Estimation of the conformance fraction in a presence of misclassification errors: a

Abstract

This paper discusses the problem of the estimation of the proportion p when the inspection system is imperfect (subject to diagnosis errors) and the sampled items are classified repeatedly m times. One assumes that no relevant information of the prior distributions of these errors is available and consequently a posterior distribution for the proportion p with high variability is generated due to non-informative prior distributions for those errors. In this paper, the authors suggest to split randomly the sample into two subsamples. Parameters of prior distributions are estimated by the first sample and a Bayesian inferential procedure is proceeded by the second sample. Numerical results indicate that such procedure yields better performance (lower variance for the posteriori distribution) rather than a single sample of size n= n₁+n₂ and non-informative prior distributions for the classification errors.