Product acceptance determinations are practical tools for quality control applications involving quality contract on product orders between the vendor and the buyer. It provides the vendor and the buyer rules for product acceptance to meet the preset product quality requirement. As the rapid advancement of manufacturing technology, more than one quality characteristic must be simultaneously considered to improve the product quality because of the product design. In this article, we introduce an efficient product acceptance procedure on the basis of the generalization index, to deal with lot sentencing problem with very low fraction of defectives. We tabulate the required sample size n and the corresponding critical acceptance value c0 for various α-risk, β-risk, and the levels of the lot fraction of defectives that correspond to acceptance and rejecting quality levels. Practitioners can use the proposed method to make reliable decisions in product acceptance. Copyright © 2012 John Wiley & Sons, Ltd.