oil pressure problem

Hello, i have a problem with my Fiat Croma 2,5TD. Actually when I start the engine (cold or hot) the oil pressure lamp stays on for 10-30 seconds. The
indicator is checked and I have tried to change oil filter and there is no change so, I think the lub oil pump needs time to increase the pressure. The question is why??? The engine is overhauled and my friend has the same problem also on his Croma TD Please if somebody know HELP.
Thanks.
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