Samples from process to be controlled

Using the above table of samples the preliminary $UC{L}_p$ is calculated as

The preliminary $LC{L}_R$ is calculated as $0.$

After discarding any points that fall outside the control limits the final $UC{L}_R$ is calculated as

the final $LC{L}_R$ is calculated as $0,$ and the $R$ control chart mean is calculated as

We now need to calculate the $\stackrel{}{x}$ charts control limits$.$ The preliminary UCL $\stackrel{}{x}$ is calculated as

and the preliminary $LC{L}_{\stackrel{}{x}}$ is calculated as

After discarding any outlying samples, and repeating until no samples are outside the limits$,$ the final mean is

with a final $UC{L}_{\stackrel{}{x}}$ of

and a final $LC{L}_x^{-}$of