Question
In: Statistics and Probability
Consider the piston ring data in the following table. Assume that specifications are 74.00 ± 0.035...
Consider the piston ring data in the following table. Assume that specifications are 74.00 ± 0.035 mm. Estimate the process capability (Cp and Cpk) using:
- Sample Range Measurements
- Sample Std Dev. Measurements
Convert the Cp found above into approximate dpm.
Inside Diameter Measurements (mm) for Automobile Piston Rings
|
Sample |
ID |
|
1 |
74.03 |
|
1 |
74.002 |
|
1 |
74.019 |
|
1 |
73.992 |
|
1 |
74.008 |
|
2 |
73.995 |
|
2 |
73.992 |
|
2 |
74.001 |
|
2 |
74.011 |
|
2 |
74.004 |
|
3 |
73.988 |
|
3 |
74.024 |
|
3 |
74.021 |
|
3 |
74.005 |
|
3 |
74.002 |
|
4 |
74.002 |
|
4 |
73.996 |
|
4 |
73.993 |
|
4 |
74.015 |
|
4 |
74.009 |
|
5 |
73.992 |
|
5 |
74.007 |
|
5 |
74.015 |
|
5 |
73.989 |
|
5 |
74.014 |
|
6 |
74.009 |
|
6 |
73.994 |
|
6 |
73.997 |
|
6 |
73.985 |
|
6 |
73.993 |
|
7 |
73.995 |
|
7 |
74.006 |
|
7 |
73.994 |
|
7 |
74 |
|
7 |
74.005 |
|
8 |
73.985 |
|
8 |
74.003 |
|
8 |
73.993 |
|
8 |
74.015 |
|
8 |
73.988 |
|
9 |
74.008 |
|
9 |
73.995 |
|
9 |
74.009 |
|
9 |
74.005 |
|
9 |
74.004 |
|
10 |
73.998 |
|
10 |
74 |
|
10 |
73.99 |
|
10 |
74.007 |
|
10 |
73.995 |
|
11 |
73.994 |
|
11 |
73.998 |
|
11 |
73.994 |
|
11 |
73.995 |
|
11 |
73.99 |
|
12 |
74.004 |
|
12 |
74 |
|
12 |
74.007 |
|
12 |
74 |
|
12 |
73.996 |
|
13 |
73.983 |
|
13 |
74.002 |
|
13 |
73.998 |
|
13 |
73.997 |
|
13 |
74.012 |
|
14 |
74.006 |
|
14 |
73.967 |
|
14 |
73.994 |
|
14 |
74 |
|
14 |
73.984 |
|
15 |
74.012 |
|
15 |
74.014 |
|
15 |
73.998 |
|
15 |
73.999 |
|
15 |
74.007 |
Solutions
Expert Solution
Solution:
Overall Range = Average of all Ranges = 0.022733
Overall Standard Deviation in this regard is: 0.00537
Calculations:
Part B:
Standard Deviation Case
Here,
CPK = 2.131
So there will be 0 DPM in this regard.
Refer the chart given below...
Range Case
Here,
CPK = 0.504,
So, there will be close to 500000 DPM in this regard.
Refer the chart given below for reference...
End of the Solution...,
orchestra answered 3 years agoRelated Solutions
Problem#: Consider the data shown. Assume that the specifications on this component are 74.05 and 73.95...
Problem#: Consider the data shown. Assume that the
specifications on this component are 74.05 and 73.95 mm.
(a)Estimate process capability for the piston-ring process, for
both Cp &Cpk and
Estimate the percentage of piston rings produced that will be
outside of the specifications?
Sample Number
Observation 1
Observation 2
Observation 3
Observation 4
Observation 5
1
74.03
74.002
74.019
73.992
74.008
2
73.995
73.992
74.001
74.011
74.004
3
73.988
74.024
74.021
74.005
74.002
4
74.002
73.996
73.993
74.015
74.009
5...
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Initial index rate 5.4%
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Total
Product
Average
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Average
Variable Cost
Average
Total Cost
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0
1
$60.00
$45.00
$105.00
$45.00
2
30.00
42.50
72.50
40.00
3
20.00
40.00
60.00
35.00
4
15.00
37.50
52.50
30.00
5
12.00
37.00
49.00
35.00
6
10.00
37.50
47.50
40.00
7
8.57
38.57
47.14
45.00
8
7.50
40.63
48.13
55.00
9
6.67
43.33
50.00
65.00
10
6.00
46.50
52.50
75.00
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