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A blank indication is the measured response obtained when the quantity of interest is assumed absent or not contributing. In analytical chemistry, an analytical blank supplies the material used for that comparison. The indication is an output of the measurement system; it is neither the material itself nor necessarily a zero reading.^[ref]

For an invented example, a blank produces5 detector-response units. A sample produces15 units. Under an additive background model, the response attributable to the sample above this blank is10 units. Converting that response into an analyte concentration requires the appropriate instrument calibration. Five detector units do not mean5 micromolar simply because both numbers describe the same measurement sequence.

A blank value is obtained when an applicable conversion model expresses the blank response as a measured quantity value.^[ref] Keeping that conversion explicit prevents confusing an instrument indication with a reported concentration. Repeated blank indications also provide information about background variability used in a limit of detection. A stable offset and a noisy background can have the same mean while supporting different detection performance; blank correction of the mean alone does not make their standard deviations equal.

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.

Instrument calibration applies measurement calibration to a particular measuring instrument: reference inputs with known measurement uncertainty are compared with its indications to obtain a relation for interpreting later readings. It determines a response and its measurement uncertainty; physically adjusting the instrument is a separate operation.^[ref]

For an original balance example, an empty pan indicates $0.020\mathrm{g}$ and a reference mass of $100.000\mathrm{g}$ indicates $100.220\mathrm{g}$. An assumed linear measurement model isA later indication $r=50.120\mathrm{g}$ givesThe correction here is $-0.120\mathrm{g}$; subtracting only the measurement zero offset leaves the scale error uncorrected. These illustrative readings are exact arithmetic inputs, not a claim of zero measurement uncertainty.

In a real comparison, apply several reference loads across the working range, remove and replace them, and repeat points while increasing and decreasing the load. Two points alone fit a line exactly and cannot establish linear response. Record environmental conditions, reference values and their measurement uncertainties, scatter and instrumental drift. Subsequent results inherit uncertainties in the indication and fitted parameters, including their covariance. Recheck after adjustment because the original response relation may have changed.

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.

A measured quantity value is a value used to represent a measurement result. It may be obtained from one observation or calculated from replicate observations, for example as an arithmetic mean. The VIM distinguishes this value from a raw measurement indication and from the fuller result with its measurement uncertainty.^[ref]

For an original electrical resistance example, suppose three instrument indications are $100.04$, $100.06$ and $100.05\Omega$. A measurement calibration gives additive indication offset $b=0.02\Omega$, so the corrected values are $100.02$, $100.04$ and $100.03\Omega$. Their arithmetic mean is the representative measured quantity valueThis value is a numerical estimate of the specified measurand, such as the resistor's resistance at a stated temperature. It is not established as an exact true value merely by correcting the indications.

The three values have sample standard deviation $s=0.01\Omega$. If repeat deviations are independent, their contribution to the mean's standard uncertainty is $s/\sqrt{3}\simeq 0.0058\Omega$. Suppose the common correction has independent standard uncertainty $u(b)=0.02\Omega$. First-order propagation of uncertainty givesRepeating the readings reduces the first term under these assumptions; it does not repeatedly remeasure and average away the same common correction. These are illustrative uncertainty inputs, not observed equipment data.

Reporting the measured quantity value therefore requires its unit and measurand definition. Reporting the complete measurement result also identifies the associated measurement uncertainty, its convention and relevant conditions. A change from ohms to milliohms changes the numerical expression, while leaving the represented physical value unchanged.

A measurement indication is the value supplied by a measurement instrument or measuring system. It may appear as a pointer position, displayed number, printed output or transmitted code. The indication and the corresponding measurand value need not be values of the same kind of quantity.^[ref]

For an original mechanical readout, suppose the indicated pointer position is a length $z$, related to input pressure $p$ byThe measurement indication $z=21.00\mathrm{mm}$ then corresponds to $p=(z-z_0)/S=100.0\mathrm{kPa}$ under this measurement model. The position is observable; the pressure value is inferred using the response relation. A printed pressure scale could carry out part of that conversion physically without changing the underlying distinction.

If the pointer position is uncertain by $0.10\mathrm{mm}$, that contribution corresponds to $0.50\mathrm{kPa}$ in this stipulated linear model. Uncertainty in the zero $z_0$, transducer sensitivity $S$, temperature response and instrumental drift can add further contributions. Closely spaced scale markings therefore do not establish the total measurement uncertainty.

Record the original indication and instrument settings when applying corrections. A corrected measured quantity value can change after improved measurement calibration even though the recorded indication remains the same. For example, revising the assumed zero from $1.00$ to $1.20\mathrm{mm}$ changes the inferred pressure from $100.0$ to $99.0\mathrm{kPa}$. The complete measurement result accompanies the inferred value with its uncertainty and relevant conditions; the raw measurement indication alone cannot supply that information.

A measurement method describes the general logical arrangement of operations used to make a measurement. A measurement procedure supplies the detailed instructions for implementing that arrangement with a particular measuring system. The VIM lists substitution measurement methods, null measurement methods, differential methods, and direct or indirect methods among the possible descriptions.^[ref]

For an original substitution measurement method, drive an unknown resistor with a fixed electric current $I$ and record a voltmeter indication. Replace it by an adjustable reference resistor without changing $I$ or the other relevant conditions, and adjust the reference until the indication agrees. In an ideal measurement model,so matching $v_x=v_s$ implies $R_x=R_s$. The common additive readout offset $v_0$ cancels. This cancellation depends on the current, connections and offset remaining common; the name of the method alone does not guarantee those conditions.

A null measurement method instead adjusts a reference to make a difference signal vanish, as in a balanced Wheatstone bridge. A resistance inferred from separately measured electric potential difference and electric current uses the relation $R=V/I$. These are descriptions of how the information is obtained; the operational record must still specify apparatus, settings, timing, reference values and the measurement uncertainty. The measurement principle concerns the physical phenomenon used, while the measurement method concerns the organization of the measurement. Different methods can exploit the same physical principle.

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.

A measurement principle is the phenomenon on which a measurement is based. The VIM gives the thermoelectric effect used to measure temperature as a physical example.^[ref] Naming that phenomenon identifies the physical connection that makes an observable signal informative about the measurand.

A thermocouple uses the Seebeck effect to produce an electric potential difference associated with temperatures along a circuit of dissimilar conductors. In a chosen approximation with constant coefficient $S$, the measurement model can be writtenwhere $T_r$ is the reference-junction temperature. For an original ideal example, choose $S=40\mu \mathrm{V}{\mathrm{K}}^{-1}$, $T_r=20{}^{\circ }\mathrm{C}$ and $V=2.00\mathrm{mV}$. The inferred temperature difference is $50\mathrm{K}$, so $T_h=70{}^{\circ }\mathrm{C}$. These stipulated values illustrate the model, not the calibration of a particular thermocouple type.

The reference condition matters physically: the same signal at $T_r=25{}^{\circ }\mathrm{C}$ would imply $T_h=75{}^{\circ }\mathrm{C}$ in this model. A readout that neglects the reference temperature can give a precise-looking indication without measuring the intended temperature correctly. The measurement principle explains why the signal arises; it does not by itself supply all corrections or the measurement uncertainty.

The measurement method describes how operations are organized around the principle, for example comparing an output with a reference. The measurement procedure specifies the actual conductors, junction arrangement, temperature references, readout settings, settling interval and calculations. Different measuring systems can share a measurement principle while implementing different methods and procedures.

A measurement procedure describes in sufficient detail how a measurement is performed, including its measurement method, measurement model and the calculations that produce a measurement result. The VIM notes that the description usually enables an operator to carry out the measurement and can include a target measurement uncertainty.^[ref] Naming an instrument or writing a final equation alone leaves much of this operational description unspecified.

Consider an original procedure for the resistance measuring system described above. Specify the test resistor and temperature, the two-terminal lead arrangement, source current, readout settings and settling time. Record the measured or assigned current with its measurement uncertainty. First replace the test resistor by a short whose resistance is negligible in the chosen model, and record indication $V_s$. Insert the test resistor without changing the declared lead configuration, allow the specified settling interval and record $V_x$. Repeating the short reading after the sample reading helps check stability.

Assume the current $I$, lead resistance $R_L$ and additive readout offset $V_0$ remain common to the paired readings. Thenso the procedure's calculation isFor stipulated $V_s=3\mathrm{mV}$, $V_x=103\mathrm{mV}$ and $I=1\mathrm{mA}$, this gives $100\Omega$. The paired measurement removes the common lead and zero contributions under the stated model.

The sequence matters because those contributions can change. If the readout offset rises by $0.5\mathrm{mV}$ between the short and sample readings, the same calculation is shifted by $0.5\mathrm{mV}/(1\mathrm{mA})=0.5\Omega$. This is an original instrumental drift example, not observed equipment performance.

Document which operations are repeated, how corrections are obtained, how deviations are handled and which uncertainty contributions remain. The procedure turns the apparatus and model into a repeatable set of operations; it does not make the supplied references, stability assumptions or recorded values exact.

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.

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.

A measurement result comprises the values attributed to a measurand together with the information needed to interpret those values. It commonly takes the form of a measured quantity value and its measurement uncertainty, but the result can contain a fuller probability distribution. A displayed number alone need not supply this information.^[ref]

For an original electrical resistance example, report a corrected value $R=100.020\Omega$ at $20{}^{\circ }\mathrm{C}$, with standard uncertainty $u(R)=0.010\Omega$. Specify that the uncertainty is a standard uncertainty, identify the resistor and the temperature condition, and retain the measurement procedure and measurement calibration records. Writing only “100.020” omits both the unit and the meaning of the last digits. Writing $100.020\pm 0.010\Omega$ without stating what the second number represents is also incomplete.

An alternative report might use expanded uncertainty $U=0.020\Omega$ with coverage factor $k=2$. This is a different uncertainty convention for the same central estimate; it is not a newly observed change in the resistor. A probability interpretation requires the distributional assumptions accompanying that convention.

An instrument's indication, a corrected measured quantity value and the complete measurement result therefore play different roles. Corrections from the measurement model, the specified measurand, environmental conditions and metrological traceability can all matter when comparing results. Extra displayed digits cannot replace the omitted measurement uncertainty.

A measurement standard realizes a specified quantity with an assigned value and associated measurement uncertainty, and is used as a reference. It can be a physical artifact, a measuring system or a suitable reference material. The value and its measurement uncertainty apply under stated conditions and at the relevant time; a nominal label alone is insufficient.^[ref]

For an original comparison, take a reference resistor with assigned electrical resistance $R_s=100.000\Omega$ and standard uncertainty $u(R_s)=0.001\Omega$. A comparison measures a working resistor's ratio $q=R_x/R_s=1.00020$, with independent $u(q)=0.00001$. The measurement model givesand first-order propagation of uncertainty givesThe reference's measurement uncertainty remains in the result even if the ratio could be read with arbitrarily many digits.^[ref]

A practical comparison records reference conditions, connecting arrangements and repeated readings while checking effects such as instrumental drift. A primary measurement standard has a particular basis for its assigned value; a working reference need not be primary to transfer useful metrological traceability. Distinguish this physical reference from a written technical specification, which is another use of the word standard.

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 measuring chain is one successive signal path through a measuring system, beginning at a sensor and ending at an output element. The VIM illustrates this with both an electro-acoustic chain and a mechanical chain; a measuring chain need not be electronic.^[ref]

Consider an original force measurement: a load cell produces an electric potential difference, an amplifier scales that signal, an analog-to-digital converter encodes it, and software converts the code to a force value. This is one measuring chain within the larger measuring system, which also includes its excitation supply, references and mounting arrangements. The load cell acts as a measuring transducer.

In an ideal linear model, let sensor response be $S=2\mathrm{mV}{\mathrm{N}}^{-1}$, amplifier gain $G=100$, and converter step $q=1\mathrm{mV}$ per code increment. If the additive output offset is $n_0=10$ increments, the numerical output isThus $n=610$ implies $F=(610-10)/200=3\mathrm{N}$. These are stipulated teaching values, not measured equipment performance.

The example exposes why measurement calibration must describe the relevant path. Changing amplifier gain changes the relation between output and force even if the load cell is untouched. A saturated stage can also discard information that later conversion cannot restore. Gain uncertainty, offsets, instrumental drift and finite conversion steps contribute at different points; treating the final display's increment as the whole measurement uncertainty overlooks those contributions.

A measuring system combines one or more measurement instruments with the other devices needed to produce measured values for specified quantities over specified intervals. A system can also consist of a single instrument when it performs the required function on its own.^[ref] The system boundary identifies which physical components and signal-processing operations contribute to a measurement result.

For an original electrical example, assemble a current source, a test resistor, two connecting leads, a voltmeter and the calculation used to infer electrical resistance. The intended measurand is the test resistor's resistance $R_x$ at stated conditions. In a chosen ideal model, the current is $I$, the leads contribute total resistance $R_L$, and the readout has additive measurement zero offset $V_0$:Here the voltmeter measures an electric potential difference across the complete resistor-and-lead path, with negligible input-current loading.

With $I=1\mathrm{mA}$, $R_L=2\Omega$, $V_0=1\mathrm{mV}$ and indicated potential difference $103\mathrm{mV}$, the model gives $R_x=100\Omega$. Dividing the indication by the current without either correction would instead give $103\Omega$. The numerical resolution of the voltmeter alone therefore does not describe the whole measuring system's result.

A measuring chain describes successive signal transformations within such an arrangement. Its physical response and subsequent calculation belong in the system description, together with measurement calibration, reference conditions and relevant measurement uncertainty. Changing a lead connection, source setting or correction can change the result while leaving the main readout instrument unchanged. The measurement procedure records how that particular system is operated.

A measuring transducer is a device whose output quantity has a specified relation to its input quantity and is used in measurement. VIM examples include a thermocouple, a strain gauge and a Bourdon tube.^[ref] A measuring transducer provides a link in a measuring chain; it need not itself display a finished measurement result.

For an original pressure readout, choose a linear modelwith pressure $p$, output electric potential difference $V$, transducer sensitivity $S=2\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, and offset $V_0=1\mathrm{mV}$. An output $V=201\mathrm{mV}$ then corresponds to $p=100\mathrm{kPa}$. An amplifier, analog-to-digital converter and display can follow the transducer, each contributing to the whole measuring system.

The inverse calculation $p=(V-V_0)/S$ exposes distinct uncertainty contributions. Holding the other inputs fixed, a small output change $\delta V$ changes inferred pressure by $\delta V/S$; a small offset error changes it by $-\delta V_0/S$. An output increment $0.2\mathrm{mV}$ corresponds to $0.1\mathrm{kPa}$ for the stipulated sensitivity, but does not establish a total measurement uncertainty of that size.

Characterize the relevant range, temperature conditions, response time and possible instrumental drift during measurement calibration. The relation can be nonlinear, in which case local transducer sensitivity is the appropriate derivative rather than one gain valid everywhere. The definition also allows input and output quantities of the same kind; it does not require changing from a mechanical quantity to an electrical one. A sensor denotes the part directly affected by the phenomenon being sensed, whereas a complete measuring chain can contain further measuring transducers.

Metrological traceability is a property of a measurement result: a documented, unbroken sequence of measurement calibrations relates it to a stated reference, and every link contributes to its measurement uncertainty. The reference can be a practical realization of a measurement unit, a measurement procedure or a measurement standard.^[ref]

Consider an original mass-measurement chain: a reference measurement standard calibrates a working mass, which is used for instrument calibration of a balance, which weighs an object. Suppose the reference contributes $2\mathrm{mg}$ of standard uncertainty, the transfer adds an independent $3\mathrm{mg}$, and the final weighing adds an independent $4\mathrm{mg}$. With unit sensitivity to these additive contributions,The intermediate working mass has $\sqrt{13}\mathrm{mg}$ of standard uncertainty. That value already includes the reference contribution; adding the same $2\mathrm{mg}$ again at the final step would double-count it. Correlated contributions require covariance terms rather than the independent-input calculation.^[ref]

Documentation must identify the reference, comparison procedures, dates, applicable conditions and uncertainty contributions. A certificate or instrument label alone does not supply the complete chain for every later result. Metrological traceability also does not ensure that the resulting measurement uncertainty is small enough for the intended use.