Designing Single Sampling Plans by Variables Using Predictive Distribution

Sampling plans by variables represent a well-known tool of acceptance sampling and often it is said that their sampling efficiency/economy is better than that of sampling plans by attributes. However, a comparison of the two types of sampling plans is questionable, because the underlying aims are different. The decision criterion in the case of sampling plans by variables is the quality of the production process, while the decision criterion of sampling plans by attributes is based on lot quality. Using sampling plans by variables is tantamount to consider the parameters of the process distribution as random variables. Based on the history of the production process, suitable prior distributions may be selected to the process parameters. In this paper, using the normal approximation for the process distribution, single sampling plans by variables are derived assuming conjugate priors for the process parameters. The performance of these plans is compared with conventional single sampling plans by variables and single sampling plans by attributes.