Verification of uncertainty budgets

Kaj Heydorn, B.S. Madsen

Research output: Contribution to journalJournal articleResearchpeer-review


The quality of analytical results is expressed by their uncertainty, as it is estimated on the basis of an uncertainty budget; little effort is, however, often spent on ascertaining the quality of the uncertainty budget. The uncertainty budget is based on circumstantial or historical data, and therefore it is essential that the applicability of the overall uncertainty budget to actual measurement results be verified on the basis of current experimental data. This should be carried out by replicate analysis of samples taken in accordance with the definition of the measurand, but representing the full range of matrices and concentrations for which the budget is assumed to be valid. In this way the assumptions made in the uncertainty budget can be experimentally verified, both as regards sources of variability that are assumed negligible, and dominant uncertainty components. Agreement between observed and expected variability is tested by means of the T-test, which follows a chi-square distribution with a number of degrees of freedom determined by the number of replicates. Significant deviations between predicted and observed variability may be caused by a variety of effects, and examples will be presented; both underestimation and overestimation may occur, each leading to correcting the influence of uncertainty components according to their influence on the variability of experimental results. Some uncertainty components can be verified only with a very small number of degrees of freedom, because their influence requires samples taken at long intervals, e.g., the acquisition of a new calibrant. It is therefore recommended to include verification of the uncertainty budget in the continuous QA/QC monitoring; this will eventually lead to a test also for such rarely occurring effects.
Original languageEnglish
JournalAccreditation and Quality Assurance
Issue number8
Pages (from-to)403-408
Publication statusPublished - 2005


  • uncertainty budget
  • T-statistic
  • verification
  • process control


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