A fuzzy-based design procedure for a single-stage sampling plan

In a single-stage sampling plan, the decision to accept or reject a lot is made based on inspecting a random sample of certain size from the lot. There are two possible errors in any sampling plan; a good lot may get rejected (known as the producer's risk), or a bad lot may get accepted (known as the consumer's risk). Conventional designs may result in needlessly large sample size. The sample size n can be reduced by relaxing the conditions on the producer's and consumer's risks. In this paper, we propose a method for constructing the membership function of the grade of satisfaction for the sample size n based on the shape of the sampling cost function. Based on that, we find a reasonable solution to the trade-off between relaxing the conditions on the actual risks and the sample size n. The membership function of the grade of satisfaction for the sample size is derived for three general sampling cost functions, and the advantages of the proposed methodology over the existing methods is illustrated via a numerical example.