MGMT 326
Self-Study Problems for Chapter 6
You do not have to turn these problems in. The answers to some problems are in the textbook.
The answers to others are at the end of this document.
Control charts for variables
1. Solved problem 3, page 210
2. A consumer products company sells toothpaste in 6-ounce tubes. Each day, the amount of
toothpaste in 10 tubes is measured. The mean measurement is 5.95, and the standard
deviation is 0.10. Find the lower and upper control limits to 2 decimal places.
3. The consumer product company also sells shampoo in 12-ounce bottles. Each day, the amount of
shampoo in 9 bottles is measured. The mean is 12.04, and the standard deviation is 0.18. Find the
lower and upper control limits for the mean to 2 decimal places.
4. Chipper Chips sells potato chips in 8-ounce bags. Using samples of size 6, the company has
found that the mean number of ounces is 7.9, and the standard deviation is 0.20. Find the
lower and upper control limits to 2 decimal places.
5. Perfect Pumps manufactures water pumps for industrial use. The company's most popular
item is a pump that should pump 10 gallons per minute. Each day for the past 25 days, the
company's quality analyst has measured the gallons actually pumped by 4 pumps. She has
found that 𝑥̿ = 10.2 and 𝑅̅ = 0.3.
(a) Compute the LCL and UCL for 𝑥̅ to 2 decimal places.
(b) Compute the LCL and UCL for R to 2 decimal places.
6. Boffo Beverages bottles soft drinks in 16-ounce bottles. Each day for the past 20 days, the quality
control analyst has measured the ounces of soft drink in 9 bottles. He has found that
𝑥̿ = 15.94 and 𝑅̅ = 0.20.
(a) Compute the LCL and UCL for 𝑥̅ to 2 decimal places.
(b) Compute the LCL and UCL for R to 2 decimal places.
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7. Quality data for a product is given below.
Sample
1
2
3
4
5
6
7
8
9
10
45
49.1
49.8
42.3
48.5
43.5
46.8
41.6
48.1
49.3
43.4
46.2
47.8
45.7
46.3
46.7
43.9
47.2
47.1
48.2
Observations
41.1
41.3
43.2
42.4
47.4
43.4
42.5
44.4
49.2
42.5
Range
(R)
7.70
7.80
7.00
4.50
8.40
4.00
4.90
7.00
9.10
x
48.3
43.9
42.8
45.9
47.5
47.4
42.8
40.4
40.1
47.9
48.8
48.4
48.6
46.8
40.1
46.4
47.4
40.2
41.8
41.8
45.32
45.78
46.44
44.62
45.96
45.48
44.68
42.76
45.26
(a) Compute x and R for sample 10 to 2 decimal places.
(b) Compute x and 𝑅̅ to 2 decimal places.
(c) Compute lower and upper control limits for x to 2 decimal places.
(d) Compute lower and upper control limits for R to 2 decimal places.
8. The following measurements have been collected:
Sample
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
12.2
11.5
12.6
11.9
10.8
12.6
13.0
12.5
11.0
11.3
12.6
11.9
13.1
12.6
12.6
12.5
12.1
12.8
13.6
11.8
11.1
12.8
12.3
11.0
11.2
11.9
12.5
12.5
13.3
11.0
Measurements
11.0
11.9
13.2
13.9
12.7
12.1
12.8
12.3
12.4
11.3
11.4
12.1
13.5
12.2
11.1
12.0
12.1
11.8
12.2
12.2
12.0
12.2
12.1
12.0
11.8
12.4
12.3
12.5
13.0
12.4
11.9
12.1
12.4
13.2
11.1
12.9
11.6
10.7
12.8
12.2
12.5
11.1
12.1
10.5
9.7
Sample
Mean
Bar
11.92
11.94
12.56
12.96
11.72
12.14
12.48
11.98
11.84
11.56
12.16
11.98
12.74
12.32
(a) Compute x and R for sample 15 to 2 decimal places.
(b) Compute x and R to 2 decimal places.
(c) Compute the LCL and UCL for x to 2 decimal places.
(d) Compute the LCL and UCL for R to 2 decimal places.
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Sample
Range
R
1.50
0.60
1.40
2.00
1.90
1.80
1.40
1.80
1.80
1.00
1.20
1.40
1.40
2.80
Process capability
9. A pump is designed to pump 5 gallons of water per minute. According to the product
specification, the gallons per minute should be between 4.8 and 5.2. After testing hundreds of
pumps, the quality control analyst has concluded that the mean gallons per minute is 5, and
the standard deviation is 0.1.
(a) Compute the process capability ratio Cp.
(b) Is the process capable? How do you know?
(c) Why could we use Cp instead of Cpk in this problem.
10. Perfect Hair sells 16-ounce bottles of conditioner. According to the product specification, the
number of ounces in each bottle should be between 15.6 and 16.4. The company has found
that the mean ounces per bottle is 15.94, with a standard deviation of 0.06.
(a) Compute the process capability index Cpk.
(b) Is the process capable? Explain your answer.
11. Boffo Beverages sells soft drinks in 12-ounce cans. According to the process specification,
the process mean should be between 11.95 and 12.05 ounces. The process mean is 11.98, and
the standard deviation is 0.03.
(a) Compute the process capability index Cpk.
(b) Is the process capable? Explain your answer.
(c) Why must we use Cpk instead of Cp in this problem?
Solutions That Are Not In The Textbook
2.
  
 0.10 
LCL    3
  5.95  3
  5.86
 n
 10 
  
 0.10 
UCL    3
  5.95  3
  6.04
 n
 10 
3. LCL = 11.86, UCL = 12.22
4. LCL = 7.66, UCL = 8.14
5. (a) LCL = 9.98, UCL = 10.42
(b) LCL = 0, UCL = 0.68
6. (a) LCL = 15.87, UCL = 16.01
(b) LCL = 0.04, UCL = 0.36
7. (a) 𝑥̅ = 45.94, R = 7.50
(b) 𝑥̿ = 45.22, 𝑅̅ = 6.79
(c) Control limits for 𝑥̅ : LCL = 41.29
(d) Control limits for R: LCL = 0
8. (a) x = 11.36, R= 2.9
(c) LCL = 11.15, UCL = 13.07
UCL = 49.16
UCL = 14.33
(b) 𝑥̿ = 12.11, 𝑅̅ = 1.66
(d) LCL = 0 UCL = 3.50
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9. (a) 0.67.
(b) Not capable. Cp < 1
(c) We can use Cp because the target and the mean are both 5 (or because the mean equals the
target).
10. ( a) 1.89
(b) Capable. Cpk > 1 (or Cpk is greater than or equal to 1).
11. (a) 0.33
(b) Not capable. Cpk < 1 (or Cpk is less than 1)
(c) The target is 12 ounces. The mean and the target are not equal.
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