Measurement bias

Measurement bias estimates systematic error for a stated measurand, reference and set of conditions. Repeated readings can cluster tightly while remaining offset. JCGM VIM3, measurement bias, systematic measurement error

In the example, a 10.006 mm mean against a 10.000 mm reference gives +0.006 mm bias and a −0.006 mm correction. The 25 independent readings have SD 0.0020 mm. Combining their mean’s uncertainty with the independent 0.0010 mm reference contribution gives about 0.00108 mm standard uncertainty for the bias estimate. A corrected production reading needs its own uncertainty evaluation.

Define the comparison and its sign

For this reference, use the convention:

estimated bias = mean observed value − reference value

Positive bias means measurements read high relative to the reference; negative bias means they read low. This agrees with Minitab's interpretation of its bias-study output. Preserve the sign and units. A magnitude alone cannot tell an inspector whether a proposed correction should be added or subtracted. Minitab: bias and linearity interpretation

The reference should represent the same measurand under compatible conditions. Identify its assigned value and uncertainty, rather than treating a nominal drawing dimension as an independently established reference. A deviation from a product target combines possible product departure with measurement effects; it is not automatically an estimate of instrument bias. Two disagreeing instruments likewise show a difference until an appropriate reference or comparison design establishes more.

Design a bias study for its intended scope

Minitab's linearity-and-bias guidance calls for reference parts with known values, randomized collection and parts covering the actual or expected range. Its conventional study uses one operator for all readings so between-operator variation is not mixed into that analysis. That is a bounded design choice, not evidence that other operators or setups will behave identically. Minitab: study data considerations

Define the fixture, alignment, contact method, software corrections, environment and repetition procedure. Repeating a reading without repositioning does not include the same influences as removing and replacing the specimen. Record the actual sequence and any warm-up, zeroing or adjustment. If conditions change midway, retain that information rather than combining all readings as though they came from one stable process.

NIST warns that calibration under favorable conditions does not necessarily establish performance in the working environment. Temperature, humidity, operator, wear, geometry and other influences can introduce offsets. A shop-floor bias study should investigate the process actually used for inspection, while separately identifying the instrument's calibration evidence. NIST: analysis of bias

Distinguish constant offset from range-dependent response

One reference point establishes information near that point, not across the entire measuring range. NIST illustrates a response model:

observed response Y = intercept a + slope b × reference X + residual

For an ideal same-unit response, a is zero and b is one. A constant offset differs from an error that changes with size. Evaluate residuals and the adequacy of the model rather than assuming any data can be fixed with one straight line. NIST identifies endpoint calibration, reference-value errors, wear and internal instrument problems as possible causes to investigate. NIST: linearity of the gauge

Minitab instead plots bias versus reference value, so its desirable slope is zero. These plots use different vertical quantities and must not be confused. When bias changes across the range, a pooled average can conceal opposite signs at different sizes. Report local bias estimates and the supported correction range rather than using a near-zero overall average as proof of satisfactory response. Minitab: interpreting linearity and bias

Correction is compensation, not disappearance of uncertainty

VIM3 defines correction as compensation for an estimated systematic effect. It may be an additive value, a factor or a table. For the additive sign convention above, correction is the negative of estimated bias. Identify whether software has already applied it to avoid correcting twice. JCGM VIM3, correction

NIST TN 1297 assumes compensation for recognized systematic effects that significantly influence a result. The associated uncertainty is the uncertainty of the correction, not the systematic error itself. Combine uncertainty components and covariance where applicable; a corrected value does not become exact. NIST TN 1297, section 5

Original bounded example: suppose a reference is assigned 10.000 mm with standard uncertainty 0.0010 mm. Twenty-five independent measurements under stable repeatability conditions have mean 10.006 mm and sample SD 0.0020 mm. Treat the reference and measurement mean as independent and temporarily omit other effects:

estimated bias = 10.006 − 10.000 = +0.006 mm
standard uncertainty of mean = 0.0020 / sqrt(25) = 0.0004 mm
standard uncertainty of bias = sqrt(0.0004² + 0.0010²)
                             ≈ 0.00108 mm
additive correction = −0.006 mm

The standard-deviation-of-the-mean approach is a Type A uncertainty evaluation; independence and a stable measurement process matter. More readings can reduce that random contribution, but do not make the common reference uncertainty vanish. NIST TN 1297, section 3

If the validated local correction applies to a subsequent 10.014 mm reading, its corrected value is 10.008 mm. That reading's uncertainty must include its own repeatability and other relevant effects as well as the correction uncertainty. The 0.00108 mm value above belongs to the simplified bias estimate; it is not automatically the uncertainty of an individual corrected production reading.

Statistical significance and practical acceptance

A statistical test of zero bias answers a different question from whether bias is small enough for the intended task. A nonsignificant result does not prove exact zero: limited data or high scatter may leave a meaningful offset unresolved. Compare the estimate and its uncertainty with the allowed measurement error and decision requirements. Avoid declaring product conformity solely from a bias p-value.

When reporting a percentage, identify its denominator. In Minitab's Gage Linearity and Bias Study, %Bias = 100 × |average bias| / process variation. It is not percent of the reference value or automatically percent of tolerance. The software also distinguishes its regression confidence bands from its individual-reference hypothesis tests; they need not yield identical zero-inclusion interpretations. Minitab: bias formulas and statistical calculations

Record the supported conclusion

Retain reference identity, certificate and uncertainty basis, raw readings, units, sign convention, operating conditions, dates, model, bias estimates and uncertainty. State whether values are raw or corrected, the correction revision and applicable range. Identify unresolved effects, corrective action and any follow-up verification. A result from one reference, operator and day should not be reported as evidence covering all parts and future conditions.

Sources were reviewed November 1, 2026. Terminology follows VIM3 rather than the older bias wording retained in parts of the NIST handbook. NIST TN 1297 is the 1994 edition; its cited web sections show later page updates, which are not new editions. Minitab support pages did not display article revision dates.

Inspection and quality documents