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:
CA(θ) = θe0.050
The average cost of downtime associated with failure is $9,000 and the average cost of a spare item is $2,000