A Modified Acceptance Test Model with Particular Applicability to Bioassay Systems

Abstract

Reducing the β error to a predetermined level can be achieved by increasing the size of the tested samples. Yet, the single sample size model may require an excessive number of sample items. Double or multiple acceptance sampling models that are extensively used in acceptance sampling for attributes require a significantly lower number of sample items for identical levels of risk. Their common basis is the identification of distinct rejection and acceptance limits, and the formation of an intermediate retest zone requiring additional sample items. When this is required, the cumulative number of nonconforming units is assessed against a rejection limit that has been set for the cumulative sample size. This article presents a modified retest zone model that can be applied to sampling by variables as well. The term retest does not mean performing additional tests on the same items but rather testing additional items. The model is based on introducing an additional rejection criterion; that is, whenever the number of successive results (N) in the retest zone accumulates to a critical number (Nc), the lot is not accepted. Nc is derived from the expression , where P rt is the proportion of the normal distribution curve's area occupied by the retest zone area (i.e., the probability of randomly obtaining an individual result within this domain). The cumulative proportion of retests becomes a function of , while the cumulative proportion of tests (CPT) that includes events of decision making without a need for additional testing is a function of . It is shown that the proposed procedure requires considerably fewer tests than the comparable single sample size procedure. This advantage bears particular relevance to biological acceptance tests where the combination of large variances, along with applying the single sample size model, might dictate an impractical number of trials.