six sigma green belt part 81).pdf · 8-1 six sigma green belt part 8 case study © 2011 iie and aft...
TRANSCRIPT
8-1
Six Sigma Green Belt
Part 8
Case Study
© 2011 IIE and Aft Systems, Inc.
© 2011 IIE and Aft Systems, Inc. 8-2
Case Study
• On the following pages are inspection results on the diameter of a component used in the transmission for a vehicle. Sample “C” came from supplier C. Sample “D” came from supplier D.
• Should the company use supplier C, or supplier D, or both, or neither? (Support with analysis.)
© 2011 IIE and Aft Systems, Inc. 8-3
Specifications
The nominal dimension for this product is 10 units
Tolerance limits are + .5 units making the specifications 9.50 and 10.50
© 2011 IIE and Aft Systems, Inc. 8-4
Supplier C
Lot Avg Range
7-Oct 10.0 9.7 10.0 9.8 9.875 0.3
14-Oct 9.9 10.0 10.2 9.7 9.950 0.5
21-Oct 10.1 10.0 9.9 10.2 10.050 0.3
28-Oct 10.0 9.9 10.1 10.0 10.000 0.2
4-Nov 10.0 9.9 10.0 10.1 10.000 0.2
11-Nov 9.9 10.0 10.0 9.9 9.950 0.1
18-Nov 10.1 10.0 9.9 9.9 9.975 0.2
25-Nov 10.0 9.8 9.9 10.0 9.925 0.2
2-Dec 10.0 10.0 10.1 9.7 9.950 0.4
9-Dec 9.9 10.0 10.0 10.0 9.975 0.1
16-Dec 9.9 10.0 10.1 10.0 10.000 0.2
23-Dec 10.0 10.2 9.8 10.1 10.025 0.4
Average: 9.973 0.258
Sample
© 2011 IIE and Aft Systems, Inc. 8-5
Supplier D
Lot Avg Range
7-Oct 9.6 10.0 10.0 9.5 9.775 0.5
14-Oct 9.5 9.9 10.5 9.6 9.875 1.0
21-Oct 10.5 10.2 10.1 9.7 10.125 0.8
28-Oct 9.9 9.8 10.3 10.5 10.125 0.7
4-Nov 9.7 9.9 10.0 10.3 9.975 0.6
11-Nov 9.6 9.8 10.1 9.8 9.825 0.5
18-Nov 10.4 10.3 9.6 10.4 10.175 0.8
25-Nov 10.1 9.8 9.7 10.2 9.950 0.5
2-Dec 10.1 10.0 10.4 9.9 10.100 0.5
9-Dec 9.5 10.3 10.4 10.0 10.050 0.9
16-Dec 9.7 10.2 10.5 10.2 10.150 0.8
23-Dec 10.0 10.2 10.5 10.1 10.200 0.5
Average: 10.03 0.675
Sample
© 2011 IIE and Aft Systems, Inc. 8-6
Expanded Normal Curve ValuesZ Proportion Z Proportion Z Proportion Z Proportion Z Proportion Z Proportion Z Proportion
3.51 0.00022405 3.82 0.00006673 4.14 0.00001737 4.25 0.00001069 4.57 0.00000244 4.89 0.00000050 5.21 0.00000009
3.52 0.00021577 3.83 0.00006407 4.15 0.00001662 4.26 0.00001022 4.58 0.00000232 4.90 0.00000048 5.22 0.00000009
3.53 0.00020778 3.84 0.00006152 4.16 0.00001591 4.27 0.00000977 4.59 0.00000222 4.91 0.00000046 5.23 0.00000008
3.54 0.00020006 3.85 0.00005906 4.17 0.00001523 4.28 0.00000934 4.60 0.00000211 4.92 0.00000043 5.24 0.00000008
3.55 0.00019262 3.86 0.00005669 4.18 0.00001458 4.29 0.00000893 4.61 0.00000201 4.93 0.00000041 5.25 0.00000008
3.56 0.00018543 3.87 0.00005442 4.19 0.00001395 4.30 0.00000854 4.62 0.00000192 4.94 0.00000039 5.26 0.00000007
3.57 0.00017849 3.88 0.00005223 4.20 0.00001335 4.31 0.00000816 4.63 0.00000183 4.95 0.00000037 5.27 0.00000007
3.58 0.00017180 3.89 0.00005012 4.21 0.00001277 4.32 0.00000780 4.64 0.00000174 4.96 0.00000035 5.28 0.00000006
3.59 0.00016534 3.90 0.00004810 4.22 0.00001222 4.33 0.00000746 4.65 0.00000166 4.97 0.00000033 5.29 0.00000006
3.60 0.00015911 3.91 0.00004615 4.23 0.00001168 4.34 0.00000712 4.66 0.00000158 4.98 0.00000032 5.30 0.00000006
3.61 0.00015310 3.92 0.00004427 4.24 0.00001118 4.35 0.00000681 4.67 0.00000151 4.99 0.00000030 5.31 0.00000005
3.62 0.00014730 3.93 0.00004247 4.25 0.00001069 4.36 0.00000650 4.68 0.00000143 5.00 0.00000029 5.32 0.00000005
3.63 0.00014171 3.94 0.00004074 4.26 0.00001022 4.37 0.00000621 4.69 0.00000137 5.01 0.00000027 5.33 0.00000005
3.64 0.00013632 3.95 0.00003908 4.27 0.00000977 4.38 0.00000593 4.70 0.00000130 5.02 0.00000026 5.34 0.00000005
3.65 0.00013112 3.96 0.00003747 4.28 0.00000934 4.39 0.00000567 4.71 0.00000124 5.03 0.00000025 5.35 0.00000004
3.66 0.00012611 3.97 0.00003594 4.29 0.00000893 4.40 0.00000541 4.72 0.00000118 5.04 0.00000023 5.36 0.00000004
3.67 0.00012128 3.98 0.00003446 4.30 0.00000854 4.41 0.00000517 4.73 0.00000112 5.05 0.00000022 5.37 0.00000004
3.68 0.00011662 3.99 0.00003304 4.31 0.00000816 4.42 0.00000494 4.74 0.00000107 5.06 0.00000021 5.38 0.00000004
3.69 0.00011213 4.00 0.00003167 4.11 0.00001978 4.43 0.00000471 4.75 0.00000102 5.07 0.00000020 5.39 0.00000004
3.70 0.00010780 4.01 0.00003036 4.12 0.00001894 4.44 0.00000450 4.76 0.00000097 5.08 0.00000019 5.40 0.00000003
3.71 0.00010363 4.02 0.00002910 4.13 0.00001814 4.45 0.00000429 4.77 0.00000092 5.09 0.00000018 5.41 0.00000003
3.72 0.00009961 4.03 0.00002789 4.14 0.00001737 4.46 0.00000410 4.78 0.00000088 5.10 0.00000017 5.42 0.00000003
3.73 0.00009574 4.04 0.00002673 4.15 0.00001662 4.47 0.00000391 4.79 0.00000083 5.11 0.00000016 5.43 0.00000003
3.74 0.00009201 4.05 0.00002561 4.16 0.00001591 4.48 0.00000373 4.80 0.00000079 5.12 0.00000015 5.44 0.00000003
3.75 0.00008842 4.06 0.00002454 4.17 0.00001523 4.49 0.00000356 4.81 0.00000075 5.13 0.00000014 5.45 0.00000003
3.76 0.00008496 4.07 0.00002351 4.18 0.00001458 4.50 0.00000340 4.82 0.00000072 5.14 0.00000014 5.46 0.00000002
3.77 0.00008162 4.08 0.00002252 4.19 0.00001395 4.51 0.00000324 4.83 0.00000068 5.15 0.00000013 5.47 0.00000002
3.78 0.00007841 4.09 0.00002157 4.20 0.00001335 4.52 0.00000309 4.84 0.00000065 5.16 0.00000012 5.48 0.00000002
3.79 0.00007532 4.10 0.00002066 4.21 0.00001277 4.53 0.00000295 4.85 0.00000062 5.17 0.00000012 5.49 0.00000002
3.80 0.00007235 4.11 0.00001978 4.22 0.00001222 4.54 0.00000281 4.86 0.00000059 5.18 0.00000011 5.50 0.00000002
3.81 0.00006948 4.12 0.00001894 4.23 0.00001168 4.55 0.00000268 4.87 0.00000056 5.19 0.00000011 5.51 0.00000002
3.82 0.00006673 4.13 0.00001814 4.24 0.00001118 4.56 0.00000256 4.88 0.00000053 5.20 0.00000010 5.52 0.00000002
© 2011 IIE and Aft Systems, Inc. 8-7
Green Belt Cheat Sheet
22 d
MRor
d
R
MeanLSLz
MeanUSLz
l
u
Cp = (Uspec – Lspec)/6
Cpk is the smaller of the following:
Cpku = (Uspec – Mean) / 3
Cpkl = (Mean – Lspec) / 3
RDLCLR
RDUCLR
RAxxLCL
RAxxUCL
3
4
2
2
MRDLCLMR
MRDUCLMR
d
MRxLCLx
d
MRxUCLx
3
4
2
2
3
3
3Level Sigma
Cpk
© 2011 IIE and Aft Systems, Inc. 8-8
28
27
26
25
24
23
22
21
20
19
18
17
16
Frequency 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
© 2011 IIE and Aft Systems, Inc. 8-9
28
27
26
25
24
23
22
21
20
19
18
17
16
Frequency 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
© 2011 IIE and Aft Systems, Inc. 8-10
28
27
26
25
24
23
22
21
20
19
18
17
16
Frequency 15
14
13
12
11
10
9
8
7
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4
3
2
1
© 2011 IIE and Aft Systems, Inc. 8-11
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27
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25
24
23
22
21
20
19
18
17
16
Frequency 15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
© 2011 IIE and Aft Systems, Inc. 8-12
Sample ID
Averages
Ranges
© 2011 IIE and Aft Systems, Inc. 8-13
Sample ID
Averages
Ranges
© 2011 IIE and Aft Systems, Inc. 8-14
Sample ID
Averages
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© 2011 IIE and Aft Systems, Inc. 8-15
Sample ID
Averages
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