The use of uncertainty estimates of test results in comparisons with acceptance limits

When a test is performed in order to qualify a material or a product for a certain use, the result is generally compared with an acceptance limit. The test result has an uncertainty which should be estimated and stated (e.g. in accordance with GUM). Very often this is not the case. Further, discussions often arise on the issue of how the uncertainty shall be considered in relationship to the acceptance limit. The intention of this note is to describe, in simple terms, the statistical background and to give some recommendations. In short, there are two clean-cut, extreme situations. The first case is when the uncertainty of the testing procedure is the dominating factor. Here it is found that the estimates of single laboratories cannot, generally, be used for comparisons with acceptance limits. One should have standardised, well-verified estimates based on comprehensive investigations of the method. It can also be concluded that comparisons between test results and acceptance limits have to be made with regard to the actual circumstances, as, e.g. how the acceptance limit is related to the risk. In the second case, the variation in the property of the material or product dominates and the uncertainty of the testing procedure is negligible. When the results are non-quantitative (go – no go), statistical methods can be used to estimate the risk taken with a certain sampling and acceptance strategy that a certain proportion of the batch to be delivered does not qualify. This should be considered more often in standardisation of product test methods. When the results are quantitative, a statistical analysis should be performed and the uncertainty should be compared with the acceptance limit as before, from the actual circumstances. When effects of testing uncertainty and product variation are comparable a sound treatment requires extensive experimental work. No short cuts can be made without loss of confidence! Received: 17 August 2001 Accepted: 21 March 2002