Question

2. Nova Ceramics manufacture specialty ceramic parts for non-metallic applications. Parts must be precision drilled such that when assembled with other parts they are a perfect fit. Inspecting parts is time consuming so the practice is for customers to inspect a sample of items from a shipment and if no more than 1 item is defective, the shipment is accepted.

a) Suppose that the on average 0.1% of units are defective. The customer makes the decision on acceptance based upon a sample of only 10 items. What is the probability that the shipment will be accepted?

b) Suppose the defect rate is really 8%. What is the probability that the customer will reject the shipment?

c) To better discriminate between good and bad quality, the customer has several options. She could only accept shipment if all units were perfect (no defects). What is the probability of accepting a shipment with 0.1% defective? What is the probability of accepting one with 8% defective?

d) Another options is to still allow for one defect in the sample, but draw a larger sample. Suppose she inspects 50 units. What is the probability of accepting a shipment with 0.1% defective? What is the probability of accepting one with 8% defective?

e) The customer is very concerned about the possibility of accepting a shipment with 8% defective. Even when there are no defects in a sample of 10 units, the risk is too high. She prefers to accept shipments only if the sample has no defects. How large a sample would she need to inspect if she would tolerate at most a 1% chance of accepting a shipment with 8% defectives.

Answer 1