[Western Phil]

" why the traffic alert and collision avoidance system would not have alerted the 737 pilots that they were about to collide with the business jet."

I'm not sure, but I believe the collision avoidance system uses derived information and not direct data such as radar. Anyone here familiar with the system in use?

Another post somewhere had the same altitude assigned to the two planes by two none-communicating traffic controllers.

[saganite]

TCAS works like a charm as long as both aircraft have the system on and operating. The aircraft exchange info on altitude and course and will command an evasive maneuver if a collision appears imminent.

The required input by the pilot is to disconnect the autopilot and follow the TCAS directed climb or descent profile. The TCAS systems decide between them which aircraft will climb and which will descend. The escape maneuver isn't violent since the climb or descend command is given in plenty of time.

[USNBandit]

You are correct that TCAS works independently of radar and ATC. TCAS equipped aircraft interrogate all Mode C and Mode S type transponders within a specified radius of their aircraft. The most basic version gives Traffic Advisories where subsequent models give Resolution Advisories.

I would imagine these aircraft would both have been equipped with latter variants of TCAS that would "command" the pilots of the aircraft to deviate in altitude to avoid the collision.

Factors that would complicate the problem would be if one or both aircraft were changing altitude, which challenges the system to figure out the altitude trend to compute the possible conflict. Another issue would be if a target aircraft was showing the wrong altitude from its Mode C.