Question

" Repairs are need on the outlet works of a small dam. For a particular 36-inch gate value, there are three available alternatives: (1) leave the valve as it is; (2) repair the valve; or (3) replace the valve. If the valve is let as it is, the probability the valve seats fail during the life of the dam is 0.54; the probability the valve stem fails is 0.39; the probability the valve body fails is 0.02; and the probability nothing in the valve fails is 0.05. If the valve is repaired, the probability the valve seats fail is 0.33; the probability the valve stem fails is 0.12; the probability the valve body fails is 0.15; and the probability nothing in the valve fails is 0.4. If the valve is replaced, the probability the valve seats fail is 0.21; the probability the valve stem fails is 0.15; the probability the valve body fails is 0.23; and the probability nothing in the valve fails is 0.41. The cost of future repairs and service disruption of a failure of the valve seats is $23,000; the cost of a failure of the valve stem is $36,000; and the cost of a failure of the valve body is $38,000. The cost to repair the valve now is $9000, and the cost to replace the valve now is $11,000. If the criterion is to minimize expected costs, enter the expected cost of the best alternative. You do not need to consider interest rates for this problem."

Answer 1