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:

  1. Sample Range Measurements
  2. 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 2 years ago
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