Monitoring the ratio between two random normal variables plays an important role in many industrial manufacturing processes. In this paper , we suggest designing two one-sided Shewhart control charts monitoring this ratio. The numerical results show that the one-sided charts have more advantages compared to the two-sided Shewhart chart proposed previously in the literature. Moreover, we investigate the effect of measurement error on the performance of these control charts where the measurement error is supposed to follow a linear covariate error model. The change of model parameters from an in-control condition to an out-of-control is presented without using a strict assumption about the independence of the shift size from measurement errors. A valuable finding from this study is that taking multiple measurements per item is not an effective way to reduce the negative effect of measurement error on the Shewhart charts' performance.