Cost Analysis of Acceptance Sampling Models Using Dynamic Programming and Bayesian Inference Considering Inspection Errors

Acceptance Sampling models have been widely applied in companies for the inspection and testing the raw material as well as the final products. A number of lots of the items are produced in a day in the industries so it may be impossible to inspect/test each item in a lot. The acceptance sampling models only provide the guarantee for the producer and consumer that the items in the lots are according to the required specifications that they can make appropriate decision based on the results obtained by testing the samples. Acceptance sampling plans are practical tools for quality control applications which consider quality contracting on product orders between the vendor and the buyer. Acceptance decision is based on sample information. In this research, dynamic programming and Bayesian inference is applied to decide among decisions of accepting, rejecting, tumbling the lot or continuing to the next decision making stage and more sampling. We employ cost objective functions to determine the optimal policy. First, we used the Bayesian modelling concept to determine the probability distribution of the nonconforming proportion of the lot and then dynamic programming is utilized to determine the optimal decision. Two dynamic programming models have been developed. First one is for the perfect inspection system and the second one is for imperfect inspection. At the end, a case study is analysed to demonstrate the application the proposed methodology and sensitivity analyses are performed.