2. Measurement Process Characterization
2.5. Uncertainty analysis
2.5.6. Uncertainty budgets and sensitivity coefficients

## Example of uncertainty budget

Example of uncertainty budget for three components of temporal uncertainty An uncertainty budget that illustrates several principles of uncertainty analysis is shown below. The reported value for a test item is the average of $$N$$ short-term measurements where the temporal components of uncertainty were estimated from a 3-level nested design with $$J$$ short-term repetitions over $$K$$ days.

The number of measurements made on the test item is the same as the number of short-term measurements in the design; i.e., $$N = J$$. Because there were no repetitions over days or runs on the test item, $$M = 1; \, P = 1$$. The sensitivity coefficients for this design are shown on the foregoing page.

Example of instrument bias This example also illustrates the case where the measuring instrument is biased relative to the other instruments in the laboratory, with a bias correction applied accordingly. The sensitivity coefficient, given that the bias correction is based on measurements on $$Q$$ artifacts, is defined as $$a_4 = 1$$, and the standard deviation, $$s_4$$, is the standard deviation of the correction.
Example of error budget for type A and type B uncertainties

 Type A components Sensitivity coefficient Standard deviation Degrees freedom 1. Repeatability $$a_1 = 0$$ $$s_1$$ $$J - 1$$ 2. Reproducibility $$a_2 = \sqrt{(K-1)/K}$$ $$s_2$$ $$K - 1$$ 3. Stability $$a_3 = 1$$ $$s_3$$ $$L - 1$$ 4. Instrument bias $$a_4 = 1$$ $$s_4$$ $$Q - 1$$