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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.

Measurement calibration establishes a relation between an instrument's indications and reference values, with the relevant measurement uncertainty. It is distinct from changing the instrument until it reads correctly: an instrument can be calibrated by determining a response curve and applying a correction afterward.

A practical voltage experiment connects a meter to several reference values across its working range and repeats the sequence in both directions. Fitting $V_{\mathrm{indicated}}=a{V}_{\mathrm{reference}}+b$ estimates a scale factor and measurement zero offset; departures from that relation test the response model. Repetition at later times checks instrumental drift. Uncertainty in the reference, the fitted parameters, and unresolved departures belongs in the measurement uncertainty budget, even if the displayed readings appear very stable.^[ref]

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.

Identify the physical coupling that causes a systematic error and change the apparatus so that it can be measured or cancelled. measurement calibration against known reference standards at several points reveals zero and gain errors; blanks and background runs measure additive contributions. Carry uncertainties of the standards and fitted corrections into the final result.

Reversal provides a particularly transparent test. If $D_{+}=S+b$ and $D_{-}=-S+b$, the combination $(D_{+}-D_{-})/2$ isolates $S$ while $(D_{+}+D_{-})/2$ measures the measurement zero offset. Interleave and repeat the reversals so drift can be detected. The cancellation assumes a stable measurement zero offset and a genuinely odd signal; a common gain error remains. null measurements and bridge comparisons can reduce dependence on detector gain. Swapping sensors or leads exposes asymmetry; checking alignment, shielding, grounding and temperature control tests specific unwanted couplings. Varying signal amplitude or measurement frequency can reveal heating, nonlinear response or pickup.

Use independent measurement principles where possible, and test the predicted response to each deliberate change. Repeated readings alone do not remove a fixed systematic error. Correct identified significant effects and retain uncertainty for imperfectly known corrections; complete elimination cannot generally be demonstrated. Type A and Type B classify how uncertainty is evaluated, rather than simply meaning random measurement errors and systematic errors.^[ref]

A systematic error is a component of measurement error that remains constant or changes predictably when measurements are repeated under specified conditions. A ruler with an incorrect scale, a thermometer with a measurement zero offset, and an unaccounted instrumental drift can all produce such effects. Closely agreeing readings can therefore have poor measurement accuracy: repetition tests their scatter, not the correctness of the shared reference.

An estimated systematic error should be corrected when possible, with the correction's measurement uncertainty included in the measurement uncertainty budget. Suppose a balance reads $m+b$ and a reference gives an estimate $\hat{b}$ of its offset. The corrected result is $m_{\mathrm{read}}-\hat{b}$; uncertainty in $\hat{b}$ remains even if the same unknown offset affected every weighing. Changing the reference, using a blank, or testing systematic-error cancellation by reversal can reveal effects that a long sequence of identical readings misses. The Type A evaluation of uncertainty and Type B evaluation of uncertainty distinction concerns how uncertainty is evaluated, so neither label is synonymous with systematic error.^[ref]