2. Measurement Process Characterization
2.5. Uncertainty analysis
2.5.2. Approach

2.5.2.1.

Steps

Steps in uncertainty analysis - define the result to be reported

The first step in the uncertainty evaluation is the definition of the result to be reported for the test item for which an uncertainty is required. The computation of the standard deviation depends on the number of repetitions on the test item and the range of environmental and operational conditions over which the repetitions were made, in addition to other sources of error, such as calibration uncertainties for reference standards, which influence the final result. If the value for the test item cannot be measured directly, but must be calculated from measurements on secondary quantities, the equation for combining the various quantities must be defined. The steps to be followed in an uncertainty analysis are outlined for two situations:

Outline of steps to be followed in the evaluation of uncertainty for a single quantity

A. Reported value involves measurements on one quantity.

1. Compute a type A standard deviation for random sources of error from:
   • Replicated results for the test item.
   • Measurements on a check standard.
   • Measurements made according to a 2-level designed experiment
   • Measurements made according to a 3-level designed experiment

2. Make sure that the collected data and analysis cover all sources of random error such as:
   • instrument imprecision
   • day-to-day variation
   • long-term variation

   and bias such as:

   • differences among instruments
   • operator differences.

3. Compute a standard deviation for each type B component of uncertainty.

4. Combine type A and type B standard deviations into a standard uncertainty for the reported result using sensitivity factors.

5. Compute an expanded uncertainty.

Outline of steps to be followed in the evaluation of uncertainty involving several secondary quantities

B. - Reported value involves more than one quantity.

1. Write down the equation showing the relationship between the quantities.
   • Write-out the propagation of error equation and do a preliminary evaluation, if possible, based on propagation of error.

2. If the measurement result can be replicated directly, regardless of the number of secondary quantities in the individual repetitions, treat the uncertainty evaluation as in (A.1) to (A.5) above, being sure to evaluate all sources of random error in the process.

3. If the measurement result cannot be replicated directly, treat each measurement quantity as in (A.1) and (A.2) and:
   • Compute a standard deviation for each measurement quantity.

   • Combine the standard deviations for the individual quantities into a standard deviation for the reported result via propagation of error.

4. Compute a standard deviation for each type B component of uncertainty.

5. Combine type A and type B standard deviations into a standard uncertainty for the reported result.

6. Compute an expanded uncertainty.

7. Compare the uncerainty derived by propagation of error with the uncertainty derived by data analysis techniques.