Let the hive mind of Engadget get that for you.
"We need a digital camera that can be switched on and fire off that first shot fast. It's not a commonly tracked statistic on any review site, and nobody seems to have this information for every camera. We were hoping other readers could inform us as to what small digital cameras can fire off their first pics in under a second (ideally under half a second). It needs to be small, but mostly, just really quick in operation. Thanks!"
Seiko Epson Corporation has had 'Instant OFf' trademarked for their PowerLite Projectors, Epson's technology enabling users to turn off, unplug and pack up the projector immediately and safely without a cool-down period.
I'm not sure what 'direct shutdown' is adding to that.