The use of sequential uniform residuals is proposed to screen outliers in process control data. The exact distribution theory of these statistics allows a precise control of the number of observations incorrectly rejected when the process is in control and generated by a normal process distribution. It is also shown that the technique given here has attractive inference properties for detecting shifts in the process distribution mean. The power for detecting a mean shift of specified magnitude is given in terms of a noncentral Studenttdistribution function, and it is observed that a central Studenttdistribution gives a good approximation to this power for most cases of interest.