Question

Use the following data to construct one mean (x-bar) chart and one range chart (R-chart). Is the process in control?

sample# a b c d e f
1 19.47 21.21 20.51 21.19 21.21 22.00
2 21.43 21.05 21.46 21.48 21.05 21.07
3 20.11 21.37 19.89 20.18 21.37 19.98
4 20.90 20.88 20.59 21.10 20.88 20.22
5 21.24 20.41 20.15 21.50 20.41 19.52
6 20.75 20.81 21.43 21.34 20.81 20.97
7 20.50 21.41 21.12 20.10 21.41 19.67
8 21.34 21.50 21.75 21.45 21.50 21.84
9 20.01 19.90 20.67 20.90 19.90 20.76
10 20.90 20.12 20.82 20.73 20.12 21.33
11 21.12 21.10 20.13 20.71 21.10 20.86
12 20.72 21.33 22.04 21.39 21.33 19.65
13 21.49 21.34 21.18 21.50 21.34 21.38
14 21.50 21.19 21.34 20.19 21.19 20.54
15 20.46 20.19 20.57 21.03 20.19 21.01
16 20.37 20.08 21.00 20.87 20.08 20.67
17 20.28 21.10 20.47 20.59 21.10 20.46
18 20.45 20.52 21.47 21.41 20.52 20.37
19 21.29 21.35 21.29 21.28 21.35 20.28
20 20.33 21.20 20.25 20.98 21.200 20.45
21 21.22 21.00 20.56 20.54 21.00 21.29
22 22.00 19.52 20.76 21.38 19.52 20.33

Answer 1

To construct a mean chart (x-bar chart), we calculate the average of each sample. The overall mean is the average of all the samples. To construct a range chart (R-chart), we calculate the range of each sample, which is the difference between the maximum and minimum values. The process is considered in control if the data points on both charts fall within the control limits.

Step-by-step explanation:

To construct a mean chart (x-bar chart), we calculate the average of each sample. The overall mean is the average of all the samples. To construct a range chart (R-chart), we calculate the range of each sample, which is the difference between the maximum and minimum values. The process is considered in control if the data points on both charts fall within the control limits.

For this data, the mean chart would show the average of each sample, and the range chart would show the range of each sample. By checking if the data points fall within the control limits, we can determine if the process is in control.