Uncertainty
Building, combining and reporting measurement uncertainty budgets.
Building an uncertainty budget step by step
Write the model, list the inputs, evaluate each as a standard uncertainty, apply sensitivity coefficients, combine in quadrature, expand with k. One table.
The reference thermometer's contribution to uncertainty
The reference contributes its certificate uncertainty, drift since calibration, and any interpolation or self-heating effect. Together they set the floor.
Resolution as an uncertainty component
A digital display of resolution d contributes a rectangular term of half-width d/2, so u = d/(2√3) ≈ 0.29 d. For a 0.1 °C logger that is 0.029 °C.
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
Stability, axial and radial gradients, loading and stem conduction decide how closely the reference and the unit under test see the same temperature.
Effective degrees of freedom and when k = 2 is not enough
k = 2 assumes you know your uncertainty well. When a Type A term from three readings dominates, Welch-Satterthwaite puts k at 4.53 and more than doubles U.
Monte Carlo evaluation of uncertainty (GUM Supplement 1)
Rather than propagate uncertainties analytically, sample each input from its distribution, compute the result many times, and read the interval off that.
What is a decision rule and why every certificate needs one
A decision rule states how measurement uncertainty is accounted for in declaring pass or fail: simple acceptance, guard banding or a non-binary statement.
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
Inhomogeneity, reference junction and extension leads join the comparison budget. At 400 °C on a type K, inhomogeneity alone carries 85 % of the variance.
Measurement uncertainty in temperature mapping results
A mapping result carries the loggers' calibration uncertainty, resolution and drift. Compare the extremes plus that uncertainty against the limits.