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Rather than inspect every item in a large lot companies generally inspect a random sample and on the basis of the results of the sample decide to accept or reject the lot. Instead of using a single sample a method called double sampling is sometimes used because it will generally require that fewer items be examined before a decision is reached. In double sampling an initial sample of size n1 is taken from the lot. If the number of defective items d1 in this sample is less than or equal to c1 the lot is accepted. If the number of defectives is larger than c2 the lot is rejected. If d1 is> c1 and <=c2, a second random sample of size n2 it taken and d2, the number of defects that it contains, is determined. If d1+d2<=c2, the lot is accepted. Otherwise the lot is rejected. Use RSPE or Excel to develop a spreadsheet model to simulate the inspection of 1000 lots. If in each lot the fraction defective is p, determine what proportion of the lots will be accepted. Run the model for the case n1=50, n2=100, c1=1 and c2=3 with p=0.05. Hint: The number of defectives in a random sample of size n when the probability of a defective is p, follows the binomial distribution. In addition, if you have a cell where you record a 1 if an event occurs and a zero if it does not, the average of the values in that cell will approximate the probability that the event will occur.
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