Perform successive rollups with Product Report

Suppose you want to use Product Report to perform successive rollups in order to determine the overall performance measures for a complex product. In this example, assume you have a product composed of the following assemblies:
  • Assembly 1 requires 2 units of subassembly 1-1 and 1 unit of subassembly 1-2.
  • Assembly 2 requires 4 units of subassembly 2-1, 2 units of subassembly 2-2, and 1 unit of subassembly 2-3.
  • Assembly 3 requires 1 unit of subassembly 3-1, 1 unit of subassembly 3-2, and 6 units of subassembly 3-3.

The end product requires 4 units of assembly 1, 2 units of assembly 2, and 1 unit of assembly 3.

Six Sigma Product Report

Rollup Statistics Opps Obs Obs per Adj Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU 1 21 1840 6 16 25.5652 2240 13440 0.0114130 2 6 602 8 4 5.5814 560 4480 0.0099668 3 8 560 3 4 8.0000 560 1680 0.0142857 4 9 567 5 4 8.8889 560 2800 0.0158730 5 7 729 2 4 5.3772 560 1120 0.0096022 6 8 297 9 2 7.5421 280 2520 0.0269360 Total 60.9548 140 26040
Component DPMO Z.Shift Z.ST YTP YRT 1 1902.2 1.220 4.114 0.988641 0.832949 2 1245.8 0.970 3.994 0.990077 0.960893 3 4761.9 1.640 4.233 0.985782 0.944330 4 3174.6 1.310 4.039 0.984227 0.938387 5 4801.1 1.360 3.950 0.990421 0.962230 6 2992.9 1.420 4.169 0.973384 0.947477 Total 2340.8 1.239 4.067 0.646617
Assembly 1, subassembly 1-1

Six Sigma Product Report

Rollup Statistics Opps Adj Obs Obs per Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU DPMO 1 8 649 3 4 7.9877 648 1944 0.0123267 4108.9 2 12 453 5 2 8.5828 324 1620 0.0264901 5298.0 3 6 360 3 2 5.4000 324 972 0.0166667 5555.6 4 3 231 4 1 2.1039 162 648 0.0129870 3246.8 5 2 212 6 1 1.5283 162 972 0.0094340 1572.3 Total 25.6027 162 6156 4159.0
Component Z.Shift Z.ST YTP YRT 1 1.410 4.053 0.987724 0.951793 2 1.330 3.886 0.973789 0.948265 3 0.870 3.409 0.983426 0.967126 4 1.160 3.882 0.987076 0.987076 5 1.090 4.043 0.990603 0.990603 Total 1.227 3.866 0.853504
Assembly 1, subassembly 1-2

Combine the data from subassembly 1-1 and subassembly 1-2 to make the report for assembly 1.

C1 C2 C3 C4 C5
Sub-assembly Defects Units Opps/Unit Z.Shift
 1-1 61 140 26040 / 140 = 186 1.24
 1-2 26 162 6156 / 162 = 38 1.23

Six Sigma Product Report

Rollup Statistics Opps Obs Obs per Adj Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU 1 61 140 186 2 61.0000 140 26040 0.435714 2 26 162 38 1 11.2346 70 2660 0.160494 Total 72.2346 70 28700
Component DPMO Z.Shift Z.ST YTP YRT 1 2342.5 1.240 4.068 0.646472 0.417926 2 4223.5 1.230 3.864 0.851434 0.851434 Total 2516.9 1.239 4.044 0.355836
Entire assembly 1

In the process of making 70 units of assembly 1, there are 72 defects. Overall, assembly 1 has a Z = 4.044 and YRT = 0.3558. Thus, the probability of making one unit of assembly 1 with 0 defects is ~ 36%.

Six Sigma Product Report

Rollup Statistics Opps Obs Obs per Adj Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU 1 9 844 3 3 7.7097 723 2169 0.0106635 2 27 1448 6 6 26.9627 1446 8676 0.0186464 3 29 842 4 3 24.9014 723 2892 0.0344418 4 3 468 2 1 1.5449 241 482 0.0064103 5 10 392 3 1 6.1480 241 723 0.0255102 6 3 347 5 1 2.0836 241 1205 0.0086455 Total 69.3503 241 16147
Component DPMO Z.Shift Z.ST YTP YRT 1 3554.5 1.220 3.912 0.989374 0.968461 2 3107.7 1.430 4.166 0.981498 0.893997 3 8610.5 1.640 4.022 0.966000 0.901430 4 3205.1 1.310 4.036 0.993600 0.993600 5 8503.4 1.160 3.547 0.974706 0.974706 6 1729.1 1.420 4.344 0.991384 0.991384 Total 4294.9 1.423 4.051 0.749337
Assembly 2, subassembly 2-1

Six Sigma Product Report

Rollup Statistics Opps Adj Obs Obs per Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU DPMO 1 10 364 8 1 8.4341 307 2456 0.0274725 3434.1 2 14 453 5 1 9.4879 307 1535 0.0309051 6181.0 3 8 307 6 1 8.0000 307 1842 0.0260586 4343.1 4 5 385 6 1 3.9870 307 1842 0.0129870 2164.5 Total 29.9089 307 7675 3896.9
Component Z.Shift Z.ST YTP YRT 1 1.410 4.113 0.972855 0.972855 2 1.330 3.832 0.969475 0.969475 3 1.160 3.784 0.974223 0.974223 4 1.090 3.943 0.987083 0.987083 Total 1.257 3.918 0.906978
Assembly 2, subassembly 2-2

Six Sigma Product Report

Rollup Statistics Opps Obs Obs per Adj Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU 1 16 837 6 4 12.3871 648 3888 0.0191159 2 11 453 5 2 7.8675 324 1620 0.0242826 3 4 360 3 2 3.6000 324 972 0.0111111 4 3 231 4 1 2.1039 162 648 0.0129870 5 4 192 6 1 3.3750 162 972 0.0208333 6 2 208 6 1 1.5577 162 972 0.0096154 7 5 226 4 1 3.5841 162 648 0.0221239 8 2 212 6 1 1.5283 162 972 0.0094340 Total 36.0036 162 10692
Component DPMO Z.Shift Z.ST YTP YRT 1 3186.0 1.350 4.078 0.981036 0.926274 2 4856.5 1.610 4.196 0.975952 0.952483 3 3703.7 1.190 3.868 0.988930 0.977983 4 3246.8 1.420 4.142 0.987076 0.987076 5 3472.2 1.080 3.779 0.979347 0.979347 6 1602.6 1.270 4.217 0.990423 0.990423 7 5531.0 1.340 3.881 0.978059 0.978059 8 1572.3 1.460 4.413 0.990603 0.990603 Total 3367.3 1.357 4.066 0.800387
Assembly 2, subassembly 2-3

Use the following data to make the report for assembly 2.

C1 C2 C3 C4 C5
Sub-assembly Defects Units Opps/Unit Z.Shift
 2-1 69 241 16147 / 241 = 67 1.42
 2-2 30 307 7675 / 307 = 25 1.26
 2-3 36 162 10692 / 162 = 66 1.36

Six Sigma Product Report

Rollup Statistics Opps Obs Obs per Adj Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU 1 69 241 67 4 68.7137 240 16080 0.286307 2 30 307 25 2 11.7264 120 3000 0.097720 3 36 162 66 1 13.3333 60 3960 0.222222 Total 93.7734 60 23040
Component DPMO Z.Shift Z.ST YTP YRT 1 4273.2 1.420 4.050 0.750571 0.317372 2 3908.8 1.260 3.920 0.906729 0.822158 3 3367.0 1.360 4.070 0.800437 0.800437 Total 4070.0 1.389 4.035 0.208858
Entire assembly 2

In the process of making 60 units of assembly 2, there are 94 defects. Overall, assembly 2 has a Z = 4.035 and YRT = 0.2089. Thus, the probability of making one unit of assembly 2 with 0 defects is ~ 21%.

Six Sigma Product Report

Rollup Statistics Opps Adj Obs Obs per Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU DPMO 1 4 214 3 1 3.7944 203 609 0.0186916 6230.5 2 9 456 6 2 8.0132 406 2436 0.0197368 3289.5 3 5 437 4 2 4.6453 406 1624 0.0114416 2860.4 4 4 812 2 4 4.0000 812 1624 0.0049261 2463.1 5 6 222 5 1 5.4865 203 1015 0.0270270 5405.4 Total 25.9393 203 7308 3549.4
Component Z.Shift Z.ST YTP YRT 1 1.370 3.869 0.981425 0.981425 2 1.260 3.977 0.980425 0.961233 3 1.590 4.353 0.988607 0.977344 4 1.380 4.192 0.995080 0.980465 5 1.420 3.969 0.973264 0.973264 Total 1.391 4.084 0.879823
Assembly 3, subassembly 3-1

Six Sigma Product Report

Rollup Statistics Opps Obs Obs per Adj Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU 1 5 268 2 1 3.9179 210 420 0.0186567 2 14 853 3 4 13.7866 840 2520 0.0164127 3 7 462 3 2 6.3636 420 1260 0.0151515 4 6 841 4 4 5.9929 840 3360 0.0071344 5 10 437 4 2 9.6110 420 1680 0.0228833 6 5 914 2 4 4.5952 840 1680 0.0054705 7 3 456 6 2 2.7632 420 2520 0.0065789 Total 47.0304 210 13440
Component DPMO Z.Shift Z.ST YTP YRT 1 9328.4 1.440 3.792 0.981430 0.981430 2 5470.9 1.610 4.155 0.983677 0.936289 3 5050.5 1.350 3.922 0.984925 0.970077 4 1783.6 1.330 4.244 0.992885 0.971841 5 5720.8 1.520 4.049 0.977312 0.955139 6 2735.2 1.410 4.188 0.994537 0.978327 7 1096.5 1.290 4.353 0.993439 0.986921 Total 3499.3 1.414 4.111 0.798921
Assembly 3, subassembly 3-2

Six Sigma Product Report

Rollup Statistics Opps Adj Obs Obs per Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU DPMO 1 14 519 4 3 12.9480 480 1920 0.0269750 6743.7 2 28 961 5 6 27.9709 960 4800 0.0291363 5827.3 3 5 187 6 1 4.2781 160 960 0.0267380 4456.3 Total 45.1969 160 7680 5885.0
Component Z.Shift Z.ST YTP YRT 1 1.440 3.911 0.973297 0.922010 2 1.380 3.902 0.971201 0.839181 3 1.570 4.185 0.973558 0.973558 Total 1.419 3.938 0.753274
Assembly 3, subassembly 3-3

Use the following data to make the report for assembly 3.

C1 C2 C3 C4 C5
Sub-assembly Defects Units Opps/Unit Z.Shift
 3-1 26 203 7308 / 203 = 36 1.39
 3-2 47 210 13440 / 210 = 64 1.41
 3-3 45 160 7680 / 160 = 48 1.42

Six Sigma Product Report

Rollup Statistics Opps Obs Obs per Adj Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU 1 26 203 36 1 7.685 60 2160 0.128079 2 47 210 64 2 26.857 120 7680 0.223810 3 45 160 48 6 101.250 360 17280 0.281250 Total 135.792 60 27120
Component DPMO Z.Shift Z.ST YTP YRT 1 3557.7 1.390 4.081 0.879583 0.879583 2 3497.0 1.410 4.107 0.799154 0.638647 3 5859.4 1.410 3.931 0.754215 0.184066 Total 5007.1 1.408 3.984 0.103398
Entire assembly 3

In the process of making 60 units of assembly 3, there are 136 defects. Overall, assembly 3 has a Z = 3.984 and YRT = 0.1034. Thus, the probability of making one unit of assembly 3 with 0 defects is ~ 10%.

Six Sigma Product Report

Rollup Statistics Opps Obs Obs per Adj Adj Total Component Defs Units Unit Cmplx Adj Defs Units Opps DPU 1 72 70 410 4 69.943 68 27880 1.02857 2 94 60 384 2 53.267 34 13056 1.56667 3 61 27 452 1 38.407 17 7684 2.25926 Total 161.617 17 48620
Component DPMO Z.Shift Z.ST YTP YRT 1 2508.7 1.240 4.046 0.357056 0.016253 2 4079.9 1.390 4.035 0.208072 0.043294 3 4998.4 1.420 3.996 0.103838 0.103838 Total 3324.1 1.309 4.023 0.000073
Entire product

You would expect to see 162 defects in 17 products. The entire product has a Z = 4.023 and YRT = 0.000073. Thus, the probability of producing an entire product with 0 defects is essentially 0. Considering the large opportunity count (48620 total opportunities divided by 17 products is 2860 opportunities per product) and the Z of 4, this result is expected.

The three assemblies are almost identical in capability, with Z values very close to 4.

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