Building an uncertainty budget step by step

The eight steps

• 1. State the measurand precisely: e.g. the correction to the indicated temperature of the unit under test at 5 °C.
• 2. Write the model: correction = t_ref + δt_ref_drift + δt_bath_gradient + δt_bath_stability − t_uut − δt_uut_resolution … each δ a correction with an expected value of zero and an uncertainty.
• 3. List the inputs and gather information: certificate uncertainties, specifications, repeatability data, resolutions.
• 4. Evaluate each as a standard uncertainty (Type A from data; Type B from limits with a distribution).
• 5. Determine sensitivity coefficients from the model.
• 6. Combine: u_c² = Σ (c_i u_i)².
• 7. Check effective degrees of freedom if any Type A component is based on few observations.
• 8. Expand: U = k u_c, usually k = 2, and report with the value rounded consistently.

A minimal temperature example

Reference certificate 0.02 °C (k=2 → 0.010); reference drift ±0.01 (rect → 0.0058); bath gradient ±0.02 (rect → 0.0115); bath stability observed SD 0.008; UUT resolution 0.1 (rect → 0.0289); UUT repeatability 0.012. Combined ≈ 0.035 °C; U ≈ 0.07 °C at k = 2. The resolution term dominates — a common finding for 0.1 °C loggers.