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A Bourdon tube pressure gauge combines a pressure-sensitive Bourdon tube with a motion-transmission mechanism, pointer and calibrated scale. Pressure-driven elastic deformation moves the free end of the tube; a linkage and geared movement convert that motion into an indication on the dial. WIKA's technical diagram identifies the tube, end piece, link, movement, pointer and pressure connection as distinct parts.^[ref]

The complete gauge is a measuring system. Its measurement indication depends on the sensing tube and the motion transmission, including possible backlash and hysteresis. For a vented case, the tube responds to pressure relative to the surrounding atmosphere, so the intended quantity is gauge pressure. The dial alone does not define an absolute pressure reference.

For an original instrument calibration comparison, connect the gauge and a suitable pressure reference to a common fluid source. Apply several increasing pressure steps, wait for stable readings, and return through the same pressures. Record each discrepancy $e=p_{\mathrm{gauge}}-p_{\mathrm{ref}}$ and distinguish the two loading directions. This tests the assembled readout rather than only the elastic element.

The locations of the pressure ports can matter as much as their shared supply. If the test gauge's port is $0.5\mathrm{m}$ below the reference port in a stationary water-filled connection, take $\rho =1000\mathrm{kg}{\mathrm{m}}^{-3}$ and $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$. Hydrostatic pressure givesWithout that correction, a correct lower gauge can appear to overread the upper reference. These are original apparatus values, not manufacturer test data.

Read the error specification for the actual model and size. WIKA's June2025 US sheet, for example, states an accuracy of $\pm 1.0\%$ of span for the specified four- and six-inch versions, while listing a different specification for the smaller version.^[ref] A percentage of span is not the same percentage of the instantaneous reading. Retain range, conditions, corrections and measurement uncertainty with the reported result.

Input-referred resolution expresses an output increment or distinguishable output change in units of the quantity applied to a measuring system. For local response $y=f(x)$ with nonzero transducer sensitivity $S=dy/dx$, an output increment $q_y$ corresponds approximately toState what output criterion is being referred: one converter-code step, a noise-based threshold and a repeatably distinguishable input change are different specifications. Walt Kester's converter tutorial distinguishes code transitions, input-referred noise and noise-based resolution measures.^[ref]

For an original pressure readout, suppose a transducer has $S=5\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, followed by an ideal 12-bit analog-to-digital converter spanning $2.048\mathrm{V}$. Its code step is $q_V=2.048/4096=0.0005\mathrm{V}$, corresponding to $q_p=0.1\mathrm{kPa}$. This arithmetic specifies a nominal increment, rather than demonstrating that two pressures separated by that amount can be reliably distinguished.

Place an ideal amplifier of gain ten before the converter. The combined sensitivity becomes $50\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, so the converter step corresponds to $0.01\mathrm{kPa}$. With zero offset in this model, the pressure span mapping onto the converter simultaneously shrinks from $409.6$ to $40.96\mathrm{kPa}$. Gain trades converter coverage against nominal input increments; it does not create an unlimited input range.

Suppose the transducer itself contributes $0.25\mathrm{mV}$ rms output noise. That is $0.05\mathrm{kPa}$ input-referred noise. The added ideal gain scales both that signal and that noise, leaving this pressure-noise contribution unchanged. More display digits therefore need not improve the useful measurement resolution.

For a nonlinear response, repeat the conversion at the relevant operating point and account for the actual observation bandwidth and processing. Near detector saturation, sensitivity can approach zero and the local conversion becomes uninformative. A complete measurement result also includes measurement uncertainty, which contains calibration and other contributions beyond the chosen resolution criterion.

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 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.

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 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 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 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.

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.

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.

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.

A substitution measurement method compares an unknown with a reference by placing them successively in the same relevant position of a measuring system. The comparison seeks a match or measures a difference while retaining as much of the system response as possible. The VIM lists substitution among measurement methods; the detailed sequence belongs to the measurement procedure.^[ref]

For a physical application, NIST's double substitution weighing procedure compares a standard and an unknown of the same nominal mass twice, using a weighing instrument as a comparator. It also determines response with a known sensitivity mass and includes measurement-assurance checks.^[ref] The measurement standard supplies the reference value; the comparator need not establish the whole mass independently from its own zero.

An original simplified drift model shows why sequence matters. Let a comparator indication at equally spaced time index $t$ bewith fixed response coefficient $a$, additive offset $b$ and linear instrumental drift $d$. Observe standard S at $t=0$, unknown X at $t=1,2$, and S again at $t=3$. The mean X indication and mean S indication have the same mean time $3/2$, givingBoth the constant offset and the stipulated linear drift cancel. For $m_S=m_0=100\mathrm{g}$, $a=500{\mathrm{g}}^{-1}$, $b=10$ and $d=2$, an unknown $m_X=100.004\mathrm{g}$ gives indications $10,14,16,16$. Their paired means differ by two, recovering $0.004\mathrm{g}$.

This teaching sequence isolates one cancellation mechanism; it is not the full NIST procedure. Nonlinear drift, unequal timing, changing response or different positioning can defeat it. NIST's procedure separately addresses buoyancy and uncertainty contributions.^[ref] A close match does not remove the reference's measurement uncertainty or establish that the substitution left every relevant condition unchanged.

Transducer sensitivity describes how much the output of a measuring transducer changes when its input changes. For an output $y$ responding smoothly to input $x$, a local model usesVIM defines sensitivity of a measuring system through the quotient of corresponding indication and input changes, noting that sensitivity can depend on the input value and that the changes used must be appreciable relative to resolution.^[ref] The derivative is the smooth local limit of that response ratio.

For an original pressure-to-potential transducer, stipulateIts transducer sensitivity isAt $p=100\mathrm{kPa}$, the output is $0.310\mathrm{V}$ and the sensitivity is $4\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$. Across the finite interval from $100$ to $110\mathrm{kPa}$, output changes by $41\mathrm{mV}$, so the measured response ratio is instead $4.1\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$. Specify the operating point or interval rather than treating these two slopes as contradictory.

An output increment $q=0.2\mathrm{mV}$ corresponds locally to input-referred resolution $q/|S|=0.05\mathrm{kPa}$ at the first operating point. This conversion is not a complete uncertainty statement. Increasing electronic gain can enlarge output noise as well as the signal; detector saturation can flatten the response and destroy local invertibility.

Estimate transducer sensitivity with known input steps, repeated outputs and checks for changing zero, loading and temperature. In a linear response $y=Sx+b$, a constant offset $b$ cancels from differences; a changing offset does not. Retain both the sensitivity relation and its uncertainty in measurement calibration, and propagate the relevant contributions when reporting a measurement result.