In the age-based maintenance policy, the goal is to minimize the following cost rate by finding the best value of t. Minimize: C(1) = C,F(T)+c,R(7) (5.1) r(t)dt Where T= Maintenance interval, decision variable R(t)= reliability function F(t), f(t)= cumulative distribution and probability density functions CF production loss in a failure replacement Cp= production loss in a planned replacement Do the following 1) Please prove that the average replacement cycle time is [ R()dt, and this value is always less than t. 2) Given R(t) = exp(-1), estimate C(t) given t=1.5. In the age-based maintenance policy, the goal is to minimize the following cost rate by finding the best value of t. Minimize: C(1) = C,F(T)+c,R(7) (5.1) r(t)dt Where T= Maintenance interval, decision variable R(t)= reliability function F(t), f(t)= cumulative distribution and probability density functions CF production loss in a failure replacement Cp= production loss in a planned replacement Do the following 1) Please prove that the average replacement cycle time is [ R()dt, and this value is always less than t. 2) Given R(t) = exp(-1), estimate C(t) given t=1.5