Confidence of compliance: A Bayesian approach for percentile standards

Rules for assessing compliance with percentile standards commonly limit the number of exceedances permitted in a batch of samples taken over a defined assessment period. Such rules are commonly developed using classical stati stical methods. Results from alternative Bayesian methods are presented (us ing beta-distributed prior information and a binomial likelihood), resultin g in "confidence of compliance" graphs. These allow simple reading of the c onsumer's risk and the supplier's risks for any proposed rule. The influenc e of the prior assumptions required by the Bayesian technique on the confid ence results is demonstrated, using two reference priors (uniform and Jeffr eys') and also using optimistic and pessimistic user-defined priors. All fo ur give less pessimistic results than does the classical technique, because interpreting classical results as "confidence of compliance" actually invo kes a Bayesian approach with an extreme prior distribution. Jeffreys' prior is shown to be the most generally appropriate choice of prior distribution . Cost savings can be expected using rules based on this approach. (C) 2001 Elsevier Science Ltd. All rights reserved.