Webster Chemical Company produces mastics and caulking for theconstruction industry. The product is blended in large mixers andthen pumped into tubes and capped. Management is concerned aboutwhether the filling process for tubes of caulking is in statisticalcontrol. The process should be centered on 8 ounces per tube.Several samples of eight tubes were? taken, each tube was? weighed,and the weights in the table below were obtained.
the ounces of caulking per tube data.
Tube number |
Sample | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
1 | 7.58 | 8.34 | 8.02 | 7.94 | 8.44 | 7.67 | 7.81 | 8.11 |
2 | 8.33 | 8.17 | 8.08 | 8.51 | 8.41 | 8.28 | 8.09 | 8.16 |
3 | 7.89 | 7.77 | 7.81 | 8.04 | 8.00 | 7.89 | 7.93 | 8.09 |
4 | 8.24 | 8.18 | 7.83 | 8.03 | 7.90 | 8.16 | 7.97 | 8.07 |
5 | 7.87 | 8.13 | 7.92 | 7.99 | 7.94 | 7.81 | 8.14 | 7.88 |
6 | 8.13 | 8.14 | 8.11 | 8.13 | 8.14 | 7.99 | 8.13 | 8.14 |
the table of factors for calculating? three-sigma limits for thex over bar x?-chart and? R-chart.
Factors for calculating? three-sigma limits for the
x overbarx?-chart
and? R-chart.
Size of Sample? (n) | Factor for UCL and LCL for x overbarx?-chart ?(Upper A 2A2?) | Factor for LCL for? R-Chart ?(Upper D 3D3?) | Factor for UCL for? R-Chart ?(Upper D 4D4?) |
2 | 1.880 | 0 | 3.267 |
3 | 1.023 | 0 | 2.575 |
4 | 0.729 | 0 | 2.282 |
5 | 0.577 | 0 | 2.115 |
6 | 0.483 | 0 | 2.004 |
7 | 0.419 | 0.076 | 1.924 |
8 | 0.373 | 0.136 | 1.864 |
9 | 0.337 | 0.184 | 1.816 |
10 | 0.308 | 0.223 | 1.777 |
a. Assume that only six samples are sufficient and develop thecontrol charts for the mean and the range.
Set up the? R-chart by specifying the center line and?three-sigma control limits below. ?(Enter your responses rounded tothree decimal? places.)
?R-chart |
UCL Subscript Upper RUCLR | equals= | |
Upper R overbarR | equals= | |
LCL Subscript Upper RLCLR | equals= | |
