Age Replacement Model. An item (e.g., battery, vehicle, tool, or electronic component) whose use is needed continuously is replaced whenever it fails or reaches age a, whichever comes first. The...

Age Replacement Model. An item (e.g., battery, vehicle, tool, or electronic component) whose use is needed continuously is replaced whenever it fails or reaches age a, whichever comes first. The successive items are independent and have the same lifetime distribution G. The cost of a failure is c_f
dollars and the cost of a replacement at age a is cr. Show that the average cost per unit time is