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
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