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13. A lot of 400 items that actually contains 3 defective items is subject to the following double sampling plan: the lot is accepted if a first sample of 5 contains no defectives; the lot is rejected if this sample contains 2 or more defectives; if the first sample contains 1 defective, a second sample of 7 is drawn; the lot is accepted if the second sample contains no more than 1 defective, otherwise the lot is rejected. Suppose that at any stage an unacceptable item is replaced by a good item.
(a) What is the probability the lot is accepted?
(b) What is the AOQ if all the defective items in unacceptable lots are replaced by good items?
(c) Show the OC curve for the sampling plan
Given that :
400 items that actually contains 3 defective items is subject to the following double sampling plan = n(s)
The lot is accepted if a first sample of 5 contains no defectives = n(a)
The lot is accepted if the second sample contains no more than 1 defective = n(b)
The lot is rejected if this sample contains 2 or more defectives = n(c)
Solution :
The probability the lot is accepted will be ,
n(A) = n(s)/n(a)+n(b)
n(A) = 400/6
n(A) = 66.667
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