Using complexity data with disproportionate sampling with Product Report

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 Obs Obs per Adj Adj Adj Total Component Defs Units Unit Cmplx Defs Units Opps DPU DPMO 1 77 184 56 * 77 184 10304 0.418478 7472.8 2 3 907 95 * 3 907 86165 0.003308 34.8 3 59 750 59 * 59 750 44250 0.078667 1333.3 4 28 567 79 * 28 567 44793 0.049383 625.1 5 73 829 64 * 73 829 53056 0.088058 1375.9 6 28 132 30 * 28 132 3960 0.212121 7070.7 7 1 547 76 * 1 547 41572 0.001828 24.1 8 5 726 30 * 5 726 21780 0.006887 229.6 9 2 78 28 * 2 78 2184 0.025641 915.8 10 89 655 55 * 89 655 36025 0.135878 2470.5 11 74 715 98 * 74 715 70070 0.103497 1056.1 12 3 453 36 * 3 453 16308 0.006623 184.0 13 99 233 10 * 99 233 2330 0.424893 42489.3 14 49 726 80 * 49 726 58080 0.067493 843.7 15 78 832 81 * 78 832 67392 0.093750 1157.4 16 50 783 1 * 50 783 783 0.063857 63857.0 17 88 807 10 * 88 807 8070 0.109046 10904.6 18 61 123 40 * 61 123 4920 0.495935 12398.4 19 4 906 57 * 4 906 51642 0.004415 77.5 20 21 696 48 * 21 696 33408 0.030172 628.6 Total 892 657092 1357.5
Component Z.Shift Z.ST YTP 1 1.500 3.934 0.657014 2 1.500 5.478 0.996698 3 1.500 4.504 0.924299 4 1.500 4.727 0.951802 5 1.500 4.494 0.915652 6 1.500 3.954 0.808257 7 1.500 5.565 0.998173 8 1.500 5.004 0.993136 9 1.500 4.616 0.974673 10 1.500 4.311 0.872802 11 1.500 4.574 0.901630 12 1.500 5.062 0.993399 13 1.500 3.223 0.647793 14 1.500 4.640 0.934708 15 1.500 4.547 0.910461 16 1.500 3.023 0.936143 17 1.500 3.794 0.896152 18 1.500 3.745 0.607116 19 1.500 5.283 0.995595 20 1.500 4.726 0.970269 Total 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.

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