Multiparameter hypothesis testing and acceptance sampling

The quality of a product might be determined by several parameters, each of which must meet certain standards before the product is acceptable. In this article, a method of determining whether all the parameters meet their respective standards is proposed. The method consists of testing each parameter individually and deciding that the product is acceptable only if each parameter passes its test. This simple method has some optimal properties including attaining exactly a prespecified consumer's risk and uniformly minimizing the producer's risk. These results are obtained from more general hypothesis-testing results concerning null hypotheses consisting of the unions of sets.