6.4. Interpretation of control charts
Once control charts have been developed, they can be used to determine whether the process is in control or out of control. The control charts are used to provide signals that something has changed. There are four primary signals indicating that a process might be out of control:
1. One or more points outside the upper or lower control limits
2. Nine or more points in a row above (or below) the center line
3. Six or more consecutive points moving in the same direction (increasing or decreasing).
These signals reduce to variation called assignable-cause variation. This variation is not random and is due to defects or problems in the manufacturing process, such as operators using the machine incorrectly, raw materials changing, etc. Assignable cause variations must be corrected in order to maintain quality in the production process.
Remark:
To use MINITAB menu follow the following instructions
1. Select Stat>Control charts>Select Xbar S
2. Enter variable location (for example, C1)
3. Enter subgroup size
4. Click OK.
Exercises
1. Data were collected on a quantitative measure with a sample of 6 observations for a sequence of thirty samples. 30 samples were collected, and following results were found
; 
a) Find the center line and lower and upper control limits for an chart.
b) Find the center line and lower and upper control limits for an chart.
2. Weights of samples of canned fruit were measured. Results were available for a sequence of thirty samples, each of seven observations. The overall mean of the sample observations was 192.6 grams, and the average sample standard deviation was 5.42.
a) Use an unbiased estimator to find an estimate of the process standard deviation.
b) Find the center line and lower and upper control limits for an chart.
c) Find the center line and lower and upper control limits for an chart.
3. The accompanying table shows sample means and sample standard deviations for a sequence of 14 samples of eight observations on a quality characteristic of a product
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Sample
1
2
3
4
5
6
7
8
9
10
11
12
13
14
146.4
152.8
150.6
149.2
150.6
150.4
151.1
152.9
147.2
154.3
151.8
149.9
146.7
152.1
4.37
6.79
3.17
4.71
4.98
6.28
6.20
6.97
4.28
7.29
3.1
5.31
4.73
6.12
a) Find the overall mean of the sample observations.
b) Find the average sample standard deviation.
c) Use an unbiased estimator to find an estimate of the process standard deviation.
d) Find the center line and lower and upper control limits for an chart.
e) Draw the chart and discuss its features.
f) Find the center line and lower and upper control limits for an chart.
g) Draw the chart and discuss its features.
4. Ten samples, each consisting of five automobile batteries, are tested for strength. The means and sample standard deviations are given here.
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Sample
Mean
Standard deviation
1
2
3
4
5
6
7
8
9
10
12.2
12.5
12.3
11.9
11.8
11.2
12.1
12.0
12.2
11.8
2.1
1.3
1.5
2.1
1.2
1.1
1.3
1.3
1.8
2.0
a) Find the overall mean of the sample observations.
b) Find the average sample standard deviation.
c) Use an unbiased estimator to find an estimate of the process standard deviation.
d) Find the center line and lower and upper control limits for an chart.
e) Draw the chart and discuss its features.
f) Find the center line and lower and upper control limits for an chart.
g) Draw the chart and discuss its features.
Answers
1.a)
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b)
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;2.a)
;b)
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c)
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3.
a) 150.43; b) 5.307;
c)
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d)
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f)
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4.
a) 12.00; b) 1.57; c) 1.67;
d)
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f)
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