The OESIDs typically created are "idealised" for engine failure from V1 (or Vef to be precise), thus, an early engine failure leaves the pilot in no doubt of immediately cancelling the SID and continuing with the EOSID (Special Procedure). The curve ball out of left field is those SIDs which require early turn, with all engines operating up to the SID turning point, and engine failure ocurring on the next leg of the SID which has not been evaluated for OEI performance. Numerous SIDs require climb gradients far in excess of available OEI performance, and even if you can meet the gradient (e.g. 3.3%), at which altitude do you accelerate?
From the EOSID design point of view in these situations I create 2 EOSIDs for such runways, one idealised for early engine failure, and the other for the worst of the published SIDs. The RTOWs for the SIDs are invariably limited to a lower weight than for the "idealised" OESID. With such data available, at the pre-flight stage the pilot then knows whether or not he/she can meet the SID following engine failure. If the SID is achievable OEI, accept the clearance and go. If not, advise ATC that the SID is unacceptable, and request alternative departure procedures.
I still sleep better at night that way
Best Regards,
Old Smokey