- #1
ptlnguyen
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Homework Statement
A system is to be operated 5000 hours per year, where
Total Cost (for 5 years) = Acquisition cost + Spares cost + Downtime cost
System acquisition cost is related to MTBF, θ, as follows:
CA(θ) = 685.2917e0.003779θ
The average cost of a spare item is $1,000 and the average cost of downtime associated with failure is $5,000.
Homework Equations
Find MTBF or θ required for a system that will result in approximate minimum total cost over a five-year period if the
The Attempt at a Solution
This is my attempt but not sure
Find θ = MTBF
1/MTBF = R/T where R= rate of failure and T= total time = 5000hrs
=> MTBF =T/R = 5000/R
Total Cost = Acquisition cost + Spares cost + Downtime cost
= 685.2917e^0.003779(5000/R) + 5000R + 1000R
= 685e^20/R + 6000R
I need to find R such that it will minimize Total Cost and I am stuck. Please check if my approach is correct. Thanks.