Out-of-specification test results from the statistical point of view

Abstract Although a generally accepted procedure has now been established for the organizational handling of out-of-specification test results, the uncertainty surrounding their statistical evaluation persists. Two statistical equations, the prediction and the confidence interval, are sufficient to examine whether data numbers indicate out-of-specification (OOS) results or not. This is demonstrated by means of 10 examples. These equations are usually sufficient to specify limit values as well. A number of consequences have been derived from a discussion of borderline cases: (A) If only one measured value is OOS, the same is true for the whole result (there are three exceptions: high data numbers, outliers, or the reportable result is not the single value but e.g. the mean). (B) The result is not automatically within specification, if this holds true for all measurements. If all measurements are close to the specification limit and the measurement error is high, an OOS results is still possible. (C) If it is clear that the obtained data will be close to the limit, a precisely working method and a relatively high data number is required. In order to obtain future measurements that remain within specification, the difference between the limit and the mean value must not become smaller than 1.65 times the standard deviation, even if very high numbers of measurements are provided. Procedures to deal with extreme values, so-called outliers, are not straightforward. The statistical evaluation is troublesome, because the probability distribution cannot be determined. This problem is discussed by another four examples. In several cases the outlier can be detected without doubt, for example, using Dixon's test or the box plot. However, there are a number of borderline cases, when a value is suspected to be an outlier, but this cannot be proven by statistics [7] , [9] .