design of economic optimal double sampling design with zero acceptance numbers

in zero acceptance number sampling plans, the sample items of an incoming lot are inspected one by one. the proposed method in this research follows these rules: if the number of nonconforming items in the first sample is equal to 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. in addition, a sensitivity analysis is done to illustrate the effect of some important parameters on the objective function. the results show that the proposed two stage sampling plan has better performance than single stage sampling plan in terms of total loss function, sample size and robustness.