Design and Evaluation of Bayesian Dependent State Sampling Inspection Plans

The theory of sampling inspection procedures by attributes is built upon the general assumptions that the manufacturing process from which lots are formed is stable and that the lot or process fraction nonconforming is a constant. However, in practice, the lots formed from any production process will have quality variations, which occur due to random fluctuations. When quality variations are present in a process, the proportion of nonconforming units in the lots will vary continually. 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 an alternative to conventional plans. This paper focuses on the concept of dependent state sampling inspection plans by attributes for continuous production with small acceptance numbers under Bayesian perspective and highlights the properties of its characteristic curves with reference to various parameters. A procedure for determining the parameters of such plans for two specified points on the operating characteristic curves under the conditions of gamma-Poisson distribution is discussed with illustrations. The closed form expressions for the parameters of the plans are also derived.