I would like to know that for all the AUTO START centrifugal pumps ( Open valve start up) , whether it should be designed for End of Curve operation?  That is , NPSHR should be less than NPSHA even even at its end of curve. I am guided to select a vendor who can satisfy the above condition. We have two pumps ( 1 running + 1 standby) . If one pump trips the other pumps should come in line in auto. we have individual NRV for these pumps . When I should propose to the vendors that my requirement of a centrifugal pump should be designed for the End of curve operation where the NPSHR is less than NPSHA at its end of the curve.

You need to draw a system head curve on the pump H/Q performance sheet- as it is possible that the pump will not reach the end of curve on start-up as the system resistance may intersect the H/Q prior to end of curve.

If the pumps can not run to end of curve there is no need for the NPSHr to be less than the NPSHa - calling for this in a contract will only result in larger and more expensive pumps which will then run too far left of their BEP in normal operation.

However, if they can run to end of curve you need to look at the running period before they run up the H/Q curve to the normal operating point - a short period of cavitation is usually not a problem. 

You are asking if the pump needs to be specified to run to end of curve.  That's a process question.  If you need those end of curve flowrates, the answer is yes.  If you don't need those end of curve flowrates, and as Artisi has already mentioned, the answer is no.

If your system curve and pump curve can intersect at high end of curve flowrates, where suction pressures drop below NPSHr, BUT you don't need to pump those high flows, just install a low suction pressure switch, or a high flowrate switch to deavtivate the pump motor, or to control a VFD, or install a flow control valve to limit flows to acceptable ranges, where suction pressure is always higher than NPSHr.

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