A manufacturer receives shipments of several thousand parts from a supplier every week. The manufacturer has the option of conducting a 100 percent inspection before accepting the parts. The decision is based on a random sample of 15 parts. If parts are not inspected, defectives become apparent during a later assembly operation, at which time replacement cost is $6.25 per unit. Inspection cost for 100 percent inspection is $1 per unit.
a. At what fraction defective would the manufacturer be indifferent between 100 percent inspection and leaving discovery of defectives until the later assembly operation?
b. For the sample size used, what is the maximum number of sample defectives that would cause the lot to be passed without 100 percent inspection, based on your answer to part a?
c. If the shipment actually contains 5 percent defective items:
(1) What is the correct decision?
(2) What is the probability it would be rejected in favor of 100 percent inspection?
(3) What is the probability that it would be accepted without 100 percent inspection?
(4) What is the probability of a Type I error? A Type II error?
d. Answer the questions in part c for a shipment that contains 20 percent defective items.