A method of assessing overall efficiency of a selective-catalytic-reduction catalyst includes monitoring instantaneous efficiency of the catalyst. The method also includes determining the overall efficiency by summing instantaneous efficiency values weighted by a first set of coefficients if the most recent instantaneous efficiency value is above an instantaneous efficiency threshold. The method additionally includes determining the overall efficiency by summing instantaneous efficiency values weighted by a second set of coefficients if the most recent instantaneous efficiency value is equal to or below the instantaneous efficiency threshold. Furthermore, the method includes determining whether the overall efficiency has dropped below an overall efficiency threshold and reporting when the overall efficiency has dropped below the overall efficiency threshold. The second set of coefficients weighs the most recent instantaneous efficiency value more heavily than preceding instantaneous efficiency values as compared with the first set of coefficients. A system and a vehicle are also disclosed.