Concerning the monitoring of Chatter, I agree with Humboldt and ornerynorsk.
Concerning the correction, IF you are talking about Grinding, then:
1) Machine and Set-up Rigidity. Grinding wheel speed, feed rates, etc.
2) Grinding wheel condition as far as Wheel Trueing, Wheel Dressing, and perhaps Conditioning or "Wear-In".
3) Grinding wheel Grade to take into account workpiece geometry, material, operation, desired stock removal, desired grinding rate, surface finish and tolerances, etc.
4) Coolant type and application method,
More specific Questions would be required for more specific answers.