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 μ1 = 1, μ2 = 2, μ3 = .5, and μ4 = .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.