Also does Joe Gibbs build their own transmissions?
No the teams are not manufacturing their own transmissions. They are bought from the manufacturer, disassembled, modified to the teams specs then reassembled. One of the areas that has shown the largest horsepower gains on the chassis dyno recently has been lowering the friction, weight and parasitic drag in the transmissions, Making these kinds of modifications can make the transmissions less reliable. This means transmission reliability can vary between teams. What I don't know is if within teams like Hendrick if the crew or car chief has different trans options. In other words can they choose less drag or more reliability? I do not know. This is the reason a transmission change sends you to the back of the field. When they had qualifying engines they had qualifying transmissions also. edit: ICE, Hendrick and at least half the field use the Andrews A431 transmission made by a motorcycle engine and transmission firm. I'm not sure what the rest of the field are using as I only have connections to some Chevrolet teams. The Jerico transmission was used extensively 7 or 8 years ago. The transmission ratios are dictated by Nascar so I doubt the transmissions have anything to do with faster restarts. edit: Here is the list using the Andrews transmission. Hendrick, Roush, Penske, Petty and EGR. The thumbs down are interesting, maybe they will post corrections to what I have said.
Any team who doesn't build their own transmissions, has the ability to modify them, and that should be expected. Along with the induction system, valvetrain, and bottom end of the engine, any team who builds the better combination will do better in a race. Also a main ingredient is the driver. And, you can build a race car to fit a particular drivers style of driving. Gibbs may be modifying each of their cars to enable their drivers to utilize their own technique. That's basically what Chad Knaus does for Jimmie Johnson with minimal resources (as a crew cheif) but with above average results.