A vehicle includes an engine, an exhaust system having a selective catalytic reduction (SCR) device, a NOx sensor, and first and second controllers. The first controller compares estimated NOx levels from an SCR model to actual levels from the sensor, and updates the SCR model when the values differ from each other. The second controller evaluates an updating frequency of the SCR model, and executes a control action when the frequency is excessive. A control system includes the sensor and two controllers noted above. A method of diagnosing the exhaust system includes measuring NOx gasses downstream of the SCR device, updating the SCR model when the deviation is present between estimated and measured NOx levels, comparing estimated ammonia (NH3) storage levels from the SCR model to modeled or estimated upper and lower NH3 storage level boundaries to determine excessive updating, and setting a diagnostic code when excessive updating is present.