Inspection error and its effects on single sampling plans with fuzzy parameters

In this paper we have designed an acceptance single sampling plan with inspection errors when the fraction of defective items is a fuzzy number. We have shown that the operating characteristics curve of this plan is like a band having high and low bounds, its width depends on the ambiguity of proportion parameter in the lot when the samples size and acceptance numbers are fixed. A comparison of the single sampling plans with and without inspection errors was done to study the effects upon the characteristics. The results of this comparison show that in the sampling plan with inspection errors, there is a lower operating characteristics band in comparison to a sampling plan without inspection errors for good processing quality. We have also shown that the incorrect classification of a good item reduces the fuzzy probability of acceptance and incorrect classification of a defective item results in a higher fuzzy probability of acceptance.