In FastBatch Biotechnology Company vials with antibodies are produced in a in ANTIbodies FAST line. The fill target of each vial weight is 62.5 mg. The Quality Control department determined an inspection of each of the filling lines to verify the weight in each of the manufacturing lines every 15 minutes. Five vials (n = 5) are collected every fifteen (15) minutes and weighed. The table below shows the results for 33 observations.

Every sample is discarded. Even though the sampling is required by regulators, it represents a significant amount of vials discarded. The Site Leader asked the ANTIbodies FAST to reconsider this situation and look for ways to reduce the amount of vials discarded.

Use Minitab to analyze the data and perform the following tasks:

1. Use the first twenty (20) observations to determine the LCL & UCL, for Xbar and R charts, using Minitab. Show control charts obtained. Show values of LCL & UCL.

2. Use the first twenty (20) observations to manually recalculate the LCL & UCL, for Xbar and R charts. Confirm your manual results with those obtained from Minitab. Hint: use an Excel spreadsheet.

3. Once you are satisfied with results in parts 1 & 2, plot the complete set of data provided (33 observations) in Xbar and R charts using the LCL & UCL obtained above. Generate a IM-R chart. What behaviors do you observe in the data? Determine if the process is stable and if it is in statistical control.

4. If necessary, revise your control limits, assume that any samples plotting outside control limits can be eliminated because are related to a new vial bottle that is bigger and replot Xbar and R control charts. Please note that only outliers that have an assignable cause can be removed from the data.

\begin{tabular}{|c|c|c|c|c|c|} \hline Samplenumber & x1 & x2 & x3 & x4 & x5 \\ \hline 1 & 62.9 & 63.0 & 62.8 & 62.6 & 62.7 \\ \hline 2 & 62.6 & 62.5 & 62.4 & 63.0 & 62.9 \\ \hline 3 & 62.8 & 62.9 & 62.4 & 62.4 & 62.4 \\ \hline 4 & 62.5 & 62.4 & 62.2 & 62.6 & 62.4 \\ \hline 5 & 62.6 & 62.6 & 62.6 & 62.9 & 61.7 \\ \hline 6 & 62.1 & 62.5 & 62.6 & 62.4 & 62.5 \\ \hline 7 & 62.7 & 62.6 & 62.5 & 62.4 & 62.1 \\ \hline 8 & 62.7 & 62.4 & 62.7 & 62.6 & 62.5 \\ \hline 9 & 62.4 & 63.1 & 62.6 & 62.7 & 62.6 \\ \hline 10 & 62.8 & 62.7 & 62.8 & 62.8 & 63.1 \\ \hline 11 & 63.1 & 62.6 & 62.7 & 62.4 & 62.4 \\ \hline 12 & 62.7 & 61.9 & 62.3 & 62.6 & 62.5 \\ \hline 13 & 62.7 & 62.7 & 62.6 & 62.8 & 63.1 \\ \hline 14 & 62.8 & 62.9 & 62.8 & 62.8 & 62.9 \\ \hline 15 & 62.6 & 62.7 & 62.1 & 62.8 & 61.8 \\ \hline 16 & 62.2 & 62.7 & 62.5 & 62.9 & 62.3 \\ \hline 17 & 62.7 & 62.7 & 62.4 & 62.2 & 62.6 \\ \hline 18 & 62.7 & 62.6 & 62.9 & 62.3 & 62.5 \\ \hline 19 & 62.5 & 62.4 & 62.7 & 62.3 & 62.3 \\ \hline 20 & 62.3 & 62.5 & 62.4 & 62.8 & 62.5 \\ \hline 21 & 62.6 & 62.4 & 62.6 & 62.9 & 62.7 \\ \hline 22 & 63.1 & 62.7 & 62.9 & 62.6 & 62.5 \\ \hline 23 & 63.1 & 62.6 & 63.1 & 63.0 & 63.0 \\ \hline 24 & 63.0 & 62.9 & 62.4 & 62.1 & 62.8 \\ \hline 25 & 62.7 & 62.9 & 62.2 & 62.3 & 62.0 \\ \hline 26 & 61.6 & 61.6 & 62.4 & 62.0 & 61.2 \\ \hline 27 & 61.9 & 62.0 & 62.2 & 62.1 & 62.3 \\ \hline 28 & 62.0 & 62.3 & 62.3 & 62.8 & 62.7 \\ \hline 29 & 62.8 & 62.5 & 62.7 & 62.9 & 62.8 \\ \hline 30 & 63.0 & 62.7 & 62.8 & 63.1 & 63.0 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|l|} \hline 31 & 62.8 & 62.7 & 62.9 & 62.7 & 62.9 \\ \hline 32 & 62.7 & 63.0 & 62.7 & 62.7 & 62.8 \\ \hline 33 & 62.7 & 63.0 & 62.2 & 62.2 & 62.6 \\ \hline \end{tabular}