148 Machine repair times. An article in IEEE Transactions

(Mar. 1990) gave an example of a flexible manufacturing system with four machines operating independently.

The repair rates for the machines (i.e., the time, in hours, it takes to repair a failed machine) are exponentially distributed with means m1 = 1, m2 = 2, m3 = .5, and m4 = .5, respectively.

a. Find the probability that the repair time for machine 1 exceeds 1 hour.

b. Repeat part a for machine 2.

c. Repeat part a for machines 3 and 4.

d. If all four machines fail simultaneously, find the probability that the repair time for the entire system exceeds 1 hour.