If I understand correctly, you have some kind of sensor that pulses once for every revolution of the shaft? If so then your pulse rate at 6000 rpm is 100 Hz, or a period of 10 milliseconds. If you are simply measuring the time between pulses to determine the RPM, this is way too fast for many PLCs, let alone a cheapo smart relay. Moreover, the difference in period between 5900 and 6000 rpm (your specified tolerance) is only 170 microseconds.... waaaaaaaay too short to be detected.
You really need to be using a PLC with a high-speed input. I'm not very familiar with Omron PLCs, but I know you can get a Micrologix 1100 (with a 20kHz input) for about $500.