In statistical process control, measurement error plays an important role which is usually ignored. Measurement error can lead to incorrect conclusions about the performance of the process. In this paper, we examined the effect of measurement error on the shift detection ability of the mixed exponentially weighted moving average-cummulative sum (EWMA-CUSUM) control chart. We investigate the performance of mixed EWMA-CUSUM chart in case of mean shift by using (i) covariate method (ii) multiple measurement method (iii) linearly increasing variance method. The performance measuring tools such as average run length (ARL) and standard deviation of run length (SDRL) are estimated by using the Monte-Carlo simulation method. It is concluded that the performance of the mixed EWMA-CUSUM control chart is adversely effected by considering the measurement error. It is revealed from the comparative study that the mixed EWMA-CUSUM control chart is performing better than EWMA and CUSUM control charts in the presence of measurement error. An illustrative example is presented to demonstrate the performance of control charts in case of measurement error.