A company packages a bulk product in bags with a 50 -pound label weight. During a typical day's operation of the fill process, 22 subgroups of five bag fills are observed. Using the observed data, $\overline{\bar{x}}$ and $\bar{R}$ are calculated to be 52.9364 pounds and 1.6818 pounds, respectively. When the $22 \vec{x}$ 's and $22 \mathrm{R}$ 's are plotted with respect to the appropriate control limits, the first 6 subgroups are found to be out of control. This is traced to a mechanical start-up problem, which is remedied. Using the remaining 16 subgroups, $\overline{\bar{x}}$ and $\bar{R}$ are calculated to be 52.5875 pounds and 1.2937 pounds, respectively.
a Calculate appropriate revised $\bar{x}$ and $R$ chart control limits.
$\mathbf{b}$ When the remaining $16 \vec{x}$ 's and $16 R$ 's are plotted with respect to the appropriate revised control limits, they are found to be within these limits. What does this imply?
Process Improvement Using Control Charts
Sampling a Process, Rational…