Compliance Testing for Random Effects Models With Joint Acceptance Criteria

For consumer protection, many governments perform random inspections on goods sold by weight or volume to ensure consistency between actual and labeled net contents. To pass inspection, random samples must jointly comply with restrictions placed on the individual sampled items and on the sample average. In this article, we consider the current United States National Institute of Standards and Technology joint acceptance criteria. Motivated by a problem from a real manufacturing process, we provide an approximation for the probability of sample acceptance that is applicable for processes with one or more known sources of variation via a random effects model. This approach also allows the assessment of the sampling scheme of the items. We use examples and simulations to assess the quality and accuracy of the approximation and illustrate how the methodology can be used to fine-tune process parameters for a prespecified probability of sample acceptance. Simulations are also used for estimating variance components.