Construct An $\bar { x }$ Chart and Determine Whether the Process Variation Is Within Statistical

Essay

Construct an $\bar { x }$ chart and determine whether the process variation is within statistical control.
$\text { Control Chart Constants }$
$\begin{array}{ccccccc}&\bar{x}&&s&&R\\\hline n & A_{2} & A_{3} & B_{3} & B_{4} & D_{3} & D_{4} \\\hline 2 & 1.880 & 2.659 & 0.000 & 3.267 & 0.000 & 3.267 \\3 & 1.023 & 1.954 & 0.000 & 2.568 & 0.000 & 2.574 \\4 & 0.729 & 1.628 & 0.000 & 2.266 & 0.000 & 2.282 \\5 & 0.577 & 1.427 & 0.000 & 2.089 & 0.000 & 2.114 \\6 & 0.483 & 1.287 & 0.030 & 1.970 & 0.000 & 2.004 \\7 & 0.419 & 1.182 & 0.118 & 1.882 & 0.076 & 1.924 \\8 & 0.373 & 1.099 & 0.185 & 1.815 & 0.136 & 1.864 \\9 & 0.337 & 1.032 & 0.239 & 1.761 & 0.184 & 1.816 \\10 & 0.308 & 0.975 & 0.284 & 1.716 & 0.223 & 1.777 \\\hline\end{array}$
A machine that is supposed to produce ball bearings with a diameter of 7 millimeters yields the following data from a test of 5 ball bearings every 20 minutes.
$\begin{array}{l|lllll|l|l}\text { Sample } &&&{\text { Ball Bearing Diameter (mm) }} &&& \overline{\boldsymbol{x}} & \text { Range } \\\hline 1 & 6.3 & 6.8 & 6.9 & 6.8 & 6.9 & 6.74 & 0.6 \\2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0 & 6.56 & 0.7 \\3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.80 & 0.5 \\4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.80 & 0.3 \\5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4 & 6.62 & 0.4 \\6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9 & 6.66 & 0.6 \\7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0 & 7.28 & 0.4 \\8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1 & 7.08 & 0.3 \\9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.40 & 0.5 \\10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.40 & 0.5 \\11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0 & 7.16 & 0.4 \\12 & 7.5 & 7.4 & 7.4 & 7.6 & 7.1 & 7.40 & 0.5\end{array}$