\begin{tabular}{|c|c|c|c|} \hline Sample, n & Mean A2 & Upper range D4 & Lower Range D3 \\ \hline 2 & 1.88 & 3.268 & 0 \\ \hline 3 & 1.023 & 2.574 & 0 \\ \hline 4 & 0.729 & 2.282 & 0 \\ \hline 5 & 0.577 & 2.115 & 0 \\ \hline 6 & 0.483 & 2.004 & 0 \\ \hline 7 & 0.419 & 1.924 & 0.076 \\ \hline 8 & 0.373 & 1.864 & 0.136 \\ \hline 9 & 0.337 & 1.816 & 0.184 \\ \hline 10 & 0.308 & 1.777 & 0.223 \\ \hline 12 & 0.266 & 1.716 & 0.284 \\ \hline \end{tabular} S.6.7, p. 269 Using formulas S6-5 and S6-6 Determine the UCLxbar and LCLxbar using 3 sigma Sample size 10. Plot the data. \begin{tabular}{|c|c|c|c|c|c|c|} \hline Day & Mean(mm)10pistons & Range (mm) & X-dbl Bar & R-bar & UCLxbar & LCLxbar \\ \hline 1 & 155.9 & 4.2 & & & & \\ \hline 2 & 152.2 & 4.6 & & & & \\ \hline 3 & 152.6 & 4.1 & & & & \\ \hline 4 & 154.5 & 5 & & & & \\ \hline 5 & 155.6 & 4.5 & & & & \\ \hline \end{tabular} For x-Charts when we don't know sigma Upper control limit (UCLxbar) =XXblbar+A2Rbar Lower control limit (LCLxbar) =XdblbarA2 Rbar