A large electronic pipe organ contains 100 fuses. Because of the power demands of the organ, the fuses burn out at a fairly regular rate, but newer fuses last longer than older ones. The probability distribution of the lifetime of a fuse is closely approximated by the Weibull law with   0.0204 and   1.8. Assume that t is hours of playing time. The fuses cost $1.35 each when replaced as a block but $12 each when replaced just after a failure.

a. Express the lifetime distribution as a discrete distribution assuming t is measured in hours. (Follow the procedure used in Example 13.11 for the Harley Brown trucking company.)

b. Determine the optimal time to replace all 100 fuses and the average hourly cost of that policy.

c. Compare the answer you obtained in part

(b) with the cost of replacing the fuses as they fail. Which policy would you recommend?