In general, acceptance sampling is a statistical tool used to help make decisions concerning whether or not a batch (or lot) of product should be released for consumer consumption or use. Acceptance sampling, which will be discussed in this paper, should not be confused with the sampling plans and acceptance criteria mentioned in the United States Pharmacopeia 25 and National Formulary 20.1 While acceptance sampling has been used extensively in many industries over the past 60 years, in far too many cases, inspection sampling and quality have been thought of as being synonymous. This is simply not the case because quality stems from a well-designed product produced from a well-designed and capable process. Once the product has been produced and the quality of the product has been fully determined, acceptance sampling can only give us a level of assurance that the product quality is at a certain level and that an Acceptable Quality Level (AQL) will be exposed to consumers. For this reason, the focus in the quality arena has changed from the inspection of finished product quality to the continuous improvement of the product design and process performance.

While most of any quality efforts should be put toward the proactive approach found in a continuous quality improvement program, acceptance sampling still plays a practical role. Situations for which acceptance sampling may be useful include: incoming inspection with a new supplier for which little is known about its capability or quality history; new processes where statistical control is trying to be achieved; processes where the quality is relatively poor; and processes that experience flare-ups or special causes. Furthermore, acceptance sampling is required in current good manufacturing practice (cGMP) in pharmaceutical research and development.2 However, the most attractive feature of acceptance sampling is that it allows one to balance two risks: the risk to the producer and the risk to the consumer. These risks need to be fully understood in order to appreciate acceptance sampling methodology.

An example will be used in order to provide the basic ideas behind acceptance sampling, giving special attention to the producer and the consumer risks. It turns out that these two types of risks uniquely determine a plan, and a thorough understanding of these basic principles will help in understanding more complex plans. Double sampling plans as well as more complex sampling plans are discussed briefly. Variables sampling plans are introduced, and the derivation of their acceptance regions is discussed. Finally, some common misconceptions associated with acceptance sampling plans are presented, and thoughts concerning the use of ANSI/ASQC3 sampling procedures are given. Theoretical justification for acceptance sampling is outside the scope of the entry but can be found in Wallis,4 Schilling,5 and Stephens.6 For a historical look at inspection sampling, see Sherman.7 Acceptance sampling is reviewed extensively from a Bayesian viewpoint by Wetherill,8 Hald,9 Moskowitz and Berry,10 and Thyregod.11 Bayesian cost models are reviewed by Hald,12 Guenther,13 Lorenzen,14 and Wadsworth and Olsen.15 Situations where the fraction nonconforming is very low are discussed in Hahn,16 Pesotchinsky,17 and Moreno and Reeves.18 Suich19 talks about the effect of inspection errors on the performance of acceptance sampling plans. Finally, the debate concerning all (100%) or nothing (0%) inspection is given by Vander Weil and Vardeman.20