Estimating a Proportion Using Stratified Data From Both Convenience and Random Samples

Estimating the proportion of an attribute present in a population can be challenging when the population is stratified by lots produced by a common manufacturing process and the available data arise from both random and convenience samples. Moreover, all of the lots may not have been sampled. This article proposes a Bayesian methodology for making inferences about a proportion that properly accounts for the potential bias of the convenience samples, the stratification by lots, and the fact that not all of the lots have been sampled. The methodology is illustrated with a simulated population; however, the solution is motivated by a similar, but proprietary, production situation.