Optimal acceptance sampling policy considering Bayesian risks

Abstract

In this paper, we propose a sampling policy considering Bayesian risks. Various definitions of producer"s risk and consumer"s risk have been made. Bayesian risks for both producer and consumer are proven to give better information to decision makers than classical definitions of the risks. So considering the Bayesian risk constraints, we seek to find optimal acceptance sampling policy by minimizing total cost, including the cost of rejecting the batch, the cost of inspection, and the cost of defective items detected during the operation. Proper distributions to construct the objective function of the model are specified. In order to demonstrate the application of the proposed model, we illustrate a numerical example. Furthermore, the results of the sensitivity analysis show that lot size, the cost of inspection and the cost of one defective item are key factors in sampling policies. The acceptable quality level, the lot tolerance proportion defective, and Bayesian risks also affect the sampling policy, but variations of Downloaded by [University of Cambridge] at 14:50 15 June 2016 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT 2 acceptable quality level and producer Bayesian risks, for values more than a specified value, cause no changes in sampling policy.

Robustness of Shape Parameter for Erlang and Weibull Bayesian Acceptance Sampling Plans

“…Lira [12] studied the probabilities of incorrectly rejecting or accepting the product using Bayesian statistics. Adibfar et al [13] proposed a sampling scheme assuming Bayesian methods. The Bayesian risks for both consumer and producer provide a better understanding for decision making than the traditional ones.…”

“…The optimal parameters of the Bayesian plan for the Weibull distribution for r=10 and m=0.1 .83807 × 10 −10 1.83807 × 10 −13 6,5 2947.91 6 1000 973.932 4.03624 × 10 −6 4.03624 × 10 −9 3,2 2956.86 8 1000 978.101 0.000149585 1.49585 × 10 −7 2,1 2962.20…”