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Statistical Process Control
1. 5
The Bayfield Mud Company supplies railroad boxcars of 50 pound bags of mud treating agents to the Wet-
Land Drilling Company. Mud treating agents are used to control the pH and other chemical properties of
the cone during oil drilling operations. Wet-Land has complained to Bayfield that it’s most recent
shipment of bags was underweight by 5%. This is a problem which Wet-Land needs corrected because the
use of under weight bags may result in poor chemical control during drilling which may hurt drilling
efficiency resulting in serious economic consequences.
Afraid of losing a long time customer, Bayfield immediately began investigating their production process.
Management suspected that the causes of the problem were their recently added third shift and the fact that
all three of the shifts were under pressure to increase output to meet increasing demand for the product.
Their quality control staff began taking random samples of the output of 3 bags per hour. They observed
the process for 36 hours beginning at 6am.
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2. 6
Sample Time Bag 1 Bag 2 Bag 3
1 6am 49.60 48.70 50.70
2 7am 50.20 49.10 51.20
3 8am 50.60 49.60 51.40
4 9am 50.80 50.20 51.80
5 10am 49.90 49.20 52.30
6 11am 50.30 48.60 51.70
7 12noon 48.60 46.20 50.40
8 1pm 49.00 46.40 50.00
9 2pm 49.00 46.00 50.60
10 3pm 49.80 48.20 50.80
11 4pm 50.30 49.20 52.70
12 5pm 51.40 50.00 55.30
13 6pm 51.60 49.20 54.70
14 7pm 51.80 50.00 55.60
15 8pm 51.00 48.60 53.20
16 9pm 50.50 49.40 52.40
17 10pm 49.20 46.10 50.70
18 11pm 49.00 46.30 50.80
19 12pm 48.40 45.40 50.20
20 1am 47.60 44.30 49.70
21 2am 47.40 44.10 49.60
22 3am 48.20 45.20 49.00
23 4am 48.00 45.50 49.10
24 5am 48.40 47.10 49.60
25 6am 48.60 47.40 52.00
26 7am 50.00 49.20 52.20
27 8am 49.80 49.00 52.40
28 9am 50.30 49.40 51.70
29 10am 50.20 49.60 51.80
30 11am 50.00 49.00 52.30
31 12noon 50.00 48.80 52.40
32 1pm 50.10 49.40 53.60
33 2pm 49.70 48.60 51.00
34 3pm 48.40 47.20 51.70
35 4pm 47.20 45.30 50.90
36 5pm 46.80 44.10 49.00
Answer the following questions.
a. What is the sample size?
3
b. Is the variability of the checkout time known or unknown?
Unknown
c. Which chart is used to analyze the variability in the bag filling process?
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3. 7
Range chart
d. Which chart is used to analyze the amount of fill in each bag?
Mean chart
e. Should the range or mean chart be analyzed first? Explain your answer.
Range chart should be analyzed before the mean chart because the variability of the process
must be in control before the mean chart can be analyzed.
Analyze the range chart by answering the following questions.
f. What is the grand range?
3.7472
g. Calculate the centerline, upper and lower control limits for the range chart?
3σ Control Chart Settings
UCL 9.6454
Centerline 3.7472
LCL 0.0000
h. Plot the range chart showing the centerline, upper and lower control limits.
Control Chart
Centerline, 3.7472
LCL, 0.0000
UCL, 9.6454
0
2
4
6
8
10
12
0 10 20 30 40 50 60 70
Range
i. Are the sample ranges within the control limits?
Yes
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4. 8
j. Based on 3-sigma control limits for the runs test, does the pattern analysis indicate the A/B runs
are random?
Yes
k. Based on 3-sigma control limits for the runs test, does the pattern analysis indicate the U/D runs
are random?
Yes
l. Is the variability of the checkout times in control (i.e is the range chart in control)? Why?
Yes. The sample ranges are within the limits, the A/B runs are random, and the U/D runs
are random.
Analyze the mean chart by answering the following questions.
m. What is the grand mean?
49.5907
n. Calculate the centerline, upper and lower control limits for the mean chart?
3σ Control Chart Settings
UCL 53.4241
Centerline 49.5907
LCL 45.7573
o. Plot the mean chart showing the centerline, upper and lower control limits.
Control Chart
Centerline, 49.5907
LCL, 45.7573
UCL, 53.4241
45
46
47
48
49
50
51
52
53
54
0 10 20 30 40 50 60 70
Mean Unknown Variation
p. Are the sample means within the control limits?
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5. 9
Yes
q. Based on 3-sigma control limits for the runs test, does the pattern analysis indicate the A/B runs
are random?
No
r. Based on 3-sigma control limits for the runs test, does the pattern analysis indicate the U/D runs
are random?
No
s. Are the average checkout times in control (i.e. is the mean chart in control)? Why?
No. While the sample means are within the limits, the A/B runs are not random, and the
U/D runs are not random.
Based on your analysis is the bag filling process in control? Why? What should management do?
No, while the range chart indicates the variability of the bag process is in control, the mean
chart indicates the mean chart is not in control. Management should take immediate
corrective action and discuss with the people who work in the bag filling process to identify
potential causes for the problem. A TQM analysis such as the fishbone (Ishikawa) diagram
could be used to identify areas for improvement to get the process under control.
Based on the mean control chart, provide an explanation of what may be occurring.
It appears the pressure to increase production (fill more bags per hour) is creating the under
filled bags.
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