Another aspect of the most critical engine consideration for jet aircraft is on those types where one engine driven hydraulic pump powers the system used for gear retraction. In the event of this engine failing, gear may still be raised, but at a slower rate due to lower capacity from electrical pumps within the same system, or power transfer via hydraulic motors from the second system. Numerous variations exist, the DC9 is an example of the latter system.
In the case of failure of the "Primary" gear raising system, 1st segment obstacle performance is at it's worst, and this engine is considered the critical engine from the performance aspect. Failure of the other engine will result in much improved 1st segment performance. Certification must, of course, be based upon the worst case, i.e. failure of the "hydraulic critical" engine.
Regards,
Old Smokey