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
Number Average x-bar Average range (R)
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
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 _____. (1 point each)
The center line for the final revised X-chart is _____.