This article demonstrates how Bayesian methods for making inferences about the number, or proportion, of nonconforming units in a quality control setting can be implemented using simulation techniques. Random draws from the posterior distribution of the target quantities of interest are used to construct the needed inferences. The same random draws from the posterior distribution are also used to perform model checking and sensitivity analysis. The methods are illustrated using two examples. The methods can be generalized to more complicated situations which are illustrated by discussing the extensions of both the examples.