Designing Bayesian New Group Chain Sampling Plan For Quality Regions

Abstract

Acceptance sampling is a well-established statistical technique in quality assurance. Acceptance sampling is used to decide, acceptance or rejection of a lot based on the inspection of its random sample. Experts concur that the Bayesian approach is the best approach to make a correct decision, when historical knowledge is available. This paper suggests a Bayesian new group chain sampling plan (BNGChSP) to estimate average probability of acceptance. Binomial distribution function is used to differentiate between defective and non-defective products. Beta distribution is considered as a suitable prior distribution. Derivation is completed for the estimation of the average proportion of defectives. This study includes four quality regions namely: (i) probabilistic quality region (PQR), (ii) quality decision region (QDR), (iii) limiting quality region (LQR), and (iv) indifference quality region (IQR). The estimated values for the BNGChSP are tabulated and the inflection point values are derived, based on different combinations of design parameters including both consumer's and producer's risks. For comparison with the existing plan, the operating characteristic curves expose that BNGChSP is a better substitute for industrial practitioners.