The presence of imprecise measurement may seriously affect the efficiency of process control and production cost. A cost model is derived to determine the design parameters of the economic asymmetric $ar{X}$ and S control charts including measurement errors. The effects of imprecise measurement on the performance of the economic asymmetric $ar{X}$ and S control charts and production cost are examined for the case where the process mean and process standard deviation may change. Application of the proposed control charts is demonstrated through an example. Numerical examples illustrate the effects of imprecise measurement on the design parameters of the proposed control charts. It shows that the imprecision measurement may seriously affrct the ability of the proposed control charts to detect process disturbances quickly, change the sampling frequency, and increase the production cost compared to the control charts excluding measurement errors.