Chain Sampling Inspection Plans Based on Bayesian Methodology

Abstract

Acceptance sampling in quality control is a statistical methodology and consists of procedures for sentencing one or more incoming lots of finished products based on the inspection of sampled items drawn randomly from the lots. The theory of such procedures by attributes is often built upon the assumptions that the production process from which lots are formed is stable and that the lot or process fraction nonconforming is a constant. However, in practice, any production process exhibits quality variations, which occur due to random fluctuations. When the quality variations are present in a process, the proportion of nonconforming units in the lots will vary continually. In such cases, for sentencing the processes generating the lots, Bayesian acceptance sampling plans, which use prior information on the process variation, can be employed as an alternative to conventional plans. This paper presents the concept of chain sampling inspection plans by attributes for continuous production using Bayesian methodology. The operating characteristic (OC) function of Bayesian chain sampling plans as a measure of performance is defined and the properties of OC curves of the plans with reference to their parameters are studied empirically. 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. The closed form expressions for the parameters of the plans are derived.