Which component does NOT play a role in the service brake system?

The transmission does not play a role in the service brake system primarily because its function is to transfer power from the engine to the wheels, allowing the vehicle to accelerate and maintain motion. The service brake system, on the other hand, is concerned with deceleration and stopping the vehicle safely.

In the service brake system, components like the brake pedal are crucial as they are the primary interface through which the driver engages the brakes. The compressor is responsible for generating the compressed air needed to operate air brakes, while the storage tank holds this compressed air, ensuring there is a sufficient supply for braking action. Each of these components directly contributes to the braking process, making them essential for effective braking. The transmission's role is separate and does not aid in the actual braking mechanism, highlighting why it is the correct choice in this context.