The manufacturer of Boston and Vermont asphalt shingles constructed control charts and analyzed several quality characteristics. One characteristic of interest is the strength of the sealant on the shingle. During each day of production, three shingles are tested for their sealant strength. (This, a subgroup is operationally defined as one day of production, and the sample size is 3.) Seperate pieces are cut from the upper and lower portion of a shingle and then reassembled to simulate shingles on a roof. A timed heating process is used to simulate the sealing process. The sealed shingle pieces are pulled apart, and the amount of force in pounds required to break the sealant bond is measured and recorded. The tab labeled 17.40 contains sealant strength measurements on 25 days of production for Boston shingles and 19 days for Vermont shingles. For the 25 days of production for Boston shingles,
a) construct a control chart for the range
b) construct a control chart for the mean
c) is the process in control?
d) for the 19 production days for Vermont Shingle, construct a control chart for the range.
e for the 19 production days for Vermont Shingle, contract a control chart for the mean
f) for the 19 production days for the vermont shingle , is the process in control?
| Sample |
Boston |
Vermont |
| 1 |
1.22 |
1.01 |
| 1 |
1.32 |
1.2 |
| 1 |
1.35 |
1.14 |
| 2 |
1.33 |
1.16 |
| 2 |
1.31 |
1.22 |
| 2 |
1.32 |
1.18 |
| 3 |
1.11 |
1.19 |
| 3 |
1.09 |
1.22 |
| 3 |
1.22 |
1.18 |
| 4 |
1.07 |
1.33 |
| 4 |
1.15 |
1.22 |
| 4 |
1.11 |
1.34 |
| 5 |
1.08 |
1.27 |
| 5 |
1.18 |
1.25 |
| 5 |
1.12 |
1.31 |
| 6 |
1.11 |
1.23 |
| 6 |
1.1 |
1.27 |
| 6 |
1.13 |
1.31 |
| 7 |
1.09 |
1.23 |
| 7 |
1.25 |
1.17 |
| 7 |
1.12 |
1.34 |
| 8 |
1.18 |
1.23 |
| 8 |
1.29 |
1.05 |
| 8 |
1.36 |
1.15 |
| 9 |
1.26 |
1.15 |
| 9 |
1.29 |
1.14 |
| 9 |
1.27 |
1.22 |
| 10 |
1.19 |
1.24 |
| 10 |
1.22 |
1.2 |
| 10 |
1.18 |
1.22 |
| 11 |
1.31 |
1.18 |
| 11 |
1.22 |
1.27 |
| 11 |
1.11 |
1.23 |
| 12 |
1.43 |
1.25 |
| 12 |
1.48 |
1.23 |
| 12 |
1.29 |
1.23 |
| 13 |
1.16 |
1.22 |
| 13 |
1.26 |
1.24 |
| 13 |
1.23 |
1.32 |
| 14 |
1.11 |
1.09 |
| 14 |
1.18 |
1.3 |
| 14 |
1.21 |
1.22 |
| 15 |
1.1 |
1.15 |
| 15 |
1.32 |
1.32 |
| 15 |
1.11 |
1.3 |
| 16 |
1.18 |
1.13 |
| 16 |
1.22 |
1.06 |
| 16 |
1.24 |
1.31 |
| 17 |
1.09 |
1.19 |
| 17 |
1.4 |
1.28 |
| 17 |
1.29 |
1.46 |
| 18 |
1.17 |
1.28 |
| 18 |
1.23 |
1.24 |
| 18 |
1 |
1.23 |
| 19 |
1.16 |
1.31 |
| 19 |
1.29 |
1.13 |
| 19 |
1.19 |
1.19 |
| 20 |
1.2 |
|
| 20 |
1.19 |
|
| 20 |
1.21 |
|
| 21 |
1.01 |
|
| 21 |
1.09 |
|
| 21 |
1.12 |
|
| 22 |
1.23 |
|
| 22 |
1.3 |
|
| 22 |
1.28 |
|
| 23 |
1.17 |
|
| 23 |
1.27 |
|
| 23 |
1.45 |
|
| 24 |
1.25 |
|
| 24 |
1.14 |
|
| 24 |
1.19 |
|
| 25 |
1.41 |
|
| 25 |
1.23 |
|
| 25 |
1.26 |
|