A company creates steel ingots for use in manufacturing plants. Complaints from customers have begun to come in, stating the ingots are smaller than the normal 25 tons. Ten samples, each consisting of 12 observations have been gathered and analyzed. The results are in the table below.
Sample Mean Range
1 25.94 0.43
2 24.91 0.67
3 25.05 0.56
4 25.18 0.72
5 25.92 0.99
6 24.86 0.57
7 25.94 0.80
8 24.27 0.93
9 24.16 1.03
10 24.37 1.14
a. Determine the upper and lower control limits for the mean and range charts assuming the process standard deviation is unknown.
b. Plot the control charts and determine if the process is in control. Support your answer.