Measurement Uncertainty

Start here: ten words every newcomer needs

Overheard on the job

Real-sounding lines from the floor, translated into plain English.

• Cert's at k equals 2, so halve it before it goes in the budget, and root three the spec line.

  TranslationThe reference standard's certificate gives an expanded uncertainty with a coverage factor of 2, so divide by two to get a standard uncertainty; the manufacturer's spec limit is treated as rectangular and divided by the square root of 3.

• Came in OOT at the top point, pull the as-found and start the impact assessment on everything it touched.

  TranslationThe instrument arrived outside its tolerance at the highest test point, so retrieve the before-adjustment data and check every measurement it made since its last good calibration.

• TUR's only 2 to 1 down there, so guard band it or the PFA blows past 2 percent.

  TranslationAt the low end the tolerance is only twice the measurement uncertainty, so pull the acceptance limits inside the tolerance or the chance of passing a bad unit exceeds the 2 percent limit.

• Repeatability's fine, the imported uncertainty is eating the whole budget, a new probe won't move U.

  TranslationThe scatter of repeated readings is small; almost all of the total uncertainty comes from the reference standard's own calibration, so buying a better probe will not reduce the expanded uncertainty.

• Don't tweak it, it's in tol, as-found equals as-left, slap a cal sticker on and send it back.

  TranslationDo not adjust the instrument because it passed; record that the before and after data are the same, label it as calibrated and return it to service.

• En came out at 1.4 on the round robin, so we've either got a bias or the budget's missing a line.

  TranslationIn the interlaboratory comparison the lab's result differed from the reference by more than the combined uncertainties allow, which points to an uncorrected systematic error or an uncertainty component left out of the budget.

• Box says NIST traceable but there's no uncertainty on the cert, so it's not traceable in my book.

  TranslationThe supplier claims traceability, but the certificate states no measurement uncertainty, so the documented chain that real traceability requires is incomplete.

• Let the Jo blocks soak overnight, we're three degrees off reference temperature and that's microns on the long stack.

  TranslationLeave the gauge blocks in the lab until they reach its temperature, because the 3 °C difference from 20 °C would cause several micrometres of thermal expansion error on a long stack.

The basic ideas behind any measurement: measurand, error, uncertainty, accuracy, precision and the model that ties them together.

• Accuracyalso measurement accuracy
  How close a measured value comes to the true value, a qualitative idea rather than a reported number.
• Biasalso measurement bias
  The estimated systematic offset of a measuring system: its average reading minus the reference value.
• Correction
  The amount added to a raw reading to cancel a known, repeatable error, equal to that error with its sign flipped.
• Definitional uncertainty
  Uncertainty that exists because the measurand itself is not defined precisely enough to have one single value.
• Erroralso measurement error
  The signed difference between a measured value and the reference value of the quantity being measured.
• GUMalso the Guide, JCGM 100
  Guide to the Expression of Uncertainty in Measurement, the core reference method for evaluating measurement uncertainty.
• Influence quantityalso influence factor
  A condition that is not the thing being measured but still changes the reading, such as temperature or humidity.
• Measurand
  The exact quantity a measurement is aimed at, pinned down tightly enough that everyone measures the same thing.
• Measurement modelalso model equation, model function
  The equation linking the output quantity you report to all the input quantities that feed into it.
• Measurement resultalso result of measurement
  The reported value of a measurand together with its uncertainty, the full answer rather than just a number.
• Precision
  How well repeat readings of the same item agree with one another, with no reference to whether they are right.
• Random erroralso random effect
  Error component that scatters readings up and down without pattern, so no two repeat readings agree exactly.
• SIalso International System of Units
  International System of Units, the coherent set of seven base units on which all traceable measurement rests.
• Systematic erroralso systematic effect
  Error component that pushes every repeat reading the same way, or follows a pattern you can predict and correct.
• True value
  The idealized exact value of a measurand, which no real measurement can reveal with certainty.
• Trueness
  Where a method's long-run average result lands relative to a reference value; small bias means good trueness.
• Uncertaintyalso measurement uncertainty, MU
  A number that states how much doubt surrounds a measured value, as a standard deviation or as a stated interval.

How individual uncertainty components are evaluated, combined, propagated and expanded into the number on the certificate.

• Combined standard uncertaintyalso combined uncertainty, u_c
  The total standard uncertainty of a result, found by combining all input uncertainties through the measurement model.
• Coverage factoralso k, k-factor
  The multiplier applied to combined standard uncertainty to obtain expanded uncertainty, usually k = 2.
• Coverage interval
  The interval around a result that contains the measurand's plausible values with a stated probability.
• Coverage probabilityalso level of confidence, confidence level
  The probability that the coverage interval contains the measurand's value, usually stated as 95 percent.
• Expanded uncertaintyalso U, U95
  Combined standard uncertainty multiplied by a coverage factor to give an interval with a stated coverage probability.
• Law of propagation of uncertaintyalso LPU, uncertainty propagation
  The first-order formula that combines input standard uncertainties, weighted by sensitivity coefficients, into the output uncertainty.
• Monte Carlo methodalso MCM, Monte Carlo simulation
  Propagating uncertainty by random sampling of input distributions through the measurement model, many thousands of times.
• RSSalso root sum square, quadrature sum
  Root sum of squares, combining independent uncertainty contributions by squaring, adding and taking the square root.
• Sensitivity coefficientalso c_i
  The factor that converts an input's uncertainty into its effect on the output, the partial derivative of the model.
• Standard uncertaintyalso standard measurement uncertainty, u
  Uncertainty expressed as one standard deviation, the common currency for combining uncertainty components.
• Two sigmaalso 2 sigma, 2-sigma
  Shop shorthand for an uncertainty quoted at k = 2, roughly 95 percent coverage. Shop talk
• Type A evaluationalso Type A, Type A uncertainty
  Putting a number on an uncertainty component by running statistics on your own repeat readings.
• Type B evaluationalso Type B, Type B uncertainty
  Sizing an uncertainty component from existing knowledge such as certificates, specs or resolution, with no new repeat data.

The probability distributions, divisors and degrees-of-freedom arithmetic that turn raw information into standard uncertainties.

• Correlationalso correlation coefficient
  A statistical link between two input quantities, so their errors move together and cannot be combined as independent.
• Degrees of freedomalso DOF, nu
  A count of the independent information behind an uncertainty estimate, showing how reliable that estimate is.
• Normal distributionalso Gaussian distribution, Gaussian
  The bell-shaped distribution assumed for most certificate values and averaged readings, set by mean and standard deviation.
• PDFalso probability density function, distribution
  Probability density function, the curve describing how likely each possible value of a quantity is.
• Rectangular distributionalso uniform distribution, rectangular
  A distribution giving equal likelihood to every value between two limits, used when only the bounds are known.
• Root threealso root-three it, divide by root three
  Shop shorthand for dividing a rectangular limit by the square root of 3 to turn it into a standard uncertainty. Shop talk
• Standard deviationalso SD, s
  The usual measure of scatter in a set of values, the square root of the average squared deviation from the mean.
• Student t-distributionalso t-distribution, Student's t
  A bell-shaped distribution with heavier tails than the normal, used to set coverage factors when data are limited.
• Triangular distributionalso triangular
  A distribution peaked at the center and falling linearly to zero at the limits, with a divisor of root six.
• U-shaped distributionalso arcsine distribution, U-shaped
  A distribution where values near the limits are most likely, used for cycling effects such as RF mismatch or room temperature.
• Welch-Satterthwaite formulaalso W-S formula, Welch-Satterthwaite
  The equation that estimates effective degrees of freedom for a combined uncertainty, used to pick the coverage factor.

Building, reviewing and reporting uncertainty budgets, certificates and the specs that feed them.

• Cal with dataalso calibration with data, data cal
  A calibration ordered with full measured readings and uncertainties on the certificate, not just a pass or fail. Shop talk
• Calibration certificatealso cal cert, cert
  The document reporting a calibration's results, uncertainties, conditions and traceability for one specific item.
• Countsalso digits, LSD
  The steps of the last digit on a digital display, used in specs such as plus or minus 2 counts. Shop talk
• Double countingalso double dipping
  Budget slang for entering the same physical effect twice under different names, which inflates the uncertainty. Shop talk
• Imported uncertaintyalso reference standard uncertainty, uncertainty of the standard
  The uncertainty carried into a measurement from the calibration certificate of the reference standard used.
• Significant digitsalso significant figures, sig figs
  The convention of reporting uncertainty to one or two significant digits and rounding the result to match.
• Specalso specs, accuracy spec
  Shop clipping for a manufacturer's accuracy specification, the published limits an instrument should stay within. Shop talk
• Uncertainty budgetalso budget, uncertainty analysis
  A table listing every uncertainty source in a measurement with its size, distribution, divisor and contribution to the total.

Standards, hierarchies, accreditation and the documented chains that link a shop gauge back to the SI.

• Adjustmentalso adjust
  Changing an instrument so its readings move closer to the correct values, a step separate from calibration.
• Artifactalso artifact standard, artefact
  A physical object that embodies a known value of a quantity, such as a mass, gauge block or standard resistor.
• Calibrationalso cal
  Comparing an instrument with a better-known standard and recording how its readings line up with the standard's values.
• Calibration hierarchyalso traceability pyramid, metrology pyramid
  The ranked levels of standards, from primary realizations down to working instruments, through which values flow.
• Calibration intervalalso cal interval, recall interval
  The scheduled time between calibrations of an instrument, set to keep the chance of drifting out of tolerance low.
• Check standardalso control standard, check artifact
  A stable item measured regularly to confirm a measurement process still behaves as it did when characterized.
• CMCalso calibration and measurement capability, best measurement capability
  Calibration and measurement capability, the best uncertainty a lab can routinely deliver for a given calibration.
• ISO 17025also ISO/IEC 17025, 17025
  The international standard setting the competence requirements for testing and calibration laboratories.
• NMIalso national metrology institute, national lab
  National metrology institute, the body that realizes a country's measurement units at the top of its traceability chain.
• Primary standardalso primary measurement standard
  A standard that gets its value straight from the unit definition, not from calibration against another standard.
• Reference standardalso lab reference, master
  A lab's highest-level standard for a quantity, used only to calibrate other standards and never for routine work.
• Traceabilityalso metrological traceability
  Proof that a result ties back to the SI or another stated reference, with every calibration in between on record.
• Traceability chainalso calibration chain, chain
  The documented sequence of calibrations linking a working instrument back to national or SI-level standards.
• Transfer standardalso travelling standard, transport standard
  A stable, portable standard used to carry a value from one lab or standard to another for comparison.
• Verificationalso check, verify
  A check that an item is good enough for its stated requirements, usually ending in pass or fail with no full calibration data.
• Working standardalso bench standard, working set
  A standard used routinely to calibrate instruments, itself checked against the lab's reference standard.

Pass or fail calls against a tolerance, and the ratios, risks and guard bands that make those calls defensible.

• Decision rule
  The agreed method for factoring measurement uncertainty into a pass or fail call against a spec.
• Guard bandalso guard banding, guardband
  A margin that pulls acceptance limits inside the tolerance limits to cut the risk of passing nonconforming items.
• MPEalso maximum permissible error, maximum permissible measurement error
  Maximum permissible error: the error limit an instrument must stay inside to conform, set by its spec, a standard or the law.
• PFAalso probability of false accept, consumer's risk
  Probability of false accept, the chance that a nonconforming item is measured and passed as good.
• PFRalso probability of false reject, producer's risk
  Probability of false reject, the chance that an item actually in tolerance is measured and failed.
• Simple acceptancealso shared risk, zero guard band
  A decision rule that passes any item whose measured value lies inside the tolerance, leaving uncertainty out of the call.
• Specific riskalso conditional risk, bench-level risk
  The probability that one particular measured item is out of tolerance, given its actual measured value.
• TARalso test accuracy ratio, accuracy ratio
  Test accuracy ratio, the UUT tolerance divided by the accuracy spec of the standard used to test it.
• Tolerancealso tol, spec limit
  The allowed deviation from nominal that an item or instrument may show and still be accepted.
• TURalso test uncertainty ratio, uncertainty ratio
  Test uncertainty ratio, the tolerance being checked divided by the expanded uncertainty of the measurement process.

Precision conditions, instrument behavior and the comparisons that show a lab's numbers hold up over time.

• Driftalso long-term drift, aging
  Gradual change in an instrument's readings over time that comes from the instrument itself, not from what it measures.
• En numberalso En, E sub n
  A score comparing a lab's result with a reference value, scaled by both expanded uncertainties; 1 or less passes.
• Hysteresis
  A reading difference at the same input depending on whether that input was approached from below or above.
• Intermediate precisionalso within-lab reproducibility, long-term precision
  Precision measured within one lab over longer periods, with changes such as different days, operators or recalibrations.
• Offsetalso zero offset, zero error
  A constant error that shifts every reading by the same amount, most often seen as a nonzero reading at zero input.
• Proficiency testingalso PT, proficiency test
  Judging a lab's performance by having it measure circulated items and scoring its results against a reference value.
• Reference temperaturealso standard reference temperature, 20 degree rule
  The standard temperature at which a quantity is specified, 20 degrees C for dimensional measurements.
• Repeatabilityalso short-term precision
  How tightly readings bunch when one person repeats a measurement with the same setup, in one place, in one short sitting.
• Reproducibilityalso between-lab precision
  How well results on the same item agree when the lab, operator, equipment or day is changed on purpose.
• Resolutionalso display resolution, readability
  The finest step an instrument can display, such as one count of the last digit on a digital readout.
• Stabilityalso long-term stability, short-term stability
  The ability of an instrument or standard to hold its calibrated values as the weeks and months pass.

The stickers, tags, shorthand and bench slang heard every day in a working calibration lab.

• As foundalso as-found data, as received
  Calibration data recorded on an instrument as received, before any adjustment or repair is made.
• As leftalso as-left data, as returned
  Calibration data recorded after adjustment or repair, showing the condition the instrument returns to service in.
• Cal duealso due date, cal due date
  The date by which an instrument must be calibrated again, printed on its sticker and tracked by the recall system. Shop talk
• Cal stickeralso cal label, cal tag
  The label on a calibrated instrument showing who calibrated it, when, and when the next calibration is due. Shop talk
• Four to onealso 4:1, 4 to 1 rule
  The rule of thumb that measurement uncertainty should be no more than a quarter of the tolerance being checked. Shop talk
• Golden unitalso golden sample, gold unit
  A known-good, carefully characterized example of a product kept to check test stations and fixtures. Shop talk
• Jo blocksalso Jo-blocks, gauge blocks
  Shop name for gauge blocks, precision steel or ceramic blocks wrung together to build reference lengths. Shop talk
• Limited calalso limited calibration, restricted cal
  A calibration covering only some ranges or functions of an instrument, flagged with a special sticker. Shop talk
• NIST traceablealso NIST-traceable, traceable to NIST
  A common label phrase claiming a measurement links back to US national standards, often used loosely. Shop talk
• OOTalso out of tolerance, out-of-tol
  Out of tolerance, an as-found calibration result outside the instrument's allowed limits. Shop talk
• Out of calalso expired, overdue
  Past its calibration due date, so the instrument is not approved for use regardless of how well it performs. Shop talk
• Pencil whipalso pencil-whipping, pencil-whipped
  Shop slang for filling in calibration or inspection records without actually doing the measurements. Shop talk
• Recallalso recall system, recall list
  The system that schedules instruments back for calibration before their due date, and the act of calling them in. Shop talk
• Red tagalso red-tagged, reject tag
  A reject tag marking an instrument as unfit for use, or the act of pulling one from service with it. Shop talk
• Round robinalso interlaboratory comparison, ILC
  An interlaboratory comparison in which one artifact or sample travels from lab to lab to be measured by each. Shop talk
• Self-calalso autocal, self-calibration
  An instrument's built-in routine that realigns its internal ranges against its own onboard reference. Shop talk
• Soakalso thermal soak, soak time
  Letting an instrument, artifact or part sit in the lab environment until it reaches thermal equilibrium. Shop talk
• Tweakalso trim, touch up
  Shop slang for making a small adjustment to an instrument to bring its readings back toward nominal. Shop talk
• UUTalso DUT, device under test
  Unit under test, the instrument being calibrated or tested, as opposed to the standard used to check it.

Frequently asked questions

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