1. A vehicle comprising: an engine; an exhaust system having a selective catalytic reduction (SCR) device which receives exhaust gas from the engine and reduces nitrogen oxide (NOx) gasses in the exhaust gas; a NOx sensor which measures an actual level of NOx gasses at a position downstream of the SCR device; a first controller having an SCR model which provides a set of output values including an estimated level of NOx gasses downstream of the SCR device, wherein the first controller compares the estimated level of NOx gasses from the SCR model to the actual level of NOx gasses from the NOx sensor, and automatically updates the SCR model when the estimated and the measured levels of NOx gasses differ from each other; and a second controller which determines an updating frequency of the SCR model, wherein the updating frequency indicates how frequently the SCR model has been automatically updated by the first controller over a calibrated duration, and diagnoses an operation of the exhaust system by automatically evaluating the updating frequency of the SCR model conducted by the first controller with respect to at least one calibrated threshold, wherein the second controller executes a control action when the updating frequency is evaluated by the second controller as exceeding the at least one calibrated threshold.