All VW diesels have a two-stage oil pressure monitoring system. The first one will activate a light if the pressure drops below ~10-15 PSI @ <1500 RPMs. The second, as stated above, activates the light and a loud buzzer if the pressure drops below ~30PSI @ >1500 RPMs. I don't know if the pressures at which the alarms activate are the same throughout the years, but the engine speeds are the same.

aklim, you're right, the PowerStroke's injectors are powered by oil pressure. The new PowerStroke's oil pump creates astronomical amounts of pressure, somewhere in the neighborhood of 120+ PSI, IIRC.