A bayesian approach to analysis of limit standards

Limit standards are probabilistic requirements or benchmarks regarding the proportion of replications conforming or not conforming to a desired threshold. Sample proportions resulting from the analysis of replications are known to be beta distributed. As a result, standard constructs for defining a confidence interval on such a proportion, based on critical points from the normal or Student´s t distribution, are increasingly inaccurate as the mean sample proportion approaches the limits of 0 or 1. We consider the Bayesian relationship between the beta and binomial distributions as the foundation for a sequential methodology in the analysis of limit standards. The benefits of using the beta distribution methodology are variance reduction, and smaller sample size (when compared to other analysis methodologies).