design of economically optimal double sampling design with zero acceptance numbers

in acceptance-sampling plans, the items of an incoming lot are inspected one by one. if the number of nonconforming items in sample is equal zero, the lot is accepted but if the number of nonconforming items is equal to one, then second sample is taken and the policy of zero acceptance number would be applied for the second sample. in this paper, a mathematical model is developed to design single stage and double stage sampling plans. proposed model can be used to determine the optimal tolerance limits and sample size. a sensitivity analysis is performed for illustrating the effect of some important parameters on the objective function. the results showed that the proposed two stage sampling plan has better performance than single stage sampling plan in terms of total loss function and sample size and also its results are more robust when parameters of the model change