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PART 2: Process Capability Bobcat Manufacturing is also concerned if the process

ID: 389791 • Letter: P

Question

PART 2: Process Capability Bobcat Manufacturing is also concerned if the process is capable of producing the part at the customer requested three-sigma quality level. The potential customer’s specifications for the part are 8.0 ± 3.0 millimeters.

Use the “Process Capability” solver in OM Explorer [Note: The table below is the same data as Part 1; combined and formatted for process capability solver.] Observations (millimeters) 9.1 8.9 8.8 7.6 8 9 8.2 9.1 8.2 8.2 8.3 7.9 10 8.1 8.9 9.2 8.1 6.9 10.1 7.9 9 8.7 9 7 7.5 8.9 7.8 9 9.3 9 9.3 9.1 10.1 8 8.8 7.7 8.8 10.8 8.7 10

(A) What is the process capability ratio (Cp)?

B) What is the process capability index (Cpk)?

(C) Is the process capable of producing three-sigma quality?

(D) If management wanted to improve the current process, should they first focus on reducing variability or centering the process?

Explanation / Answer

Let us first find SD

Sl no

Obs

Mean

diff

Square of diff

1

9.1

8.6

0.5

0.25

2

8.9

8.6

0.3

0.09

3

8.8

8.6

0.2

0.04

4

7.6

8.6

-1

1

5

8

8.6

-0.6

0.36

6

9

8.6

0.4

0.16

7

8.2

8.6

-0.4

0.16

8

9.1

8.6

0.5

0.25

9

8.2

8.6

-0.4

0.16

10

8.2

8.6

-0.4

0.16

11

8.3

8.6

-0.3

0.09

12

7.9

8.6

-0.7

0.49

13

10

8.6

1.4

1.96

14

8.1

8.6

-0.5

0.25

15

8.9

8.6

0.3

0.09

16

9.2

8.6

0.6

0.36

17

8.1

8.6

-0.5

0.25

18

6.9

8.6

-1.7

2.89

19

10.1

8.6

1.5

2.25

20

7.9

8.6

-0.7

0.49

21

9

8.6

0.4

0.16

22

8.7

8.6

0.1

0.01

23

9

8.6

0.4

0.16

24

7

8.6

-1.6

2.56

25

7.5

8.6

-1.1

1.21

26

8.9

8.6

0.3

0.09

27

7.8

8.6

-0.8

0.64

28

9

8.6

0.4

0.16

29

9.3

8.6

0.7

0.49

30

9

8.6

0.4

0.16

31

9.3

8.6

0.7

0.49

32

9.1

8.6

0.5

0.25

33

10.1

8.6

1.5

2.25

34

8

8.6

-0.6

0.36

35

8.8

8.6

0.2

0.04

36

7.7

8.6

-0.9

0.81

37

8.8

8.6

0.2

0.04

38

10.8

8.6

2.2

4.84

39

8.7

8.6

0.1

0.01

40

10

8.6

1.4

1.96

347

28.44

Mean = sum of obs/ no of obs

Mean = 347/40 = 8.6

SD = sum of square of diff/no of obs

SD = 28.44/40 = 0.711

Cp = (USL – LSL)/ 6 sigma

USL =11.0

LSL =5.0

Cp = (11-5)/6(0.711)

Cp = 0.001

If Cp is less than 1 process variation exceed specification and hence significant number of defects are made.

Cpk = (USL-Mean)/3 sigma or (Mean – LSL)/ 3Sigma which ever is lower

Cpk = (11- 8.6)/(3*0.711) or (8.6-5)/(3*0.711)

Cpk = 1.12 or 1.69

Cpk = 1.12

Since Cpk is less then 1.33 process is not capable

No, the process is not capable of producing 3 Sigma

Since Cp is less than 1 management should focus on process variability.

Sl no

Obs

Mean

diff

Square of diff

1

9.1

8.6

0.5

0.25

2

8.9

8.6

0.3

0.09

3

8.8

8.6

0.2

0.04

4

7.6

8.6

-1

1

5

8

8.6

-0.6

0.36

6

9

8.6

0.4

0.16

7

8.2

8.6

-0.4

0.16

8

9.1

8.6

0.5

0.25

9

8.2

8.6

-0.4

0.16

10

8.2

8.6

-0.4

0.16

11

8.3

8.6

-0.3

0.09

12

7.9

8.6

-0.7

0.49

13

10

8.6

1.4

1.96

14

8.1

8.6

-0.5

0.25

15

8.9

8.6

0.3

0.09

16

9.2

8.6

0.6

0.36

17

8.1

8.6

-0.5

0.25

18

6.9

8.6

-1.7

2.89

19

10.1

8.6

1.5

2.25

20

7.9

8.6

-0.7

0.49

21

9

8.6

0.4

0.16

22

8.7

8.6

0.1

0.01

23

9

8.6

0.4

0.16

24

7

8.6

-1.6

2.56

25

7.5

8.6

-1.1

1.21

26

8.9

8.6

0.3

0.09

27

7.8

8.6

-0.8

0.64

28

9

8.6

0.4

0.16

29

9.3

8.6

0.7

0.49

30

9

8.6

0.4

0.16

31

9.3

8.6

0.7

0.49

32

9.1

8.6

0.5

0.25

33

10.1

8.6

1.5

2.25

34

8

8.6

-0.6

0.36

35

8.8

8.6

0.2

0.04

36

7.7

8.6

-0.9

0.81

37

8.8

8.6

0.2

0.04

38

10.8

8.6

2.2

4.84

39

8.7

8.6

0.1

0.01

40

10

8.6

1.4

1.96

347

28.44