Selection of Bayesian Single Sampling Plans by Attributes with Desired Discrimination

Acceptance sampling is one of the celebrated techniques in quality assurance. The application of acceptance sampling methodology has been widespread in the industrial environment and the concept is being used primarily for incoming or receiving inspection. It is concerned with inspection of one or more samples drawn randomly from a lot or lots of finished products or materials and with decision making regarding lots on the basis of the information contained in the sample(s) about the quality of the products. A sampling plan under acceptance sampling is a rule that precisely specifies the parameters of the sampling process and acceptance/rejection criteria and may be one of two categories, viz., attributes and variables. The theory of acceptance sampling plans by attributes is based on the implicit assumption that the production process from which lots are formed is stable and the lot or process fraction nonconforming is a constant. However, the lots formed from a process, in practice, have quality variations, which occur due to random fluctuations, and thereby the proportion of non-conforming units in the lots will vary continuously. Hence, in such cases, a framework of Bayesian methodology, which uses prior information on the process variation for making decisions about the submitted lots, can be employed as an alternative to conventional plans. Such plans are called Bayesian acceptance sampling plans. In this paper, Bayesian single sampling plans by attributes are developed under the conditions of Poisson distribution for sampling information and gamma distribution for prior process information. The methodology for determining the plan parameters based on unity values with operating ratio as a measure of discrimination is discussed. The procedures for the determination of an optimum plan and for the construction of operating characteristic curve are also presented. The Bayesian plans are compared with the plan under conventional method through an illustration.