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)