The probability density function for the time to failure in years if the drive train on a rapid transit authority bus is given by

f(t) =0.2-0.02t 0 t 10 yr

a .- If the bus undergoes preventive maintenance every six months that restores it to as-good-as-new condition, determine its reliability at the end of the 15-month warranty. Answer = 0.7758

b .- Compute the MTTF under the preventive maintenance plan in part (a) Answer = 4.871 yr