Graphite production. A graphite manufacturer makes long rolls of f lexible graphite to be used to seal components in combustion engines. The specifications state that the mean strength should be 21.2 ounces per square yard with a standard deviation of 0.29. Further specifications state that no roll should have strength less than 20.2 or more than 22.2 ounces per square yard. If there is a defect in terms of the strength of the graphite rolls, the seal will not hold. After the roll is created, a beta scanner takes readings of the basis weight in ounces per square yard. The data is separated into 3 lanes with 20 scans in each lane.

A sample consists of one roll from each lane. The results from 20 samples follow:

Sample Lane 1 Lane 2 Lane 3 1 20.65 21.01 20.76 2 21.27 21.53 21.53 3 21.69 21.53 21.14 4 21.06 20.38 20.62 5 21.18 21.29 20.95 6 21.14 21.01 21.37 7 20.89 20.63 21.24 8 21.73 21.39 20.87 9 21.55 21.34 21.17 10 21.72 21.97 21.84 11 21.26 20.77 21.24 12 21.05 20.70 20.87 13 22.23 22.09 21.62 14 21.27 21.71 21.89 15 21.60 21.03 20.68 16 21.37 21.29 21.13 17 21.19 21.80 21.36 18 21.56 21.64 21.67 19 21.12 20.56 20.57 20 20.88 20.57 20.37

a) Using the given mean and standard deviation, create an X chart for these samples.

b) Using the given mean and standard deviation, create an R chart for these samples.

c) Is the company’s process for making f lexible graphite sheets out of control?

d) Do all the rolls meet the specification limits?

Sample Lane 1 Lane 2 Lane 3 Lane 4 Lane 5 Lane 6 Lane 7 Lane 8 Lane 9 Lane 10 1 21.56 21.59 21.26 21.16 21.01 21.10 21.22 20.95 20.78 20.66 2 21.42 21.54 21.43 21.44 20.99 21.10 20.78 21.17 21.21 21.10 3 21.48 21.23 21.19 21.34 21.63 21.47 21.18 21.05 21.21 21.22 4 21.14 21.26 21.57 21.34 21.36 21.37 21.42 21.48 21.14 21.02 5 21.53 21.26 21.43 21.26 20.95 20.86 20.99 20.90 20.69 20.80 6 21.40 21.26 21.19 21.38 21.57 21.30 20.97 20.72 20.78 20.70 7 21.84 21.51 21.71 21.34 21.38 21.32 21.32 21.05 20.57 20.27 8 21.83 21.83 21.56 21.17 20.74 20.83 21.00 21.35 21.54 21.41 9 21.60 21.57 21.44 20.99 20.60 20.83 20.85 20.90 21.14 21.36 10 21.84 21.93 21.99 21.97 21.57 21.56 21.17 20.89 21.20 21.28 11 21.96 21.50 21.48 21.37 21.57 21.68 21.82 21.65 21.20 21.19 12 21.27 21.53 21.31 21.22 21.33 21.31 21.46 21.68 21.69 21.52 13 22.03 21.90 22.02 21.46 21.34 21.35 21.44 21.84 21.55 21.63 14 21.30 21.36 21.28 21.29 21.00 20.82 20.55 20.48 20.46 20.68 15 21.65 21.18 20.77 20.98 20.92 20.99 21.27 21.56 21.72 21.67 16 21.46 21.52 21.47 21.45 21.31 21.76 21.92 21.34 21.11 21.19 17 21.72 21.69 21.77 21.44 21.13 21.12 20.91 20.60 20.69 21.07 18 21.67 22.02 21.78 21.34 21.00 20.80 20.30 20.54 20.59 21.16 19 21.44 21.28 21.15 20.97 20.85 21.17 21.87 21.67 21.59 21.20 20 21.38 21.32 20.91 21.10 21.17 21.58 21.53 21.54 21.12 20.69 21 21.23 21.30 21.57 21.42 21.52 21.42 20.90 20.85 20.60 20.71 22 21.65 21.33 21.44 21.27 21.06 20.80 20.82 20.84 20.98 21.22 23 21.59 21.58 21.13 21.34 21.57 21.47 21.55 21.83 21.56 21.02 24 20.92 20.74 20.30 20.07 20.48 20.39 20.81 20.90 21.18 21.18 25 21.02 21.03 21.00 21.04 21.15 21.10 21.24 21.09 21.25 20.86