Alico Steel Manufactures Steel Tubes That Are Used in Gas $\text { Number Average x-bar Average range (R) }$

Alico Steel manufactures steel tubes that are used in gas grills for residential customers. The tube's overall length is crucial to assure a proper fit, and this dimension has been targeted as an important dimension to be stabilized for the steel tube manufacturing process. Gas grill performance and customer safety are key objectives and highlight the importance of producing high quality steel tubes. Tubes are cut from rolls of steel tubing using a punch press. The tubes are measured using an operationally defined method, and Table 1 below summarizes the results. Appendix B with all factors for control charts will be given as a separate class handout.Table 1 Tube Length (in centimeters)
Sample Observations 1 to 6
$\text { Number Average x-bar Average range (R) }$
$\begin{array}{lll}\hline 1 & 12.90 & 0.35 \\2 & 13.30 & 0.50 \\3 & 12.87 & 0.32 \\4 & 10.93 & 0.44 \\5 & 11.43 & 0.91 \\6 & 11.93 & 0.42 \\7 & 12.90 & 0.29 \\8 & 13.03 & 0.58 \\9 & 13.70 & 0.21 \\10 & 13.70 & 0.11 \\\hline\end{array}$
Total 126.69 4.13
(a) The center line for the trial R-chart is _____.
The center line for the trial X-chart is _____.
The trial UCL for the R-chart is _____.
The trial LCL for the R-chart is _____.

(b) Assuming that special causes for out-of-control situations in (a) are investigated and corrected using the seven tools of quality management, find the "final set of revised control limits" (i.e., take out any special cause sample(s) from your trial charts and recompute the following). (6 points)

The center line for the final revised R-chart is _____.
The center line for the final revised X-chart is _____.
The final revised UCL for the R-chart is _____.
The final revised LCL for the R-chart is _____.
The final revised UCL for the x-bar chart is _____.
The final revised LCL for the x-bar chart is _____.
(c)Plot the X-chart below and make sure you label the chart correctly.

(d) Is the process in statistical process control (SPC)? Justify and explain using facts. What action would you take given your "management by fact" data analysis?