Drift as an uncertainty component

A reference thermometer calibrated in January and used in November has probably changed. If successive certificates show the ice-point resistance moving by an amount equivalent to 0.01 °C per year, then at any time during the year the error is somewhere within about ±0.01 °C of the certificate value — a rectangular distribution with u = 0.01/√3 ≈ 0.006 °C.

Refinements

• Time-proportional: use the time elapsed since calibration rather than the full interval.
• Corrected drift: if the change is linear and consistent, apply a correction and carry the uncertainty of the fit.
• Interim checks: an ice-point or fixed-point check mid-interval can tighten the estimate and catch abnormal behaviour.

A new instrument with no history has unknown drift; use the manufacturer's stability specification as a conservative rectangular limit until history exists.

Three ways to treat it, with the arithmetic

Take a reference thermometer whose certificates show the error moving by 0.010 °C per year, consistently in one direction, on a twelve-month interval. There are three defensible treatments and they give very different numbers.

The first is what most budgets use and it is rarely wrong. The second is a free improvement for any laboratory that records when a measurement was made, which is all of them. The third requires committing to a prediction, and it collapses the moment the instrument is dropped, repaired or thermally shocked — so it needs interim checks behind it rather than faith.

Drift and the calibration interval are the same argument

A drift component and an interval are two ways of describing one decision. Lengthening the interval to two years doubles the rectangular half-width and increases the component by √2 in the time-proportional treatment and by a factor of 2 in the full-interval one. If the drift term is already the largest item in the budget, a longer interval is not a cost saving; it is a decision to report a larger uncertainty.

The converse is the more useful move. An instrument whose drift term is negligible against the rest of the budget is being calibrated more often than the measurement requires, and the certificates are the evidence for extending the interval.

Instruments with no history

• Use the manufacturer's long-term stability specification as a conservative rectangular bound. These are typically pessimistic, which is the right direction to be wrong in.
• Replace it with your own data at the second certificate, and re-examine the budget then. The term usually shrinks.
• Thermocouples do not obey the slow-and-smooth model: their change depends on thermal history rather than elapsed time, so a couple used at high temperature needs a shorter interval and interim checks regardless of what a calendar says.
• Interim checks — an ice point, or a check standard measured monthly and trended — are what let you locate when a change began. On the day an out-of-tolerance finding triggers a look-back across every certificate since the last calibration, that record is the difference between assessing three months of work and assessing twelve.