Concept explainers
Interpretation: The control over production process is to be assessed using the
Concept Introduction:
Answer to Problem 2CSQD
The mean and range values are well within the control limits as seen from the x bar and R charts. Hence, the production process is in control.
Explanation of Solution
Given information:
The
The sample mean and range are calculated and shown below:
Sample | X1 | X2 | X3 | Sample mean(X1+X2+X3)/3 | Sample Range |
1 | 31 | 42 | 28 | 33.67 {(31+42+28)/3=33.67} | 14 |
2 | 26 | 18 | 35 | 26.33 | 17 |
3 | 25 | 30 | 34 | 29.67 | 9 |
4 | 17 | 25 | 21 | 21.00 | 8 |
5 | 38 | 29 | 35 | 34.00 | 9 |
6 | 41 | 42 | 36 | 39.67 | 6 |
7 | 21 | 17 | 29 | 22.33 | 12 |
8 | 32 | 26 | 28 | 28.67 | 6 |
9 | 41 | 34 | 33 | 36.00 | 8 |
10 | 29 | 17 | 30 | 25.33 | 13 |
11 | 26 | 31 | 40 | 32.33 | 14 |
12 | 23 | 19 | 25 | 22.33 | 6 |
13 | 17 | 24 | 32 | 24.33 | 15 |
14 | 43 | 35 | 17 | 31.67 | 26 |
15 | 18 | 25 | 29 | 24.00 | 11 |
16 | 30 | 42 | 31 | 34.33 | 12 |
17 | 28 | 36 | 32 | 32.00 | 8 |
18 | 40 | 29 | 31 | 33.33 | 11 |
19 | 18 | 29 | 28 | 25.00 | 11 |
20 | 22 | 34 | 26 | 27.33 | 12 |
21 | 18 | 24 | 30 | 24.00 | 12 |
22 | 24 | 28 | 19 | 23.67 | 9 |
23 | 27 | 32 | 20 | 26.33 | 12 |
24 | 39 | 26 | 19 | 28.00 | 20 |
25 | 17 | 32 | 27 | 25.33 | 15 |
Total | 710.67 | 296 | |||
Average | 28.43 | 11.84 |
From the 3-sigma standard control chart, the coefficient values are obtained as follows:
And the control limits are calculated
The
The mean and range values are well within the control limits and hence the process is in control.
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