Establish an approximate design to MTBF required for a system that will result in an approximate minimum total cost over a five year period if the system is to be operated 7500 hours per year, where

Total Cost (for 5 years) = Acquisition cost + Spare cost + Downtime cost

System acquisition cost is related to MTBF, θ, as follows:

C_{A}(θ) = θe^{0.050}

The average cost of downtime associated with failure is $9,000 and the average cost of a spare item is $2,000

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