Insights
Uncertainty
Building, combining and reporting measurement uncertainty budgets.
Building an uncertainty budget step by step
Write the measurement model, list every input, evaluate each as a standard uncertainty, apply sensitivity coefficients, combine in quadrature, expand with k. Eight steps, one table.
The reference thermometer's contribution to uncertainty
The reference contributes its certificate uncertainty, its drift since calibration, and any interpolation or self-heating effects. Together they set the floor of what can be claimed.
Resolution as an uncertainty component
A digital display of resolution d contributes a rectangular component of half-width d/2, giving u = d/(2√3) ≈ 0.29 d. For a 0.1 °C logger that is 0.029 °C — often the largest term in its calibration.
Drift as an uncertainty component
Between calibrations an instrument's error moves. Its history tells you how much; that amount enters the budget for any result obtained during the interval.
Uncertainty from the calibration bath or dry block
The source's stability, axial and radial gradients, and (for dry blocks) loading and stem-conduction effects determine how well the reference and the unit under test see the same temperature.
Effective degrees of freedom and when k = 2 is not enough
When Type A components rest on few observations, the combined uncertainty has limited degrees of freedom and k must come from the t-distribution. Welch–Satterthwaite gives the number.
Monte Carlo evaluation of uncertainty (GUM Supplement 1)
Instead of propagating standard uncertainties analytically, sample every input from its distribution, compute the result many times, and read the interval off the output histogram.
What is a decision rule and why every certificate needs one
A decision rule states how measurement uncertainty is accounted for when declaring pass or fail against a tolerance. Simple acceptance, guard banding and non-binary statements are the common choices.
Guard banding explained with a worked example
A guard band narrows the acceptance zone by a multiple of the uncertainty so that a 'pass' has a controlled probability of being wrong. Here is the arithmetic.
Uncertainty budget for a thermocouple calibration
Thermocouples add inhomogeneity, reference-junction and extension-lead terms to the usual comparison budget — and inhomogeneity is often the largest.
Measurement uncertainty in temperature mapping results
A mapping conclusion — the space is within 2–8 °C — carries the loggers' calibration uncertainty, their resolution and any drift since calibration. Compare the extremes plus uncertainty with the limits.