From reference standards to a calibration curve

Choose reference standards appropriate to the quantity, range, and target uncertainty. A standard is not magically exact: its assigned value has an uncertainty and applies under stated conditions. Compare the instrument against several values spanning its intended range, and repeat selected points to inspect repeatability. Record temperature, loading, timing, and configuration so the relation being calibrated matches the conditions of use. A comparison made under different conditions may need an additional correction rather than a more elaborate fitted curve.

Calibration differs from adjustment, which changes the instrument to produce prescribed indications. It also differs from verification, which asks whether specified requirements are met. An instrument can be calibrated and found unsuitable for a particular tolerance. Conversely, turning its zero adjustment until a display looks right does not by itself establish the remaining scale or its uncertainty. If an adjustment changes the response, check the resulting calibration instead of treating the old relation as automatically valid.

A straight line is a hypothesis about instrument behavior, not a default truth. Inspect residuals against input, time, and measurement direction. A curved pattern suggests nonlinearity; a difference between ascending and descending runs suggests hysteresis; a changing zero suggests drift. Replication at fixed inputs helps distinguish scatter from a lack of fit. When uncertainties of reference inputs are important, ordinary least squares that treats those inputs as exact may be an inadequate model of the calibration data.

Interpolation uses the calibration relation between tested inputs. Extrapolation applies it beyond them, where untested saturation or nonlinear response can dominate. A small fitting residual within the tested interval does not justify arbitrary extrapolation. Also distinguish uncertainty of the inferred mean calibration response from uncertainty for a new individual indication: the latter usually includes a new repeatability contribution. State what the uncertainty applies to, or a precise-looking curve can lead to overconfident future measurements.

The calibration certificate is an input to later measurements, not a replacement for their uncertainty budgets. Subsequent results can also depend on resolution, repeatability, environmental corrections, transport effects, or changes since calibration. Keep the sign convention for corrections explicit: an indication error is indication minus reference, so its additive correction has the opposite sign. A certificate that reports error cannot be applied by adding that error again without checking the definition used.

A recalibration interval should be justified by stability evidence, use, and required performance rather than a universal calendar rule. Intermediate check standards can reveal changes between full calibrations. If a check fails, investigate which measurements could have been affected since the last satisfactory evidence. Maintaining a calibration history helps distinguish gradual drift from an abrupt fault and informs the next experimental design. The usable inference remains conditional on the instrument still behaving like the one that was characterized.