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 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 defects that would cause a lot to be passed without 100-percent inspection, assuming that AQL 15% and .4?
c. If the shipment actually contains 5 percent defective items and AQL 15%:
(1) What is the correct decision?
(2) What is the probability it would be rejected in favour of 100-percent inspection if acceptable number c 2?
(3) What is the probability that it would be accepted without 100-percent inspection if c 2?
d. Answer the questions in part c for a shipment that contains 20 percent defective items