An item is maintained under age replacement policy where the item is replaced upon failure

or at a pre$-$fixed operational age $t_0,$ whichever comes first. The failure time of the item

follows gamma distribution with scale parameter one and shape parameter three. Here, it is

assumed that the time to replace the item is negligible and after replacement the item is $"$as

good as new'. Let each replacement whether planned or not costs c$,$ and each failure incurs

an addition cost of K$.$ Find mean time between replacements, expected time between

actual failures for the item, and total cost per unit time.