Measurement uncertainty in temperature mapping results

Mapping reports frequently present minimum and maximum temperatures to two decimals and compare them with limits as if they were exact. A logger with U = 0.3 °C reading 7.9 °C is consistent with 8.2 °C at the product. Whether that matters depends on the acceptance criteria and the decision rule — but it should be stated.

Components for a mapped position

• Logger calibration uncertainty at the nearest calibrated point.
• Drift or as-found error at the post-study check, if performed.
• Resolution of the logger.
• Response-time effects, if the logger is buffered differently from the acceptance criterion's intent.

ValiTrac's mapping engine records each logger's calibration data alongside its statistics so the acceptance evaluation can include uncertainty explicitly rather than by silent omission.

A worked acceptance decision

A cold room is mapped against 2.0–8.0 °C. The warmest sensor records a maximum of 7.9 °C. The loggers carry U = 0.3 °C at k = 2 from their certificates. Does the study pass?

Most mapping reports in circulation apply the first rule without saying so, by printing 7.9 °C next to 8.0 °C and drawing a conclusion. That is a legitimate choice only if it was chosen, written into the protocol, and stated in the report — which is the same requirement ISO/IEC 17025 places on a calibration certificate, for the same reason.

What goes into a mapped position's uncertainty

• Logger calibration uncertainty at the nearest calibrated point, from the certificate, divided by its coverage factor.
• Drift since calibration, or better, the as-found error from a post-study check. A post-study check is worth doing precisely because it replaces an estimate with a measurement.
• Resolution: 0.29 d, which for a 0.1 °C logger is 0.029 °C and is often not the largest term here, unlike in a calibration.
• Response-time and buffering effects, where a logger is buffered differently from the product or from the monitoring probe it is being compared with.
• Spatial representativeness — how well the sensor's position stands for the volume around it. This is usually the largest term of all and the hardest to quantify, which is why sensor count and placement matter more than logger accuracy.

The term nobody quantifies

The last item deserves the emphasis. A logger with U = 0.1 °C placed 400 mm from the actual warmest point in a room with a 3 °C gradient is not a 0.1 °C measurement of the extreme; it is a very precise measurement of somewhere else. Adding sensors reduces this term and improving logger accuracy does not, which is why a study with twelve modest loggers beats one with six excellent ones almost every time.

It cannot usually be given a number, but it can be bounded and discussed: how far apart are neighbouring sensors, and how much did they differ? A 0.2 °C spread between adjacent positions suggests good coverage; a 2 °C spread means the true extreme is very likely between them, and the report should say so rather than quoting the highest reading to two decimals.

Printing a mapped maximum to two decimal places while omitting the uncertainty is the most common statistical overclaim in mapping reports. Either state the uncertainty and the rule, or round to a precision the measurement supports.