2.78\mu \mathrm{m}$. This is a descriptive statistic for these observations, not a universal estimator prescribed by the definition of measurement reproducibility. Reporting only the three within-laboratory spreads would conceal the disagreement.

The physical comparison must also monitor transport damage, reference stability and temperature corrections. A changing reference block could imitate a laboratory difference. Measurement reproducibility alone does not establish measurement trueness: all laboratories could share the same erroneous reference value or correction. The changed apparatus and conditions belong alongside the reported statistic.

Measurement trueness describes how closely the mean of indefinitely many replicate measured values would agree with a reference value. It concerns systematic error, rather than the random spread described by measurement precision. The VIM treats measurement trueness as qualitative: a numerical error or bias estimate is not itself a numerical value of trueness.^[ref]

An original measurement model separates the two issues:Here $b$ is a fixed offset from the stipulated reference and $\epsilon$ is random measurement error. Thus $\mathbb{E}[X]-x_{\mathrm{ref}}=b$, while the standard deviation of individual readings is $\sigma$. For $n$ independent random variables following this same model, averaging givesMore readings reduce the random scatter of the mean without removing $b$.

For a stipulated length example, instrument A has $b=0.40\mathrm{mm}$ and $\sigma =0.10\mathrm{mm}$; instrument B has $b=0$ and $\sigma =0.50\mathrm{mm}$. A is more precise, while B's limiting mean agrees better with the reference. With 25 independent readings each, the means have standard deviations $0.02\mathrm{mm}$ and $0.10\mathrm{mm}$ respectively, and their expected offsets remain $0.40\mathrm{mm}$ and zero. These are chosen model parameters, not experimental determinations.

Experimentally, compare repeated readings of a stable measurement standard with its assigned value under specified conditions. A finite observed mean difference estimates an offset; its interpretation includes sampling variation and the reference's measurement uncertainty. Determine an appropriate correction through measurement calibration, apply it in the measurement model, and check it with further reference measurements. Neither a small sample spread nor a single reading equal to the reference establishes measurement trueness.

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.

A reproducibility condition of measurement belongs to a declared set of conditions used to assess measurement reproducibility. The VIM set includes different locations, operators and measuring systems, with replicate measurements on the same or similar objects. The systems may also use different measurement procedures; the specification should identify both changed and unchanged conditions.^[ref]

For an original physical comparison, laboratories A and B measure the same stable reference block's length at a stated reference temperature. Each laboratory uses its own operator and differential length comparator. Record the block identity, temperature observations, applied corrections, procedure version and instrument reference in each result. Measurements before and after transport help distinguish reference changes from laboratory differences.

Suppose the stipulated readings, in millimetres, areThe laboratory means are $50.001$ and $50.011\mathrm{mm}$, differing by $10\mu \mathrm{m}$. Each pair has sample standard deviation $\sqrt{2}\mu \mathrm{m}$. Small within-laboratory scatter therefore does not remove the difference between laboratory means.

Because location, operator and system changed together, this comparison alone cannot identify which caused the difference. In a chosen additive measurement model,a $10\mu \mathrm{m}$ difference could be assigned entirely to a system contribution or entirely to a location contribution, with the same predicted means. Separating those explanations needs additional comparisons that vary their combinations.

The conditions describe the experiment's scope; they are not a numerical precision result by themselves. Report the complete measurand and what remained common, including any shared measurement standard. A common reference error can affect both laboratories, so agreement under changed conditions does not by itself establish measurement trueness.