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Title: Confidence Levels Of Measurement Based Decisions
Author: Jos G.M. Van Der Grinten
Source: Flomeko 2003
Year Published: 2003
Abstract: Metrological decisions are based on measurements that have uncertainties. Examples are car velocity measurements for law enforcement, initial verifications that lead to the decision to approve or reject an instrument, and the significance of differences found during intercomparisons. The paper shows for each of these examples the relationship between acceptance criterion, tolerance, uncertainty and confidence level. From the discussion of these examples it can be concluded that uncertainties must be known in order to evaluate the risk on an erroneous decision. Confidence levels are associated with decisions for which it is impossible to achieve 100% confidence. Conformance and non-conformance are not two complementary notions. If the accepted risk on an erroneous decision is less than 50% there is a range of observations for which the instrument is not conforming and not non-conforming at the same time. For verifications an increasing number of verification points leads to an increased risk of making an incorrect decision. In order to appreciate the extra information of more observations a curve fit procedure described by Van der Grinten and Peters 1 can be followed. If there are sufficient data, i.e. at least 6 degrees of freedom, it is best to make a curve fit with a 95% confidence envelope. In all of the above-discussed examples the statistical distribution of the observed results is not known. So the risk analysis is based on the assumption of a Gaussian distribution of the measurement results that is the worst-case representation of our knowledge. If other distributions can be demonstrated to describe the measurement results this will certainly lead to a higher degree of confidence or acceptance criteria that are closer to the tolerances.

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