The Power Broker Company, a moderate-size Midwest electric utility company, maintains two turbine generators on-line with two spare generators on standby. A generator will fail on the average of once every three days (MTBF), at which time a single repair crew (if available) will restore the generator to as good as new condition. The mean time to repair is one day. The component inventory levels are poor, resulting in a system expected supply delay time (SDT) of one-half of a day. Failures are Poisson, and the restoration time is exponential.
(a) Determine the probability distribution for the number of generators in repair.
(b) Find the expected number in repair and the expected number operating.
(c) Determine the percentage operating.
In order to placate the irate consumer, the percentage operating in part (c) must be improved by adding either another spare generator or a second repair crew. The discounted present-value cost (investment plus operating cost) of a spare generator is $175,000, and the cost of a second repair crew is $60,000. Which alternative should the utility company implement, and what would be the new operating percentage?