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Very different perspectives to the same situation. Respondents have covered all the three control charts as the most appropriate to be used in this situation. However, what is missing is the rationale for the choice and hence there is no winner for this question. The choice is of the time period or the frequency at which the control chart should be plotted. It is one of the inputs that goes into deciding the right control chart and it is a balance between cost of sampling and testing versus cost of not detecting shifts in Mean or variation. Sampling less frequently will not allow for sufficient detection of shifts in the process and hence the customer suffers. Sampling too frequently will incur additional cost and hence the organization suffers. Given a choice, do not be afraid to sample more frequently to begin with and then reduce the frequency once the process seems to be stable. As a rule of thumb, I-MR chart should always be used first to understand the shifts and drifts in individual points and will allow for better process control. Once the process is reasonably stable, you could then move to either Xbar-R or Xbar-S. Illustration, I generated some random numbers for 10 days. All 3 charts given below I-MR Chart shows that process is unstable. Xbar-R chart (shift wise) shows that the process is stable. Xbar-S chart (day wise) shows process is stable. Now if we directly start using Xbar-R or Xbar-S chart, then we will never realize that the process is going out of control within a shift.