A Bayesian approach to the consumer's and producer's risks in measurement

In industrial practice, the decision to accept or reject an inspected item is usually made on the basis of measurement information. Since this information is rarely complete, it is not possible in general to be absolutely certain about the value of the measurand. As a consequence, incorrect decisions may be made. In this paper, formulae for the probabilities of improperly accepting or rejecting an item are derived. Bayesian statistics provides the theoretical framework, and use is made of the Principle of Maximum Entropy. Applications to the inspection of workpieces and to the verification of measuring instruments are considered and examples are given. The conventional, frequency-based approach is also discussed.