Bicycle Mechanics - Issue with SRAM Red Crankset

My bike is a 2010 Specialized Roubaix Comp with SRAM components. I upgraded the S300 Crankset to a Red, the FD and RD are both Rival, as are the shifters. I have been having problems with the chain coming off the big ring and I don't know why. At first I was dropping the chain when moving from the big ring (50) to the small ring (34), the chain would miss the (34) and end up between the ring and frame. I finally figured out this was happening when I was in the big ring/big ring combination (cross chaining); bad thing to do anyway so I corrected my shifting. Now the chain is coming off the big ring and dropping on to the crank arm. I am concerned firstly about dropping the chain but also this could cause me to crash should it get caught on my shoe during the pedal stroke. It happened today twice, both time the chain was in the middle rings of the cassette (no cross chaining) and I was starting a climb. Is this a crankset issue or a FD issue? I was thinking of moving to a Force FD, would it help? I never had this problem with my Ultegra components.

Have you adjusted the high/low limit screws on the front derailer?

My bike is a 2010 Specialized Roubaix Comp with SRAM components. I upgraded the S300 Crankset to a Red, the FD and RD are both Rival, as are the shifters. I have been having problems with the chain coming off the big ring and I don't know why. At first I was dropping the chain when moving from the big ring (50) to the small ring (34), the chain would miss the (34) and end up between the ring and frame. I finally figured out this was happening when I was in the big ring/big ring combination (cross chaining); bad thing to do anyway so I corrected my shifting. Now the chain is coming off the big ring and dropping on to the crank arm. I am concerned firstly about dropping the chain but also this could cause me to crash should it get caught on my shoe during the pedal stroke. It happened today twice, both time the chain was in the middle rings of the cassette (no cross chaining) and I was starting a climb. Is this a crankset issue or a FD issue? I was thinking of moving to a Force FD, would it help? I never had this problem with my Ultegra components.

You need to do a FULL front derailleur adjustment. The chain shouldn't drop no matter how you're shifting (extreme circumstances exception). http://www.parktool.com/repair/readhowto.asp?id=75

As others have said, it isn't a crankset issue, it's an FD adjustment issue.

My guess is that when you changed cranks you didn't see the need adjust the FD, because it seemed fine as is. However the new cranks are probably a smidgen more outboard than the old ones, making the FD adjustment off. You should do a proper FD adjustment any time you change cranksets, but in your case you might bet by my trimming the inner limit in a bit to bring the FD out more at it's innermost (low gear) position.