Selection of Bayesian Double Sampling Inspection Plans by Attributes with Small Acceptance Numbers

Sampling inspection is a product control technique and consists of rules or procedures for taking decisions on the disposition of lots of finished products based on the inspection of individual units in one or more random samples drawn from the lots. The basic assumption underlying the theory of such procedures by attributes is that the lot or process fraction nonconforming is a constant. Evidently, this assumption is not fulfilled, even if the production process is stable, i.e., if the nonconforming probability is a constant. However, in practice, the lots formed from a process will have different fractions nonconforming, which occur due to random fluctuations. In such cases, Bayesian acceptance sampling plans (BASP), which use prior information on the process variation for taking decisions about the submitted lots, can be employed as alternative to conventional plans. This paper presents a double sampling inspection plan by attributes with small acceptance numbers using the Bayesian methodology. The properties of its characteristic curves with reference to various parameters are highlighted. The design problem of selecting such sampling plans with reference to two prescribed points on the operating characteristic curve under the condition of gamma-Poisson distribution is addressed.