A critical piece of equipment which runs 24 hours a day, seven days a week, has two cooling water circulating pumps. If both pumps are running, the time to failure for each pump is an exponential random variable with a mean of 3000 hours. However if only one pump is operating, the time to failure for that pump is an exponential random variable with a mean of 400 hours. If both pumps stop, the critical piece of equipment has to be shut down. The time to repair a stopped pump is an exponential random variable with a mean of 16 hours.

Draw an appropriate rate diagram for this problem, letting the state be the number of pumps not operating and suitable to determine the systems availability. That is the probability that the system is running at a randomly-selected time.

Find the availability of the system. You may use MatLab or MS Excel to do the calculations. Express your answer rounded to three significant figures places.