Question: A decision has been made to perform certain repairs on the outlet works of a small dam. For a particular 36-inch gate valve. There are three available Alternatives:

a) If the valve is replaced; the probability of failure of valve seats, over the life of the project is 30% the probability OF FAILURE OF THE VALVE STEM IS 20%; AND OF FAILURE OF THE VALVE BODY IS 10%

b) If the valve is repaired; the probability of failure of valve seats, over the life of the project is 40%; the probability of failure of the valve stem is 30%, and of failure of the valve body is 20%

c) If the valve is left as it is; the probability of a failure of valve seats, over the life of the project is 60%; the probability of failure of the valve stem is 50%; and of failure of the valve body is 40%

The present worth of cost of future repairs and service disruption of failure of the seats is $10,000; the probability of the cost of a failure of stem is $20,000; and the present worth of cost of failure of the body 430,000 repairing the valve now is $10,000; and replacing it is $20,000

If the criterion is to minimize expected costs, which alternatives is best?