Download Quality Test 2: SPC

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Quality Test 2: SPC NAME:_________________________
Show all work, be neat, explain anything you feel needs explaining.
1. The following data (20 samples) was collected on a production line to determine whether
or not the process was in a state of statistical control and to hopefully use SPC to monitor
the process in the future.
Sample
1
2
…
19
20
X1
135.83
126.56
…
121.24
140.04
X2
134.22
126.74
…
134.49
137.39
X3
121.07
128.10
…
131.86
123.55
X4
125.70
127.97
…
125.29
130.72
X5
X-Bar
R
137.62
130.89
16.55
126.56
127.19
1.54
…
…
…
121.06
126.79
13.44
113.45
129.03
26.59
X-Bar-Bar = 130.30
R-Bar = 12.53
X-Bar
X-Bar Chart
138
134
130
126
122
1
3
5
7
9
11 13 15 17 19
Sample
R
R Chart
30
25
20
15
10
5
0
1
3
5
7
9
11
13
15
17
19
Sample
a. Calculate control limits for X-Bar and R chart.
b. Show the control chart limits on control charts and determine if process appears to be
in a state of statistical control.
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2. When setting up a control chart to determine if a process was stable, 20 samples of size
5 were collected with X-Bar-Bar = 130.3 and R-Bar = 12.53. After the process was
determined to be stable, you are asked the following questions.
a. What is the standard deviation of the process?
b. What is the capability index Cp assuming the spec is 130 + 20?
c.
What is the capability index Cpk assuming the spec is 130 + 20?
d. Explain why you would consider this process either capable or not capable.
e. Draw a picture of the process and show spec limits as well as the edges of the
process.
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3. You are currently using X-Bar and R charts to monitor a process that has been very stable for
some time. During today’s production run, the first 9 values for X-Bar and R are shown below
reflecting a process that is still in control. Show what you would expect the charts to look like for
the next 11 observations if the mean were to dramatically decrease and the standard deviation
were to stay the same after the 9th observation (that means obs. 10 -20). MAKE IT OBVIOUS.
X-bar Chart for X Bar
X-bar
123
UCL = 122.47
122
CTR = 119.79
121
LCL = 117.10
120
119
118
117
0
2
4
6
8
10
12
14
16
18
20
Subgroup
Range Chart for R
10
UCL = 9.84
Range
8
CTR = 4.66
LCL = 0.00
6
4
2
0
0
2
4
6
8
10
12
Subgroup
14
16
18
20
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4. You are currently using X-Bar and R charts to monitor a process that has been very stable for
some time. During today’s production run, the first 9 values for X-Bar and R are shown below
reflecting a process that is still in control. Show what you would expect the charts to look like for
the next 11 observations if the mean were to dramatically increase and the standard deviation
were to dramatically increase after the 9th observation (that means obs. 10-20). MAKE IT
OBVIOUS.
X-bar Chart for X Bar
X-bar
123
UCL = 122.47
122
CTR = 119.79
121
LCL = 117.10
120
119
118
117
0
2
4
6
8
10
12
14
16
18
20
Subgroup
Range Chart for R
10
UCL = 9.84
Range
8
CTR = 4.66
LCL = 0.00
6
4
2
0
0
2
4
6
8
10
12
Subgroup
14
16
18
20
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5. The government is concerned about the population of golden eagles in the
national forests because they are considered an endangered species. They
do not want the number of eagles to get too large since there is a limited
supply of food and too many eagles would result in starvation. Also, they do
not want the number of eagles to decline because they are considered a
national treasure. Your boss has suggested that you fly over a randomly
selected number of acres each spring and count the number of eagles seen.
A young intern who just completed a course in quality control suggest that
your boss use SPC to monitor the eagle population. Everyone agrees that
an acceptable state for the eagle population is 16 eagles/100 acres. The
intern suggests that they randomly select 100 acres each spring and count
the number of eagles spotted. If the count exceeds the upper control limit,
they could capture some eagles in the park and transport them elsewhere. If
the count was below the lower control limit, they could put out eagle food and
bring in eagle doctors to cure any diseases that the population of eagles may
have until the population increases back to the desired level.
a. Suggest what control chart would be appropriate for this application.
b. Calculate the control chart limits for the one you selected.
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6. When setting up X-Bar and R charts, discuss the following issues
a. How large should your sample size be at each point in time? Use power curves to
help explain the impact sample size has on the effectiveness of the control charts.
b. How frequent should you take your samples? What are the issues that would
influence the frequency of your samples [every 5 minutes, every 15 minutes, etc.]
7. Briefly explain Type I and Type II errors as they pertain to control charts.
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8. Your boss has ask you to set up X-Bar and R control charts to monitor the fill
volume of 12 oz. cans of Koke. The spec for Koke is 12 + 0.6 oz. [Target
mean is 12 and maximum allowable standard deviation is 0.2]. After
collecting data [25 samples of size 4 during an eight hour production run]
your X-Bar-Bar was 11.8 oz. resulting in your X-Bar control chart being
centered at 11.8 oz. rather than the target value of 12.0 oz. When you boss
saw this, she became very upset because “the mean fill is suppose to be
12.0, not 11.8”. She told you to go get X-Bar and R control charts that
would force the process to meet spec [Mean = 12.0 and standard deviation
equal to 0.2]. In other words, assume the mean and standard deviation of
the process was 12.0 and 0.2 respectively. Use these values to determine
the upper and lower limits for your X-Bar and R control charts.
a. X-Bar Chart:
UCL =
Center line =
LCL =
b. R-Chart:
UCL =
Center line =
LCL =