An insertion machine in printed circuit board manufacturing has an insertion rate of 5000 parts per hour. From historical data, it is known that the error rate is 300 parts per million parts inserted. The errors occur randomly and independently.
(a) What is the probability of observing no more than 5 errors in 2 hours of operation?
(b) What is the probability of an error-free insertion (rolled throughput yield) in 2 hours of operation? In 3 hours of operation?
(c) Suppose that the desired probability of an error-free insertion in 2 hours of operation is 0.001. What must be the hourly error rate of the insertion machine to accomplish this?