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, x̅ and R̅ are calculated to be 52.9364 pounds and 1.6818 pounds, respectively. When the 22 x̅ ’s and 22 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, x̅̅ and R̅ re calculated to be 52.5875 pounds and 1.2937 pounds, respectively.
a. Calculate appropriate revised x̅ and R chart control limits.
b. When the remaining 16 x̅’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?