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Approximation is alright:

Find the MTBF for a product that will have a minimum cost over a 5 year period if the product will be operated 5,000 hours per year where, TC for 5 yrs = Sys cost + spare avg cost ($2,000) + downtime with failure cost ($20,000) The System cost is related to MTBF, (theta) Sys cost(theta) = (theta)*e^(0.03*theta)

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