Suppose you want to generate various benchmark statistics for your product,
but you do not have the complexity data available.
Six Sigma Product Report
Rollup Statistics
Opps
per Adj Total
Component Obs Defs Obs Units Unit Cmplx Adj Defs Adj Units Opps
1 77 184 56 * 77 184 10304
2 3 907 95 * 3 907 86165
3 59 750 59 * 59 750 44250
4 28 567 79 * 28 567 44793
5 73 829 64 * 73 829 53056
6 28 132 30 * 28 132 3960
7 1 547 76 * 1 547 41572
8 5 726 30 * 5 726 21780
9 2 78 28 * 2 78 2184
10 89 655 55 * 89 655 36025
11 74 715 98 * 74 715 70070
12 3 453 36 * 3 453 16308
13 99 233 10 * 99 233 2330
14 49 726 80 * 49 726 58080
15 78 832 81 * 78 832 67392
16 50 783 1 * 50 783 783
17 88 807 10 * 88 807 8070
18 61 123 40 * 61 123 4920
19 4 906 57 * 4 906 51642
20 21 696 48 * 21 696 33408
Total 892 657092
Component DPU DPMO Z.Shift Z.ST YTP
1 0.418478 7472.8 1.500 3.934 0.657014
2 0.003308 34.8 1.500 5.478 0.996698
3 0.078667 1333.3 1.500 4.504 0.924299
4 0.049383 625.1 1.500 4.727 0.951802
5 0.088058 1375.9 1.500 4.494 0.915652
6 0.212121 7070.7 1.500 3.954 0.808257
7 0.001828 24.1 1.500 5.565 0.998173
8 0.006887 229.6 1.500 5.004 0.993136
9 0.025641 915.8 1.500 4.616 0.974673
10 0.135878 2470.5 1.500 4.311 0.872802
11 0.103497 1056.1 1.500 4.574 0.901630
12 0.006623 184.0 1.500 5.062 0.993399
13 0.424893 42489.3 1.500 3.223 0.647793
14 0.067493 843.7 1.500 4.640 0.934708
15 0.093750 1157.4 1.500 4.547 0.910461
16 0.063857 63857.0 1.500 3.023 0.936143
17 0.109046 10904.6 1.500 3.794 0.896152
18 0.495935 12398.4 1.500 3.745 0.607116
19 0.004415 77.5 1.500 5.283 0.995595
20 0.030172 628.6 1.500 4.726 0.970269
Total 1357.5 1.500 4.498
The total opportunities count is 657,092. The total DPMO is 1357.5, which
translates to an overall Z.ST of 4.498. Now, consider Component 16, which has
the lowest Z.ST (that is, the worst capability). Suppose that, because of an
upcoming scheduled downtime for the process that makes Component 16, you
produce 100 times as many units of Component 16, and also observe 100 times as
many defects.
Six Sigma Product Report
Rollup Statistics
Opps
per Adj Total
Component Obs Defs Obs Units Unit Cmplx Adj Defs Adj Units Opps
1 77 184 56 * 77 184 10304
2 3 907 95 * 3 907 86165
3 59 750 59 * 59 750 44250
4 28 567 79 * 28 567 44793
5 73 829 64 * 73 829 53056
6 28 132 30 * 28 132 3960
7 1 547 76 * 1 547 41572
8 5 726 30 * 5 726 21780
9 2 78 28 * 2 78 2184
10 89 655 55 * 89 655 36025
11 74 715 98 * 74 715 70070
12 3 453 36 * 3 453 16308
13 99 233 10 * 99 233 2330
14 49 726 80 * 49 726 58080
15 78 832 81 * 78 832 67392
16 5000 78300 1 * 5000 78300 78300
17 88 807 10 * 88 807 8070
18 61 123 40 * 61 123 4920
19 4 906 57 * 4 906 51642
20 21 696 48 * 21 696 33408
Total 5842 734609
Component DPU DPMO Z.Shift Z.ST YTP
1 0.418478 7472.8 1.500 3.934 0.657014
2 0.003308 34.8 1.500 5.478 0.996698
3 0.078667 1333.3 1.500 4.504 0.924299
4 0.049383 625.1 1.500 4.727 0.951802
5 0.088058 1375.9 1.500 4.494 0.915652
6 0.212121 7070.7 1.500 3.954 0.808257
7 0.001828 24.1 1.500 5.565 0.998173
8 0.006887 229.6 1.500 5.004 0.993136
9 0.025641 915.8 1.500 4.616 0.974673
10 0.135878 2470.5 1.500 4.311 0.872802
11 0.103497 1056.1 1.500 4.574 0.901630
12 0.006623 184.0 1.500 5.062 0.993399
13 0.424893 42489.3 1.500 3.223 0.647793
14 0.067493 843.7 1.500 4.640 0.934708
15 0.093750 1157.4 1.500 4.547 0.910461
16 0.063857 63857.0 1.500 3.023 0.936143
17 0.109046 10904.6 1.500 3.794 0.896152
18 0.495935 12398.4 1.500 3.745 0.607116
19 0.004415 77.5 1.500 5.283 0.995595
20 0.030172 628.6 1.500 4.726 0.970269
Total 7952.5 1.500 3.911
The total opportunity count was not affected much. It went from 657,092 to
734,609. However, total DPMO went from 1357 to 7952.5 (6 times as high). And
total Z.ST went from 4.498 to 3.911, a dramatic reduction of about one-half
sigma. All these changes are the result of increasing the production of
Component 16, not the result of any decay in capability.
Here is the same analysis with complexity data.
Six Sigma Product Report
Rollup Statistics
Opps
Obs Obs per Adj Adj Total
Component Defs Units Unit Cmplx Adj Defs Units Opps DPU
1 77 184 56 1 32.641 78 4368 0.418478
2 3 907 95 6 1.548 468 44460 0.003308
3 59 750 59 5 30.680 390 23010 0.078667
4 28 567 79 4 15.407 312 24648 0.049383
5 73 829 64 5 34.343 390 24960 0.088058
6 28 132 30 1 16.545 78 2340 0.212121
7 1 547 76 3 0.428 234 17784 0.001828
8 5 726 30 5 2.686 390 11700 0.006887
9 2 78 28 1 2.000 78 2184 0.025641
10 89 655 55 4 42.394 312 17160 0.135878
11 74 715 98 5 40.364 390 38220 0.103497
12 3 453 36 3 1.550 234 8424 0.006623
13 99 233 10 1 33.142 78 780 0.424893
14 49 726 80 5 26.322 390 31200 0.067493
15 78 832 81 5 36.563 390 31590 0.093750
16 50 783 1 5 24.904 390 390 0.063857
17 88 807 10 5 42.528 390 3900 0.109046
18 61 123 40 1 38.683 78 3120 0.495935
19 4 906 57 6 2.066 468 26676 0.004415
20 21 696 48 5 11.767 390 18720 0.030172
Total 436.561 78 335634
Component DPMO Z.Shift Z.ST YTP YRT
1 7472.8 1.500 3.934 0.657014 0.657014
2 34.8 1.500 5.478 0.996698 0.980350
3 1333.3 1.500 4.504 0.924299 0.674627
4 625.1 1.500 4.727 0.951802 0.820704
5 1375.9 1.500 4.494 0.915652 0.643655
6 7070.7 1.500 3.954 0.808257 0.808257
7 24.1 1.500 5.565 0.998173 0.994530
8 229.6 1.500 5.004 0.993136 0.966147
9 915.8 1.500 4.616 0.974673 0.974673
10 2470.5 1.500 4.311 0.872802 0.580315
11 1056.1 1.500 4.574 0.901630 0.595856
12 184.0 1.500 5.062 0.993399 0.980327
13 42489.3 1.500 3.223 0.647793 0.647793
14 843.7 1.500 4.640 0.934708 0.713475
15 1157.4 1.500 4.547 0.910461 0.625614
16 63857.0 1.500 3.023 0.936143 0.718970
17 10904.6 1.500 3.794 0.896152 0.577976
18 12398.4 1.500 3.745 0.607116 0.607116
19 77.5 1.500 5.283 0.995595 0.973857
20 628.6 1.500 4.726 0.970269 0.859926
Total 1300.7 1.500 4.511 0.003598
Now, the total DPMO is 1300.7, with a total Z.ST of 4.511. Remember, these
values should be slightly different from the original values because you used
the complexity data to adjust the unit counts and the defect counts. Now, you
increase the production of Component 16 as before, but with the complexity
data.
Six Sigma Product Report
Rollup Statistics
Opps
per Adj Adj Total
Component Obs Defs Obs Units Unit Cmplx Adj Defs Units Opps
1 77 184 56 1 32.641 78 4368
2 3 907 95 6 1.548 468 44460
3 59 750 59 5 30.680 390 23010
4 28 567 79 4 15.407 312 24648
5 73 829 64 5 34.343 390 24960
6 28 132 30 1 16.545 78 2340
7 1 547 76 3 0.428 234 17784
8 5 726 30 5 2.686 390 11700
9 2 78 28 1 2.000 78 2184
10 89 655 55 4 42.394 312 17160
11 74 715 98 5 40.364 390 38220
12 3 453 36 3 1.550 234 8424
13 99 233 10 1 33.142 78 780
14 49 726 80 5 26.322 390 31200
15 78 832 81 5 36.563 390 31590
16 5000 78300 1 5 24.904 390 390
17 88 807 10 5 42.528 390 3900
18 61 123 40 1 38.683 78 3120
19 4 906 57 6 2.066 468 26676
20 21 696 48 5 11.767 390 18720
Total 436.561 78 335634
Component DPU DPMO Z.Shift Z.ST YTP YRT
1 0.418478 7472.8 1.500 3.934 0.657014 0.657014
2 0.003308 34.8 1.500 5.478 0.996698 0.980350
3 0.078667 1333.3 1.500 4.504 0.924299 0.674627
4 0.049383 625.1 1.500 4.727 0.951802 0.820704
5 0.088058 1375.9 1.500 4.494 0.915652 0.643655
6 0.212121 7070.7 1.500 3.954 0.808257 0.808257
7 0.001828 24.1 1.500 5.565 0.998173 0.994530
8 0.006887 229.6 1.500 5.004 0.993136 0.966147
9 0.025641 915.8 1.500 4.616 0.974673 0.974673
10 0.135878 2470.5 1.500 4.311 0.872802 0.580315
11 0.103497 1056.1 1.500 4.574 0.901630 0.595856
12 0.006623 184.0 1.500 5.062 0.993399 0.980327
13 0.424893 42489.3 1.500 3.223 0.647793 0.647793
14 0.067493 843.7 1.500 4.640 0.934708 0.713475
15 0.093750 1157.4 1.500 4.547 0.910461 0.625614
16 0.063857 63857.0 1.500 3.023 0.936143 0.718970
17 0.109046 10904.6 1.500 3.794 0.896152 0.577976
18 0.495935 12398.4 1.500 3.745 0.607116 0.607116
19 0.004415 77.5 1.500 5.283 0.995595 0.973857
20 0.030172 628.6 1.500 4.726 0.970269 0.859926
Total 1300.7 1.500 4.511 0.003598
You can see that the only differences are in the observed units and observed
defects for Component 16. Using complexity data completely removed any effect
that is from the disproportionate production and sampling of Component 16.
