Precision T1500 that keeps forgetting how much memory it has

I have a Precision T1500 that keeps forgetting how much memory it has (6GB). Sometimes it will boot with 6GB ok, at other times it will display a POST warning that "memory has decreased" and BIOS shows only 4GB. Then when booting up on a different day the POST might say "memory has increased"  and BIOS shows 6GB again.

Obviously one of the RAM sticks is faulty. Is there an application that will allow me to detect which RAM stick is faulty?