We are unfamiliar with the term "accumulation" in this context.  The customer defines it as the pressure difference when the relief valve starts relieving and the pressure when the valve is fully open.  This makes no sense to us, as this ratio would change with the relief valve setting.
Accumulation is the overpressure between when the valve initially opens and where its capacity is rated.  This is defined by the ASME Boiler and Pressure Vessel code, which is recognized as law by most states. 
ASME Section VIII safety-relief valves reach rated capacity at 10% accumulation, and generally reclose on 10% blowdown, or 10% below initial set pressure.   Sec VIII valves are intended for non-fired pressure vessels. 
ASME section 1 Safety valves operate with 3% accumulation. Sec 1 valves are for fired pressure vessels (boilers)
The ratio does NOT change with relief valve setting.  The springs used for setting a relief valve have a very narrow range.  You can't just crank down on the adjuster or a 50 psi valve and reset it to 100 psi. 
Spring-operated safety-relief valves may need the overpressure to operate stably.  You might get away better with limited accumulation if you offer a pilot-operated safety-relief valve.  The valve-manufacturer will de-rate the capacity if the accumulation is less than 10%.

MORE NEWS