Twenty-five consecutive samples of size n = 5 were collected to construct an x-chart. The sample means and ranges for the data are shown in

Twenty-five consecutive samples of size n = 5 were collected to construct an xÌ…-chart. The sample means and ranges for the data are shown in the table.

a. Calculate the mean of the sample means, x, and the mean of the sample ranges, R.
b. Calculate and plot the centerline and the upper and lower control limits for the xÌ…-chart.
c. Calculate and plot the A, B, and C zone boundaries of the xÌ…-chart.
d. Plot the 25 sample means on the xÌ…-chart and use the six pattern-analysis rules to determine whether the process is under statistical control.

Sample Sample 14 83.1 10.2 80.2 79.1 83.2 81.0 77.6 7.2 9.0 4.7 5.6 10.1 79.6 80.0 83.2 75.9 15 16 17 18 7.8 6.1 8.4 9.9 3 5 6. 81.7 80.4 77.5 79.8 85.3 77.7 8.6 4.4 6.2 7.9 7.1 9.8 10.7 9.2 19 20 21 22 23 24 78.1 81.4 81.7 80.9 78.4 79.6 6.0 7.4 10.4 9.1 7.3 8.0 8 10 11 12 13 82.3 79.5 25 81.6 7.6