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 made based on a random sample of 20 parts. If parts are
not inspected, defectives become apparent during a later assembly
operation, at which time replacement cost is $12.50 per unit. The
cost for 100 percent inspection is $1 per unit.
At what fraction defective would the manufacturer be
indifferent between 100 percent inspection and leaving discovery of
defectives until the later assembly operation?
For the sample size used (n=20), what is the maximum number of
sample defectives (i.e., c=?) that would cause the lot to be passed
without 100 percent inspection, based on your answer to part
(a)?
If the shipment actually contains 5 percent defective items:
What is the correct decision?
What is the probability it would be rejected in favor of 100
percent inspection?
What is the probability that it would be accepted without 100
percent inspection?
What is the probability of a Type I error (a)? A Type II error
(b)?
Answer the question in part (c) for a shipment that contains 10
percent defective items.