Compute control limits for the $\overline{X}$ and R control charts.

Question

Samples on n = 8 items each are taken from a manufacturing process at regular intervals. A quality characteristic is measured, and $\overline{X}$ and R values are calculate for each sample. After 50 samples, we have

      Assume that the quality characteristic is normally distributed.

1. Compute control limits for the $\overline{X}$ and R control charts.
2. All points on both control charts fall between the control limits computed in part (i). What are the natural tolerance limits of the process?
3. If the specification limits are 41 ± 5.0, what are your conclusions regarding the ability of the process to produce items within these specifications?
4. Assuming that if an item exceeds the upper specification limit it can be reworked, and if it is below the lower specification limit it must be scrapped, what percent scrap and rework is the process producing?
5. Make suggestions as to how the process performance can be improved.