Many firms utilize sampling plans to control the quality of manufactured items ready for shipment. To illustrate the use of a sampling plan, suppose that a particular company produces and ships electronic computer chips in lots, each lot consisting of 1000 chips. This company’s sampling plan specifies that quality control personnel should randomly sample 50 chips from each lot and accept the lot for shipping if the number of defective chips is four or fewer. The lot will be rejected if the number of defective chips is five or more.
a. Find the probability of accepting a lot as a function of the actual fraction of defective chips. In particular, let the actual fraction of defective chips in a given lot equal any of 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18. Then compute the lot acceptance probability for each of these lot defective fractions.
b. Construct a graph showing the probability of lot acceptance for each of the lot defective fractions, and interpret your graph.
c. Repeat parts a and b under a revised sampling plan that calls for accepting a given lot if the number of defective chips found in the random sample of 50 chips is five or fewer. Summarize any notable differences between the two graphs.