tablas estadisticas rev. 5

z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

-4 0.000032 0.000030 0.000029 0.000028 0.000027 0.000026 0.000025 0.000024 0.000023 0.000022

-3.9 0.000048 0.000046 0.000044 0.000042 0.000041 0.000039 0.000037 0.000036 0.000034 0.000033

-3.8 0.000072 0.000069 0.000067 0.000064 0.000062 0.000059 0.000057 0.000054 0.000052 0.000050

-3.7 0.000108 0.000104 0.000100 0.000096 0.000092 0.000088 0.000085 0.000082 0.000078 0.000075

-3.6 0.000159 0.000153 0.000147 0.000142 0.000136 0.000131 0.000126 0.000121 0.000117 0.000112

-3.5 0.000233 0.000224 0.000216 0.000208 0.000200 0.000193 0.000185 0.000178 0.000172 0.000165

-3.4 0.000337 0.000325 0.000313 0.000302 0.000291 0.000280 0.000270 0.000260 0.000251 0.000242

-3.3 0.000483 0.000466 0.000450 0.000434 0.000419 0.000404 0.000390 0.000376 0.000362 0.000349

-3.2 0.000687 0.000664 0.000641 0.000619 0.000598 0.000577 0.000557 0.000538 0.000519 0.000501

-3.1 0.000968 0.000935 0.000904 0.000874 0.000845 0.000816 0.000789 0.000762 0.000736 0.000711

-3 0.001350 0.001306 0.001264 0.001223 0.001183 0.001144 0.001107 0.001070 0.001035 0.001001

-2.9 0.001866 0.001807 0.001750 0.001695 0.001641 0.001589 0.001538 0.001489 0.001441 0.001395

-2.8 0.002555 0.002477 0.002401 0.002327 0.002256 0.002186 0.002118 0.002052 0.001988 0.001926

-2.7 0.003467 0.003364 0.003264 0.003167 0.003072 0.002980 0.002890 0.002803 0.002718 0.002635

-2.6 0.004661 0.004527 0.004396 0.004269 0.004145 0.004025 0.003907 0.003793 0.003681 0.003573

-2.5 0.006210 0.006037 0.005868 0.005703 0.005543 0.005386 0.005234 0.005085 0.004940 0.004799

-2.4 0.008198 0.007976 0.007760 0.007549 0.007344 0.007143 0.006947 0.006756 0.006569 0.006387

-2.3 0.010724 0.010444 0.010170 0.009903 0.009642 0.009387 0.009137 0.008894 0.008656 0.008424

-2.2 0.013903 0.013553 0.013209 0.012874 0.012545 0.012224 0.011911 0.011604 0.011304 0.011011

-2.1 0.017864 0.017429 0.017003 0.016586 0.016177 0.015778 0.015386 0.015003 0.014629 0.014262

-2 0.022750 0.022216 0.021692 0.021178 0.020675 0.020182 0.019699 0.019226 0.018763 0.018309

-1.9 0.028717 0.028067 0.027429 0.026803 0.026190 0.025588 0.024998 0.024419 0.023852 0.023295

-1.8 0.035930 0.035148 0.034380 0.033625 0.032884 0.032157 0.031443 0.030742 0.030054 0.029379

-1.7 0.044565 0.043633 0.042716 0.041815 0.040930 0.040059 0.039204 0.038364 0.037538 0.036727

-1.6 0.054799 0.053699 0.052616 0.051551 0.050503 0.049471 0.048457 0.047460 0.046479 0.045514

-1.5 0.066807 0.065522 0.064255 0.063008 0.061780 0.060571 0.059380 0.058208 0.057053 0.055917

-1.4 0.080757 0.079270 0.077804 0.076359 0.074934 0.073529 0.072145 0.070781 0.069437 0.068112

-1.3 0.096800 0.095098 0.093418 0.091759 0.090123 0.088508 0.086915 0.085343 0.083793 0.082264

-1.2 0.115070 0.113139 0.111232 0.109349 0.107488 0.105650 0.103835 0.102042 0.100273 0.098525

-1.1 0.135666 0.133500 0.131357 0.129238 0.127143 0.125072 0.123024 0.121000 0.119000 0.117023

-1 0.158655 0.156248 0.153864 0.151505 0.149170 0.146859 0.144572 0.142310 0.140071 0.137857

-0.9 0.184060 0.181411 0.178786 0.176186 0.173609 0.171056 0.168528 0.166023 0.163543 0.161087

-0.8 0.211855 0.208970 0.206108 0.203269 0.200454 0.197663 0.194895 0.192150 0.189430 0.186733

-0.7 0.241964 0.238852 0.235762 0.232695 0.229650 0.226627 0.223627 0.220650 0.217695 0.214764

-0.6 0.274253 0.270931 0.267629 0.264347 0.261086 0.257846 0.254627 0.251429 0.248252 0.245097

-0.5 0.308538 0.305026 0.301532 0.298056 0.294599 0.291160 0.287740 0.284339 0.280957 0.277595

-0.4 0.344578 0.340903 0.337243 0.333598 0.329969 0.326355 0.322758 0.319178 0.315614 0.312067

-0.3 0.382089 0.378280 0.374484 0.370700 0.366928 0.363169 0.359424 0.355691 0.351973 0.348268

-0.2 0.420740 0.416834 0.412936 0.409046 0.405165 0.401294 0.397432 0.393580 0.389739 0.385908

-0.1 0.460172 0.456205 0.452242 0.448283 0.444330 0.440382 0.436441 0.432505 0.428576 0.424655

0 0.500000 0.503989 0.507978 0.511966 0.515953 0.519939 0.523922 0.527903 0.531881 0.535856

0.1 0.539828 0.543795 0.547758 0.551717 0.555670 0.559618 0.563559 0.567495 0.571424 0.575345

0.2 0.579260 0.583166 0.587064 0.590954 0.594835 0.598706 0.602568 0.606420 0.610261 0.614092

0.3 0.617911 0.621720 0.625516 0.629300 0.633072 0.636831 0.640576 0.644309 0.648027 0.651732

0.4 0.655422 0.659097 0.662757 0.666402 0.670031 0.673645 0.677242 0.680822 0.684386 0.687933

0.5 0.691462 0.694974 0.698468 0.701944 0.705401 0.708840 0.712260 0.715661 0.719043 0.722405

0.6 0.725747 0.729069 0.732371 0.735653 0.738914 0.742154 0.745373 0.748571 0.751748 0.754903

0.7 0.758036 0.761148 0.764238 0.767305 0.770350 0.773373 0.776373 0.779350 0.782305 0.785236

0.8 0.788145 0.791030 0.793892 0.796731 0.799546 0.802337 0.805105 0.807850 0.810570 0.813267

0.9 0.815940 0.818589 0.821214 0.823814 0.826391 0.828944 0.831472 0.833977 0.836457 0.838913

1 0.841345 0.843752 0.846136 0.848495 0.850830 0.853141 0.855428 0.857690 0.859929 0.862143

1.1 0.864334 0.866500 0.868643 0.870762 0.872857 0.874928 0.876976 0.879000 0.881000 0.882977

1.2 0.884930 0.886861 0.888768 0.890651 0.892512 0.894350 0.896165 0.897958 0.899727 0.901475

1.3 0.903200 0.904902 0.906582 0.908241 0.909877 0.911492 0.913085 0.914657 0.916207 0.917736

1.4 0.919243 0.920730 0.922196 0.923641 0.925066 0.926471 0.927855 0.929219 0.930563 0.931888

1.5 0.933193 0.934478 0.935745 0.936992 0.938220 0.939429 0.940620 0.941792 0.942947 0.944083

1.6 0.945201 0.946301 0.947384 0.948449 0.949497 0.950529 0.951543 0.952540 0.953521 0.954486

1.7 0.955435 0.956367 0.957284 0.958185 0.959070 0.959941 0.960796 0.961636 0.962462 0.963273

1.8 0.964070 0.964852 0.965620 0.966375 0.967116 0.967843 0.968557 0.969258 0.969946 0.970621

1.9 0.971283 0.971933 0.972571 0.973197 0.973810 0.974412 0.975002 0.975581 0.976148 0.976705

2 0.977250 0.977784 0.978308 0.978822 0.979325 0.979818 0.980301 0.980774 0.981237 0.981691

2.1 0.982136 0.982571 0.982997 0.983414 0.983823 0.984222 0.984614 0.984997 0.985371 0.985738

2.2 0.986097 0.986447 0.986791 0.987126 0.987455 0.987776 0.988089 0.988396 0.988696 0.988989

2.3 0.989276 0.989556 0.989830 0.990097 0.990358 0.990613 0.990863 0.991106 0.991344 0.991576

2.4 0.991802 0.992024 0.992240 0.992451 0.992656 0.992857 0.993053 0.993244 0.993431 0.993613

2.5 0.993790 0.993963 0.994132 0.994297 0.994457 0.994614 0.994766 0.994915 0.995060 0.995201

2.6 0.995339 0.995473 0.995604 0.995731 0.995855 0.995975 0.996093 0.996207 0.996319 0.996427

2.7 0.996533 0.996636 0.996736 0.996833 0.996928 0.997020 0.997110 0.997197 0.997282 0.997365

2.8 0.997445 0.997523 0.997599 0.997673 0.997744 0.997814 0.997882 0.997948 0.998012 0.998074

2.9 0.998134 0.998193 0.998250 0.998305 0.998359 0.998411 0.998462 0.998511 0.998559 0.998605

3 0.998650 0.998694 0.998736 0.998777 0.998817 0.998856 0.998893 0.998930 0.998965 0.998999

3.1 0.999032 0.999065 0.999096 0.999126 0.999155 0.999184 0.999211 0.999238 0.999264 0.999289

3.2 0.999313 0.999336 0.999359 0.999381 0.999402 0.999423 0.999443 0.999462 0.999481 0.999499

3.3 0.999517 0.999534 0.999550 0.999566 0.999581 0.999596 0.999610 0.999624 0.999638 0.999651

3.4 0.999663 0.999675 0.999687 0.999698 0.999709 0.999720 0.999730 0.999740 0.999749 0.999758

3.5 0.999767 0.999776 0.999784 0.999792 0.999800 0.999807 0.999815 0.999822 0.999828 0.999835

3.6 0.999841 0.999847 0.999853 0.999858 0.999864 0.999869 0.999874 0.999879 0.999883 0.999888

3.7 0.999892 0.999896 0.999900 0.999904 0.999908 0.999912 0.999915 0.999918 0.999922 0.999925

3.8 0.999928 0.999931 0.999933 0.999936 0.999938 0.999941 0.999943 0.999946 0.999948 0.999950

3.9 0.999952 0.999954 0.999956 0.999958 0.999959 0.999961 0.999963 0.999964 0.999966 0.999967

4 0.999968 0.999970 0.999971 0.999972 0.999973 0.999974 0.999975 0.999976 0.999977 0.999978

IND 214 Tabla N 1 - Areas bajo la curva normal estandar, desde -infinito a z = (x-media)/desviacion estandar

A A2 A3 c4 1/c4 B3 B4 B5 B6 d2 1/d2 d3 D1 D2 D3 D4 d2*2 2.1210 1.8806 2.6586 0.7979 1.2533 0 3.2664 0 2.6063 1.1280 0.8865 0.8530 0 3.6870 0 3.269 1.411

3 1.7320 1.0231 1.9545 0.8862 1.1284 0 2.5684 0 2.2761 1.6930 0.5907 0.8880 0 4.3570 0 2.574 1.907

4 1.5000 0.7285 1.6281 0.9213 1.0854 0 2.2662 0 2.0879 2.0590 0.4857 0.8800 0 4.6990 0 2.282 2.239

5 1.3420 0.5768 1.4273 0.9400 1.0638 0 2.0889 0 1.9635 2.3260 0.4299 0.8640 0 4.9180 0 2.114 2.476

6 1.2250 0.4833 1.2872 0.9515 1.0510 0.0300 1.9700 0.0286 1.8744 2.5340 0.3946 0.8480 0 5.0780 0 2.004 2.668

7 1.1340 0.4193 1.1819 0.9594 1.0423 0.1180 1.8820 0.1133 1.8055 2.7040 0.3698 0.8330 0.2050 5.2030 0.0758 1.924 2.830

8 1.0610 0.3726 1.0991 0.9650 1.0363 0.1847 1.8153 0.1783 1.7517 2.8470 0.3512 0.8200 0.3870 5.3070 0.1359 1.864 2.960

9 1.0000 0.3367 1.0317 0.9693 1.0317 0.2390 1.7610 0.2317 1.7069 2.9700 0.3367 0.8080 0.5460 5.3940 0.1838 1.816 3.084

10 0.9490 0.3082 0.9753 0.9727 1.0281 0.2843 1.7157 0.2765 1.6689 3.0780 0.3249 0.7970 0.6870 5.4690 0.2232 1.777 3.179

11 0.9050 0.2851 0.9273 0.9754 1.0252 0.3220 1.6780 0.3141 1.6367 3.1730 0.3152 0.7870 0.8120 5.5340 0.2559 1.744 3.273

12 0.8660 0.2658 0.8859 0.9776 1.0229 0.3541 1.6459 0.3462 1.6090 3.2580 0.3069 0.7780 0.9240 5.5920 0.2836 1.716 3.344

13 0.8320 0.2494 0.8496 0.9794 1.0210 0.3815 1.6185 0.3736 1.5852 3.3360 0.2998 0.7700 1.0260 5.6460 0.3076 1.692 3.409

14 0.8020 0.2353 0.8173 0.9810 1.0194 0.4067 1.5933 0.3990 1.5630 3.4070 0.2935 0.7630 1.1180 5.6960 0.3281 1.672 3.469

15 0.7750 0.2231 0.7886 0.9823 1.0180 0.4279 1.5721 0.4204 1.5442 3.4720 0.2880 0.7560 1.2040 5.7400 0.3468 1.653 3.525

16 0.7500 0.2123 0.7626 0.9835 1.0168 0.4482 1.5518 0.4408 1.5262 3.5320 0.2831 0.7500 1.2820 5.7820 0.3630 1.637 3.578

17 0.7280 0.2028 0.7391 0.9845 1.0157 0.4656 1.5344 0.4583 1.5107 3.5880 0.2787 0.7440 1.3560 5.8200 0.3779 1.622 3.627

18 0.7070 0.1943 0.7176 0.9854 1.0148 0.4817 1.5183 0.4746 1.4962 3.6400 0.2747 0.7390 1.4230 5.8570 0.3909 1.609 3.674

19 0.6880 0.1866 0.6979 0.9862 1.0140 0.4964 1.5036 0.4895 1.4829 3.6890 0.2711 0.7340 1.4870 5.8910 0.4031 1.597 3.718

20 0.6710 0.1796 0.6797 0.9869 1.0133 0.5096 1.4904 0.5029 1.4709 3.7350 0.2677 0.7290 1.5480 5.9220 0.4145 1.586 3.760

21 0.6550 0.1733 0.6629 0.9876 1.0126 0.5231 1.4769 0.5166 1.4586 3.7780 0.2647 0.7240 1.6060 5.9500 0.4251 1.575 3.799

22 0.6400 0.1675 0.6472 0.9882 1.0119 0.5350 1.4650 0.5287 1.4477 3.8190 0.2618 0.7200 1.6590 5.9790 0.4344 1.566 3.837

23 0.6260 0.1621 0.6327 0.9887 1.0114 0.5451 1.4549 0.5390 1.4384 3.8580 0.2592 0.7160 1.7100 6.0060 0.4432 1.557 3.874

24 0.6120 0.1572 0.6191 0.9892 1.0109 0.5555 1.4445 0.5495 1.4289 3.8950 0.2567 0.7120 1.7590 6.0310 0.4516 1.548 3.908

25 0.6000 0.1526 0.6063 0.9896 1.0105 0.5639 1.4361 0.5581 1.4211 3.9310 0.2544 0.7080 1.8070 6.0550 0.4597 1.540 3.941

Carta para rangos

Del apendice C

Manual MSA AIAGObservaciones

en la muestra,

n

IND 214 Tabla N 2 - Factores para el calculo de las lineas centrales y limites de control por variables

Factores para los lmites de

control

Factores para la

lnea central Factores para los lmites de control

Factores para la

lnea central Factores para los lmites de control

Carta de promedios Carta para desviaciones estndar

c0 0.9900 0.9900 0.9802 0.9802 0.9704 0.9704 0.9608 0.9608 0.9512 0.9512 0.9418 0.9418 0.9324 0.9324 0.9231 0.9231 0.9139 0.9139 0.9048 0.9048 0.8869 0.8869 0.8694 0.8694

1 0.0099 1.0000 0.0196 0.9998 0.0291 0.9996 0.0384 0.9992 0.0476 0.9988 0.0565 0.9983 0.0653 0.9977 0.0738 0.9970 0.0823 0.9962 0.0905 0.9953 0.1064 0.9934 0.1217 0.9911

2 0.0000 1.0000 0.0002 1.0000 0.0004 1.0000 0.0008 1.0000 0.0012 1.0000 0.0017 1.0000 0.0023 0.9999 0.0030 0.9999 0.0037 0.9999 0.0045 0.9998 0.0064 0.9997 0.0085 0.9996

3 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 1.0000 0.0001 1.0000 0.0001 1.0000 0.0002 1.0000 0.0003 1.0000 0.0004 1.0000

0 0.8521 0.8521 0.8353 0.8353 0.8187 0.8187 0.7788 0.7788 0.7408 0.7408 0.7047 0.7047 0.6703 0.6703 0.6376 0.6376 0.6065 0.6065 0.5769 0.5769 0.5488 0.5488 0.5220 0.5220

1 0.1363 0.9885 0.1503 0.9856 0.1637 0.9825 0.1947 0.9735 0.2222 0.9631 0.2466 0.9513 0.2681 0.9384 0.2869 0.9246 0.3033 0.9098 0.3173 0.8943 0.3293 0.8781 0.3393 0.8614

2 0.0109 0.9994 0.0135 0.9992 0.0164 0.9989 0.0243 0.9978 0.0333 0.9964 0.0432 0.9945 0.0536 0.9921 0.0646 0.9891 0.0758 0.9856 0.0873 0.9815 0.0988 0.9769 0.1103 0.9717

3 0.0006 1.0000 0.0008 1.0000 0.0011 0.9999 0.0020 0.9999 0.0033 0.9997 0.0050 0.9995 0.0072 0.9992 0.0097 0.9988 0.0126 0.9982 0.0160 0.9975 0.0198 0.9966 0.0239 0.9956

4 0.0000 1.0000 0.0000 1.0000 0.0001 1.0000 0.0001 1.0000 0.0003 1.0000 0.0004 1.0000 0.0007 0.9999 0.0011 0.9999 0.0016 0.9998 0.0022 0.9997 0.0030 0.9996 0.0039 0.9994

5 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 1.0000 0.0001 1.0000 0.0002 1.0000 0.0002 1.0000 0.0004 1.0000 0.0005 0.9999

0 0.4966 0.4966 0.4724 0.4724 0.4493 0.4493 0.4274 0.4274 0.4066 0.4066 0.3867 0.3867 0.3679 0.3679 0.3329 0.3329 0.3012 0.3012 0.2725 0.2725 0.2466 0.2466 0.2231 0.2231

1 0.3476 0.8442 0.3543 0.8266 0.3595 0.8088 0.3633 0.7907 0.3659 0.7725 0.3674 0.7541 0.3679 0.7358 0.3662 0.6990 0.3614 0.6626 0.3543 0.6268 0.3452 0.5918 0.3347 0.5578

2 0.1217 0.9659 0.1329 0.9595 0.1438 0.9526 0.1544 0.9451 0.1647 0.9371 0.1745 0.9287 0.1839 0.9197 0.2014 0.9004 0.2169 0.8795 0.2303 0.8571 0.2417 0.8335 0.2510 0.8088

3 0.0284 0.9942 0.0332 0.9927 0.0383 0.9909 0.0437 0.9889 0.0494 0.9865 0.0553 0.9839 0.0613 0.9810 0.0738 0.9743 0.0867 0.9662 0.0998 0.9569 0.1128 0.9463 0.1255 0.9344

4 0.0050 0.9992 0.0062 0.9989 0.0077 0.9986 0.0093 0.9982 0.0111 0.9977 0.0131 0.9971 0.0153 0.9963 0.0203 0.9946 0.0260 0.9923 0.0324 0.9893 0.0395 0.9857 0.0471 0.9814

5 0.0007 0.9999 0.0009 0.9999 0.0012 0.9998 0.0016 0.9997 0.0020 0.9997 0.0025 0.9995 0.0031 0.9994 0.0045 0.9990 0.0062 0.9985 0.0084 0.9978 0.0111 0.9968 0.0141 0.9955

6 0.0001 1.0000 0.0001 1.0000 0.0002 1.0000 0.0002 1.0000 0.0003 1.0000 0.0004 0.9999 0.0005 0.9999 0.0008 0.9999 0.0012 0.9997 0.0018 0.9996 0.0026 0.9994 0.0035 0.9991

7 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 1.0000 0.0001 1.0000 0.0001 1.0000 0.0002 1.0000 0.0003 0.9999 0.0005 0.9999 0.0008 0.9998

0 0.2019 0.2019 0.1827 0.1827 0.1653 0.1653 0.1496 0.1496 0.1353 0.1353 0.1225 0.1225 0.1108 0.1108 0.1003 0.1003 0.0907 0.0907 0.0821 0.0821 0.0743 0.0743 0.0672 0.0672

1 0.3230 0.5249 0.3106 0.4932 0.2975 0.4628 0.2842 0.4337 0.2707 0.4060 0.2572 0.3796 0.2438 0.3546 0.2306 0.3309 0.2177 0.3084 0.2052 0.2873 0.1931 0.2674 0.1815 0.2487

2 0.2584 0.7834 0.2640 0.7572 0.2678 0.7306 0.2700 0.7037 0.2707 0.6767 0.2700 0.6496 0.2681 0.6227 0.2652 0.5960 0.2613 0.5697 0.2565 0.5438 0.2510 0.5184 0.2450 0.4936

3 0.1378 0.9212 0.1496 0.9068 0.1607 0.8913 0.1710 0.8747 0.1804 0.8571 0.1890 0.8386 0.1966 0.8194 0.2033 0.7993 0.2090 0.7787 0.2138 0.7576 0.2176 0.7360 0.2205 0.7141

4 0.0551 0.9763 0.0636 0.9704 0.0723 0.9636 0.0812 0.9559 0.0902 0.9473 0.0992 0.9379 0.1082 0.9275 0.1169 0.9162 0.1254 0.9041 0.1336 0.8912 0.1414 0.8774 0.1488 0.8629

5 0.0176 0.9940 0.0216 0.9920 0.0260 0.9896 0.0309 0.9868 0.0361 0.9834 0.0417 0.9796 0.0476 0.9751 0.0538 0.9700 0.0602 0.9643 0.0668 0.9580 0.0735 0.9510 0.0804 0.9433

6 0.0047 0.9987 0.0061 0.9981 0.0078 0.9974 0.0098 0.9966 0.0120 0.9955 0.0146 0.9941 0.0174 0.9925 0.0206 0.9906 0.0241 0.9884 0.0278 0.9858 0.0319 0.9828 0.0362 0.9794

7 0.0011 0.9997 0.0015 0.9996 0.0020 0.9994 0.0027 0.9992 0.0034 0.9989 0.0044 0.9985 0.0055 0.9980 0.0068 0.9974 0.0083 0.9967 0.0099 0.9958 0.0118 0.9947 0.0139 0.9934

8 0.0002 1.0000 0.0003 0.9999 0.0005 0.9999 0.0006 0.9998 0.0009 0.9998 0.0011 0.9997 0.0015 0.9995 0.0019 0.9994 0.0025 0.9991 0.0031 0.9989 0.0038 0.9985 0.0047 0.9981

9 0.0000 1.0000 0.0001 1.0000 0.0001 1.0000 0.0001 1.0000 0.0002 1.0000 0.0003 0.9999 0.0004 0.9999 0.0005 0.9999 0.0007 0.9998 0.0009 0.9997 0.0011 0.9996 0.0014 0.9995

10 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 1.0000 0.0001 1.0000 0.0001 1.0000 0.0002 1.0000 0.0002 0.9999 0.0003 0.9999 0.0004 0.9999

0 0.0608 0.0608 0.0498 0.0498 0.0408 0.0408 0.0334 0.0334 0.0273 0.0273 0.0224 0.0224 0.0183 0.0183 0.0150 0.0150 0.0123 0.0123 0.0101 0.0101 0.0082 0.0082 0.0067 0.0067

1 0.1703 0.2311 0.1494 0.1991 0.1304 0.1712 0.1135 0.1468 0.0984 0.1257 0.0850 0.1074 0.0733 0.0916 0.0630 0.0780 0.0540 0.0663 0.0462 0.0563 0.0395 0.0477 0.0337 0.0404

2 0.2384 0.4695 0.2240 0.4232 0.2087 0.3799 0.1929 0.3397 0.1771 0.3027 0.1615 0.2689 0.1465 0.2381 0.1323 0.2102 0.1188 0.1851 0.1063 0.1626 0.0948 0.1425 0.0842 0.1247

3 0.2225 0.6919 0.2240 0.6472 0.2226 0.6025 0.2186 0.5584 0.2125 0.5152 0.2046 0.4735 0.1954 0.4335 0.1852 0.3954 0.1743 0.3594 0.1631 0.3257 0.1517 0.2942 0.1404 0.2650

4 0.1557 0.8477 0.1680 0.8153 0.1781 0.7806 0.1858 0.7442 0.1912 0.7064 0.1944 0.6678 0.1954 0.6288 0.1944 0.5898 0.1917 0.5512 0.1875 0.5132 0.1820 0.4763 0.1755 0.4405

5 0.0872 0.9349 0.1008 0.9161 0.1140 0.8946 0.1264 0.8705 0.1377 0.8441 0.1477 0.8156 0.1563 0.7851 0.1633 0.7531 0.1687 0.7199 0.1725 0.6858 0.1747 0.6510 0.1755 0.6160

6 0.0407 0.9756 0.0504 0.9665 0.0608 0.9554 0.0716 0.9421 0.0826 0.9267 0.0936 0.9091 0.1042 0.8893 0.1143 0.8675 0.1237 0.8436 0.1323 0.8180 0.1398 0.7908 0.1462 0.7622

7 0.0163 0.9919 0.0216 0.9881 0.0278 0.9832 0.0348 0.9769 0.0425 0.9692 0.0508 0.9599 0.0595 0.9489 0.0686 0.9361 0.0778 0.9214 0.0869 0.9049 0.0959 0.8867 0.1044 0.8666

8 0.0057 0.9976 0.0081 0.9962 0.0111 0.9943 0.0148 0.9917 0.0191 0.9883 0.0241 0.9840 0.0298 0.9786 0.0360 0.9721 0.0428 0.9642 0.0500 0.9549 0.0575 0.9442 0.0653 0.9319

9 0.0018 0.9993 0.0027 0.9989 0.0040 0.9982 0.0056 0.9973 0.0076 0.9960 0.0102 0.9942 0.0132 0.9919 0.0168 0.9889 0.0209 0.9851 0.0255 0.9805 0.0307 0.9749 0.0363 0.9682

10 0.0005 0.9998 0.0008 0.9997 0.0013 0.9995 0.0019 0.9992 0.0028 0.9987 0.0039 0.9981 0.0053 0.9972 0.0071 0.9959 0.0092 0.9943 0.0118 0.9922 0.0147 0.9896 0.0181 0.9863

11 0.0001 1.0000 0.0002 0.9999 0.0004 0.9999 0.0006 0.9998 0.0009 0.9996 0.0013 0.9994 0.0019 0.9991 0.0027 0.9986 0.0037 0.9980 0.0049 0.9971 0.0064 0.9960 0.0082 0.9945

12 0.0000 1.0000 0.0001 1.0000 0.0001 1.0000 0.0002 0.9999 0.0003 0.9999 0.0004 0.9998 0.0006 0.9997 0.0009 0.9996 0.0013 0.9993 0.0019 0.9990 0.0026 0.9986 0.0034 0.9980

13 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 1.0000 0.0001 1.0000 0.0002 0.9999 0.0003 0.9999 0.0005 0.9998 0.0007 0.9997 0.0009 0.9995 0.0013 0.9993

14 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 1.0000 0.0001 1.0000 0.0001 0.9999 0.0002 0.9999 0.0003 0.9999 0.0005 0.9998

0 0.0025 0.0025 0.0009 0.0009 0.0003 0.0003 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

1 0.0149 0.0174 0.0064 0.0073 0.0027 0.0030 0.0011 0.0012 0.0005 0.0005 0.0002 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2 0.0446 0.0620 0.0223 0.0296 0.0107 0.0138 0.0050 0.0062 0.0023 0.0028 0.0010 0.0012 0.0004 0.0005 0.0002 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

3 0.0892 0.1512 0.0521 0.0818 0.0286 0.0424 0.0150 0.0212 0.0076 0.0103 0.0037 0.0049 0.0018 0.0023 0.0008 0.0011 0.0004 0.0005 0.0002 0.0002 0.0001 0.0001 0.0000 0.0000

4 0.1339 0.2851 0.0912 0.1730 0.0573 0.0996 0.0337 0.0550 0.0189 0.0293 0.0102 0.0151 0.0053 0.0076 0.0027 0.0037 0.0013 0.0018 0.0006 0.0009 0.0003 0.0004 0.0001 0.0002

5 0.1606 0.4457 0.1277 0.3007 0.0916 0.1912 0.0607 0.1157 0.0378 0.0671 0.0224 0.0375 0.0127 0.0203 0.0070 0.0107 0.0037 0.0055 0.0019 0.0028 0.0010 0.0014 0.0005 0.0007

6 0.1606 0.6063 0.1490 0.4497 0.1221 0.3134 0.0911 0.2068 0.0631 0.1301 0.0411 0.0786 0.0255 0.0458 0.0152 0.0259 0.0087 0.0142 0.0048 0.0076 0.0026 0.0040 0.0014 0.0021

7 0.1377 0.7440 0.1490 0.5987 0.1396 0.4530 0.1171 0.3239 0.0901 0.2202 0.0646 0.1432 0.0437 0.0895 0.0281 0.0540 0.0174 0.0316 0.0104 0.0180 0.0060 0.0100 0.0034 0.0054

8 0.1033 0.8472 0.1304 0.7291 0.1396 0.5925 0.1318 0.4557 0.1126 0.3328 0.0888 0.2320 0.0655 0.1550 0.0457 0.0998 0.0304 0.0621 0.0194 0.0374 0.0120 0.0220 0.0072 0.0126

9 0.0688 0.9161 0.1014 0.8305 0.1241 0.7166 0.1318 0.5874 0.1251 0.4579 0.1085 0.3405 0.0874 0.2424 0.0661 0.1658 0.0473 0.1094 0.0324 0.0699 0.0213 0.0433 0.0135 0.0261

10 0.0413 0.9574 0.0710 0.9015 0.0993 0.8159 0.1186 0.7060 0.1251 0.5830 0.1194 0.4599 0.1048 0.3472 0.0859 0.2517 0.0663 0.1757 0.0486 0.1185 0.0341 0.0774 0.0230 0.0491

11 0.0225 0.9799 0.0452 0.9467 0.0722 0.8881 0.0970 0.8030 0.1137 0.6968 0.1194 0.5793 0.1144 0.4616 0.1015 0.3532 0.0844 0.2600 0.0663 0.1848 0.0496 0.1270 0.0355 0.0847

12 0.0113 0.9912 0.0263 0.9730 0.0481 0.9362 0.0728 0.8758 0.0948 0.7916 0.1094 0.6887 0.1144 0.5760 0.1099 0.4631 0.0984 0.3585 0.0829 0.2676 0.0661 0.1931 0.0504 0.1350

13 0.0052 0.9964 0.0142 0.9872 0.0296 0.9658 0.0504 0.9261 0.0729 0.8645 0.0926 0.7813 0.1056 0.6815 0.1099 0.5730 0.1060 0.4644 0.0956 0.3632 0.0814 0.2745 0.0658 0.2009

14 0.0022 0.9986 0.0071 0.9943 0.0169 0.9827 0.0324 0.9585 0.0521 0.9165 0.0728 0.8540 0.0905 0.7720 0.1021 0.6751 0.1060 0.5704 0.1024 0.4657 0.0930 0.3675 0.0800 0.2808

15 0.0009 0.9995 0.0033 0.9976 0.0090 0.9918 0.0194 0.9780 0.0347 0.9513 0.0534 0.9074 0.0724 0.8444 0.0885 0.7636 0.0989 0.6694 0.1024 0.5681 0.0992 0.4667 0.0906 0.3715

16 0.0003 0.9998 0.0014 0.9990 0.0045 0.9963 0.0109 0.9889 0.0217 0.9730 0.0367 0.9441 0.0543 0.8987 0.0719 0.8355 0.0866 0.7559 0.0960 0.6641 0.0992 0.5660 0.0963 0.4677

17 0.0001 0.9999 0.0006 0.9996 0.0021 0.9984 0.0058 0.9947 0.0128 0.9857 0.0237 0.9678 0.0383 0.9370 0.0550 0.8905 0.0713 0.8272 0.0847 0.7489 0.0934 0.6593 0.0963 0.5640

18 0.0000 1.0000 0.0002 0.9999 0.0009 0.9993 0.0029 0.9976 0.0071 0.9928 0.0145 0.9823 0.0255 0.9626 0.0397 0.9302 0.0554 0.8826 0.0706 0.8195 0.0830 0.7423 0.0909 0.6550

19 0.0000 1.0000 0.0001 1.0000 0.0004 0.9997 0.0014 0.9989 0.0037 0.9965 0.0084 0.9907 0.0161 0.9787 0.0272 0.9573 0.0409 0.9235 0.0557 0.8752 0.0699 0.8122 0.0814 0.7363

20 0.0000 1.0000 0.0000 1.0000 0.0002 0.9999 0.0006 0.9996 0.0019 0.9984 0.0046 0.9953 0.0097 0.9884 0.0177 0.9750 0.0286 0.9521 0.0418 0.9170 0.0559 0.8682 0.0692 0.8055

21 0.0000 1.0000 0.0000 1.0000 0.0001 1.0000 0.0003 0.9998 0.0009 0.9993 0.0024 0.9977 0.0055 0.9939 0.0109 0.9859 0.0191 0.9712 0.0299 0.9469 0.0426 0.9108 0.0560 0.8615

22 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 0.9999 0.0004 0.9997 0.0012 0.9990 0.0030 0.9970 0.0065 0.9924 0.0121 0.9833 0.0204 0.9673 0.0310 0.9418 0.0433 0.9047

23 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0002 0.9999 0.0006 0.9995 0.0016 0.9985 0.0037 0.9960 0.0074 0.9907 0.0133 0.9805 0.0216 0.9633 0.0320 0.9367

24 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 1.0000 0.0003 0.9998 0.0008 0.9993 0.0020 0.9980 0.0043 0.9950 0.0083 0.9888 0.0144 0.9777 0.0226 0.9594

25 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 0.9999 0.0004 0.9997 0.0010 0.9990 0.0024 0.9974 0.0050 0.9938 0.0092 0.9869 0.0154 0.9748

26 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0002 0.9999 0.0005 0.9995 0.0013 0.9987 0.0029 0.9967 0.0057 0.9925 0.0101 0.9848

27 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 0.9999 0.0002 0.9998 0.0007 0.9994 0.0016 0.9983 0.0034 0.9959 0.0063 0.9912

28 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 0.9999 0.0003 0.9997 0.0009 0.9991 0.0019 0.9978 0.0038 0.9950

29 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 1.0000 0.0002 0.9999 0.0004 0.9996 0.0011 0.9989 0.0023 0.9973

30 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 0.9999 0.0002 0.9998 0.0006 0.9994 0.0013 0.9986

31 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0000 1.0000 0.0001 0.9999 0.0003 0.9997 0.0007 0.9993

0.5

0.7 0.75 0.8 1.2

IND 214 Tabla N 3 - Distribucion Poisson - (np o l)

0.3

1.1

0.01

0.16 0.18 0.2 0.25

0.02 0.03

0.45

0.05 0.06 0.07 0.08

0.85 0.9 0.95 1

2.1 2.2

0.04

0.35 0.4

2 2.3

6 7 8 9

1.6 1.7 1.8 1.9

13

2.8 3 3.2 3.4 3.6

10

2.4

17

3.8 4 4.2 4.4

11 12

0.6

0.1 0.12

14 15 16

1.3 1.4

2.5 2.6

0.140.09

4.6 4.8 5

1.5

2.7

0.650.55

Grados de libertad 2

20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 0.00000 0.04877 0.09516 0.13929 0.18127 0.22120 0.25918 0.29531 0.32968 0.36237

1 0.39347 0.42305 0.45119 0.47795 0.50341 0.52763 0.55067 0.57259 0.59343 0.61326

2 0.63212 0.65006 0.66713 0.68336 0.69881 0.71350 0.72747 0.74076 0.75340 0.76543

3 0.77687 0.78775 0.79810 0.80795 0.81732 0.82623 0.83470 0.84276 0.85043 0.85773

4 0.86466 0.87127 0.87754 0.88352 0.88920 0.89460 0.89974 0.90463 0.90928 0.91371

5 0.91792 0.92192 0.92573 0.92935 0.93279 0.93607 0.93919 0.94216 0.94498 0.94766

6 0.95021 0.95264 0.95495 0.95715 0.95924 0.96123 0.96312 0.96492 0.96663 0.96825

7 0.96980 0.97128 0.97268 0.97401 0.97528 0.97648 0.97763 0.97872 0.97976 0.98075

8 0.98168 0.98258 0.98343 0.98424 0.98500 0.98574 0.98643 0.98709 0.98772 0.98832

9 0.98889 0.98943 0.98995 0.99044 0.99090 0.99135 0.99177 0.99217 0.99255 0.99292

10 0.99326 0.99359 0.99390 0.99420 0.99448 0.99475 0.99501 0.99525 0.99548 0.99570

11 0.99591 0.99611 0.99630 0.99648 0.99665 0.99682 0.99697 0.99712 0.99726 0.99739

12 0.99752 0.99764 0.99776 0.99787 0.99797 0.99807 0.99816 0.99825 0.99834 0.99842

13 0.99850 0.99857 0.99864 0.99871 0.99877 0.99883 0.99889 0.99894 0.99899 0.99904

14 0.99909 0.99913 0.99917 0.99922 0.99925 0.99929 0.99932 0.99936 0.99939 0.99942

15 0.99945 0.99947 0.99950 0.99952 0.99955 0.99957 0.99959 0.99961 0.99963 0.99965

16 0.99966 0.99968 0.99970 0.99971 0.99973 0.99974 0.99975 0.99976 0.99978 0.99979

17 0.99980 0.99981 0.99982 0.99982 0.99983 0.99984 0.99985 0.99986 0.99986 0.99987

18 0.99988 0.99988 0.99989 0.99989 0.99990 0.99990 0.99991 0.99991 0.99992 0.99992

19 0.99993 0.99993 0.99993 0.99994 0.99994 0.99994 0.99994 0.99995 0.99995 0.99995

20 0.99995 0.99996 0.99996 0.99996 0.99996 0.99996 0.99997 0.99997 0.99997 0.99997


20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 0.00000 0.00121 0.00468 0.01019 0.01752 0.02650 0.03694 0.04867 0.06155 0.07544

1 0.09020 0.10573 0.12190 0.13862 0.15580 0.17336 0.19121 0.20928 0.22752 0.24586

2 0.26424 0.28263 0.30097 0.31923 0.33737 0.35536 0.37318 0.39079 0.40817 0.42530

3 0.44217 0.45877 0.47507 0.49107 0.50675 0.52212 0.53716 0.55187 0.56625 0.58029

4 0.59399 0.60736 0.62039 0.63307 0.64543 0.65745 0.66915 0.68051 0.69156 0.70229

5 0.71270 0.72281 0.73262 0.74212 0.75134 0.76027 0.76892 0.77730 0.78541 0.79326

6 0.80085 0.80820 0.81530 0.82216 0.82880 0.83521 0.84140 0.84738 0.85316 0.85873

7 0.86411 0.86930 0.87431 0.87914 0.88380 0.88829 0.89262 0.89679 0.90081 0.90469

8 0.90842 0.91202 0.91548 0.91881 0.92202 0.92511 0.92809 0.93095 0.93370 0.93635

9 0.93890 0.94135 0.94371 0.94598 0.94816 0.95025 0.95227 0.95420 0.95607 0.95785

10 0.95957 0.96122 0.96281 0.96433 0.96580 0.96720 0.96855 0.96985 0.97109 0.97229

11 0.97344 0.97454 0.97559 0.97661 0.97758 0.97852 0.97941 0.98027 0.98110 0.98189

12 0.98265 0.98338 0.98408 0.98475 0.98539 0.98600 0.98659 0.98716 0.98770 0.98823

13 0.98872 0.98920 0.98966 0.99010 0.99052 0.99093 0.99131 0.99168 0.99204 0.99238

14 0.99270 0.99302 0.99332 0.99360 0.99388 0.99414 0.99439 0.99463 0.99487 0.99509

15 0.99530 0.99550 0.99570 0.99588 0.99606 0.99623 0.99639 0.99655 0.99670 0.99684

16 0.99698 0.99711 0.99724 0.99736 0.99747 0.99758 0.99769 0.99779 0.99789 0.99798

17 0.99807 0.99815 0.99823 0.99831 0.99838 0.99846 0.99852 0.99859 0.99865 0.99871

18 0.99877 0.99882 0.99887 0.99892 0.99897 0.99901 0.99906 0.99910 0.99914 0.99918

19 0.99921 0.99925 0.99928 0.99931 0.99934 0.99937 0.99940 0.99943 0.99945 0.99948

20 0.99950 0.99952 0.99954 0.99956 0.99958 0.99960 0.99962 0.99964 0.99965 0.99967

21 0.99968 0.99970 0.99971 0.99972 0.99974 0.99975 0.99976 0.99977 0.99978 0.99979

22 0.99980 0.99981 0.99982 0.99983 0.99983 0.99984 0.99985 0.99985 0.99986 0.99987

23 0.99987 0.99988 0.99988 0.99989 0.99989 0.99990 0.99990 0.99991 0.99991 0.99992


20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 0.00000 0.00016 0.00089 0.00236 0.00467 0.00788 0.01200 0.01703 0.02297 0.02978

1 0.03743 0.04590 0.05512 0.06507 0.07569 0.08693 0.09875 0.11110 0.12393 0.13720

2 0.15085 0.16486 0.17916 0.19373 0.20853 0.22350 0.23863 0.25388 0.26921 0.28460

3 0.30001 0.31543 0.33082 0.34616 0.36143 0.37661 0.39169 0.40664 0.42144 0.43610

4 0.45058 0.46489 0.47901 0.49292 0.50663 0.52012 0.53338 0.54642 0.55923 0.57179

5 0.58412 0.59620 0.60804 0.61962 0.63096 0.64205 0.65289 0.66349 0.67383 0.68393

6 0.69378 0.70339 0.71276 0.72189 0.73078 0.73944 0.74787 0.75608 0.76406 0.77182

7 0.77936 0.78669 0.79381 0.80073 0.80745 0.81397 0.82030 0.82644 0.83239 0.83817

8 0.84376 0.84919 0.85445 0.85954 0.86447 0.86925 0.87388 0.87835 0.88269 0.88688

9 0.89094 0.89486 0.89865 0.90232 0.90587 0.90929 0.91260 0.91580 0.91890 0.92188

10 0.92476 0.92755 0.93024 0.93283 0.93534 0.93775 0.94009 0.94234 0.94451 0.94660

11 0.94862 0.95057 0.95244 0.95425 0.95600 0.95768 0.95930 0.96086 0.96237 0.96382

12 0.96521 0.96656 0.96785 0.96910 0.97030 0.97146 0.97257 0.97364 0.97467 0.97567

13 0.97662 0.97754 0.97843 0.97928 0.98009 0.98088 0.98164 0.98237 0.98307 0.98374

14 0.98439 0.98501 0.98561 0.98619 0.98674 0.98727 0.98778 0.98828 0.98875 0.98920

15 0.98964 0.99006 0.99046 0.99085 0.99122 0.99157 0.99192 0.99225 0.99256 0.99286

16 0.99316 0.99344 0.99370 0.99396 0.99421 0.99445 0.99468 0.99489 0.99510 0.99531

17 0.99550 0.99569 0.99586 0.99604 0.99620 0.99636 0.99651 0.99665 0.99679 0.99693

18 0.99705 0.99718 0.99729 0.99741 0.99752 0.99762 0.99772 0.99781 0.99791 0.99799

19 0.99808 0.99816 0.99824 0.99831 0.99838 0.99845 0.99851 0.99858 0.99864 0.99870

20 0.99875 0.99880 0.99885 0.99890 0.99895 0.99899 0.99904 0.99908 0.99912 0.99915

21 0.99919 0.99922 0.99926 0.99929 0.99932 0.99935 0.99938 0.99940 0.99943 0.99945

22 0.99948 0.99950 0.99952 0.99954 0.99956 0.99958 0.99960 0.99961 0.99963 0.99965

23 0.99966 0.99968 0.99969 0.99970 0.99972 0.99973 0.99974 0.99975 0.99976 0.99977

IND 214 Tabla N 4 - Areas bajo la curva 2 desde cero a 20

n x 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15 0.155

6 0 0.5314 0.5140 0.4970 0.4805 0.4644 0.4488 0.4336 0.4189 0.4046 0.3907 0.3771 0.3640

1 0.8857 0.8758 0.8655 0.8551 0.8444 0.8335 0.8224 0.8111 0.7997 0.7882 0.7765 0.7647

2 0.9842 0.9819 0.9794 0.9768 0.9739 0.9709 0.9676 0.9642 0.9605 0.9567 0.9527 0.9484

3 0.9987 0.9985 0.9982 0.9978 0.9975 0.9970 0.9966 0.9960 0.9955 0.9948 0.9941 0.9934

4 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9998 0.9997 0.9997 0.9996 0.9995

5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

n x 0.14 0.145 0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195

12 0 0.1637 0.1526 0.1422 0.1325 0.1234 0.1149 0.1069 0.0994 0.0924 0.0859 0.0798 0.0741

1 0.4834 0.4632 0.4435 0.4242 0.4055 0.3873 0.3696 0.3525 0.3359 0.3198 0.3043 0.2893

2 0.7697 0.7529 0.7358 0.7185 0.7010 0.6833 0.6656 0.6477 0.6298 0.6119 0.5940 0.5761

3 0.9250 0.9167 0.9078 0.8984 0.8886 0.8784 0.8676 0.8564 0.8448 0.8328 0.8205 0.8077

4 0.9819 0.9791 0.9761 0.9727 0.9690 0.9651 0.9607 0.9561 0.9511 0.9457 0.9400 0.9339

5 0.9967 0.9961 0.9954 0.9945 0.9935 0.9925 0.9912 0.9899 0.9884 0.9867 0.9849 0.9828

6 0.9996 0.9995 0.9993 0.9992 0.9990 0.9988 0.9985 0.9983 0.9979 0.9976 0.9971 0.9966

7 1.0000 0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997 0.9996 0.9995

8 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999

n x 0.14 0.145 0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195

14 0 0.1211 0.1116 0.1028 0.0946 0.0871 0.0801 0.0736 0.0677 0.0621 0.0570 0.0523 0.0480

1 0.3969 0.3764 0.3567 0.3376 0.3193 0.3017 0.2848 0.2686 0.2531 0.2383 0.2242 0.2107

2 0.6889 0.6684 0.6479 0.6273 0.6068 0.5863 0.5659 0.5457 0.5256 0.5058 0.4862 0.4670

3 0.8790 0.8665 0.8535 0.8399 0.8258 0.8112 0.7962 0.7807 0.7649 0.7487 0.7321 0.7153

4 0.9641 0.9589 0.9533 0.9472 0.9406 0.9335 0.9259 0.9179 0.9093 0.9002 0.8907 0.8807

5 0.9918 0.9902 0.9885 0.9865 0.9843 0.9818 0.9791 0.9760 0.9727 0.9691 0.9651 0.9608

6 0.9985 0.9982 0.9978 0.9973 0.9968 0.9961 0.9954 0.9945 0.9936 0.9925 0.9913 0.9899

7 0.9998 0.9997 0.9997 0.9996 0.9995 0.9994 0.9992 0.9990 0.9988 0.9986 0.9983 0.9980

8 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997

n x 0.14 0.145 0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195

16 0 0.0895 0.0816 0.0743 0.0676 0.0614 0.0558 0.0507 0.0461 0.0418 0.0379 0.0343 0.0311

1 0.3227 0.3029 0.2839 0.2659 0.2487 0.2324 0.2170 0.2024 0.1885 0.1755 0.1632 0.1516

2 0.6074 0.5843 0.5614 0.5386 0.5162 0.4941 0.4723 0.4510 0.4302 0.4098 0.3899 0.3706

3 0.8237 0.8071 0.7899 0.7722 0.7540 0.7354 0.7164 0.6972 0.6777 0.6580 0.6381 0.6181

4 0.9382 0.9299 0.9209 0.9114 0.9012 0.8904 0.8789 0.8669 0.8542 0.8410 0.8273 0.8130

5 0.9829 0.9799 0.9765 0.9727 0.9685 0.9638 0.9588 0.9533 0.9473 0.9408 0.9338 0.9263

6 0.9962 0.9954 0.9944 0.9933 0.9920 0.9905 0.9888 0.9869 0.9847 0.9823 0.9796 0.9766

7 0.9993 0.9992 0.9989 0.9987 0.9984 0.9980 0.9976 0.9970 0.9964 0.9957 0.9949 0.9940

8 0.9999 0.9999 0.9998 0.9998 0.9997 0.9997 0.9996 0.9995 0.9993 0.9992 0.9990 0.9988

9 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998

n x 0.14 0.145 0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195

18 0 0.0662 0.0596 0.0536 0.0482 0.0434 0.0389 0.0349 0.0313 0.0281 0.0252 0.0225 0.0202

1 0.2602 0.2416 0.2241 0.2075 0.1920 0.1774 0.1638 0.1510 0.1391 0.1280 0.1176 0.1080

2 0.5287 0.5040 0.4797 0.4559 0.4327 0.4100 0.3881 0.3668 0.3462 0.3264 0.3073 0.2889

3 0.7618 0.7413 0.7202 0.6988 0.6771 0.6552 0.6331 0.6109 0.5888 0.5666 0.5446 0.5227

4 0.9041 0.8922 0.8794 0.8660 0.8518 0.8369 0.8213 0.8051 0.7884 0.7711 0.7533 0.7350

5 0.9690 0.9638 0.9581 0.9518 0.9449 0.9374 0.9292 0.9205 0.9111 0.9010 0.8903 0.8790

6 0.9919 0.9902 0.9882 0.9859 0.9833 0.9804 0.9771 0.9735 0.9694 0.9649 0.9600 0.9546

7 0.9983 0.9978 0.9973 0.9966 0.9959 0.9950 0.9940 0.9928 0.9914 0.9898 0.9880 0.9860

8 0.9997 0.9996 0.9995 0.9993 0.9992 0.9990 0.9987 0.9984 0.9980 0.9976 0.9971 0.9964

9 1.0000 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9997 0.9996 0.9995 0.9994 0.9993

10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9999 0.9999

n x 0.065 0.145 0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195

200 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

3 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

4 0.0030 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

5 0.0090 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

6 0.0225 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

7 0.0485 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

8 0.0922 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

9 0.1570 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

10 0.2430 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

11 0.3463 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

IND 214 Tabla N 5 Binomial

p

Valores de no para valores de c y riesgos tipicos de productores y consumidores

P = 0.99 P = 0.95 P = 0.90 P = 0.10 P = 0.05 P = 0.01 Ratio of

c (=0.01) (=0.05) (=0.10) (=0.10) (=0.05) (=0.01) P0.10/P0.95

0 0.010 0.051 0.105 2.303 2.996 4.605 44.890

1 0.149 0.355 0.532 3.890 4.744 6.638 10.946

2 0.436 0.818 1.102 5.322 6.296 8.406 6.509

3 0.823 1.366 1.745 6.681 7.754 10.045 4.890

4 1.279 1.970 2.433 7.994 9.154 11.605 4.057

5 1.785 2.613 3.152 9.275 10.513 13.108 3.549

6 2.330 3.286 3.895 10.532 11.842 14.571 3.206

7 2.906 3.981 4.656 11.771 13.148 16.000 2.957

8 3.507 4.695 5.432 12.995 14.434 17.403 2.768

9 4.130 5.426 6.221 14.206 15.705 18.783 2.618

10 4.771 6.169 7.021 15.407 16.962 20.145 2.497

11 5.428 6.924 7.829 16.598 18.208 21.490 2.397

12 6.099 7.690 8.646 17.782 19.442 22.821 2.312

13 6.782 8.464 9.470 18.958 20.668 24.139 2.240

14 7.477 9.246 10.300 20.128 21.886 25.446 2.177

15 8.181 10.035 11.135 21.292 23.098 26.743 2.122

IND 214 - Tabla N 6 Valores de np

S-1 S-2 S-3 S-4 I II III

2 a 8 A A A A A A B

9 a 15 A A A A A B C

16 a 25 A A B B B C D

26 a 50 A B B C C D E

51 a 90 B B C C C E F

91 a 150 B B C D D F G

151 a 280 B C D E E G H

281 a 500 B C D E E H J

501 a 1 200 C C E F F J K

1 201 a 3 200 C D E G G K L

3 201 a 10 000 C D F G G L M

10 001 a 35 000 C D F H H M N

35001 a 150 000 D E G J J N P

150 001 a 500 000 D E G J J P Q

500 0001 en adelante D E H K K Q R

Niveles de inspeccion generalesNiveles de inspeccion especialesTamao de lote o carga

IND 214 MIL-STD 105E Tabla I

0.010 0.015 0.025 0.040 0.065 0.10 0.15 0.25 0.40 0.65 1.0 1.5 2.5 4.0 6.5 10 15 25 40 65 100 150 250 400 650 1000

Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re Ac Re

A 2 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22 30 31

B 3 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22 30 31 44 45

C 5 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22 30 31 44 45

D 8 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22 30 31 44 45

E 13 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

F 20 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

G 32 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

H 50 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

J 80 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

K 125 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

L 200 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

M 315 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

N 500 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

P 800 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

Q 1250 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

R 2000 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22

Usar el primer plan de muestreo debajo de la flecha. Si el tamao de la muestra es igual, o exede, el tamao del lote o carga, hacer una inspeccion al 100%

Usar el primer plan de muestreo arriba de la flecha

Ac Numero de aceptacion

Re Numero de rechazo

Tamao de la

muestra

Letra de codigo

para el tamao

de la muestra

Niveles de calidad aceptables (inspeccion normal)

IND 214 MIL-STD 105E TABLA II-A

0.010 0.015 0.025 0.040 0.065 0.10 0.15 0.25 0.40 0.65 1.0 1.5 2.5 4.0 6.5 10 15 25 40 65 100 150 250 400 650 1000


A 2 1 2 2 3 3 4 5 6 10 11 12 13 18 19 27 28

B 3 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19 27 28 41 42

C 5 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19 27 28 41 42

D 8 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19 27 28 41 42

E 13 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19 27 28 41 42

F 20 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

G 32 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

H 50 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

J 80 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

K 125 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

L 200 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

M 315 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

N 500 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

P 800 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

Q 1250 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

R 2000 0 1 1 2 2 3 3 4 5 6 8 9 12 13 18 19

S 3150 1 2





Letra de codigo

para el tamao

de la muestra

Tamao de la

muestra

Niveles de calidad aceptables (inspeccion rigurosa)

IND 214 MIL-STD 105E TABLA II-B

0.010 0.015 0.025 0.040 0.065 0.10 0.15 0.25 0.40 0.65 1.0 1.5 2.5 4.0 6.5 10 15 25 40 65 100 150 250 400 650 1000


A 2 0 1 1 2 2 3 3 4 5 6 7 8 10 11 14 15 21 22 30 31

B 2 0 1 0 2 1 3 2 4 3 5 5 6 7 8 10 11 14 15 21 22 30 31

C 2 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13 14 17 21 24

D 3 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13 14 17 21 24

E 5 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13 14 17 21 24

F 8 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13

G 13 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13

H 20 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13

J 32 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13

K 50 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13

L 80 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13

M 125 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13

N 200 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13

P 315 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13

Q 500 0 1 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13

R 800 0 2 1 3 1 4 2 5 3 6 5 8 7 10 10 13





* Si se ha excedido el nmero de aceptacion, pero no se ha alcanzado el nmero de rechazo, aceptar el lote, pero establecer de nuevo la inspeccin normal

Letra de codigo

para el tamao

de la muestra

Tamao de la

muestra

Niveles de calidad aceptables (inspeccion reducida)

IND 214 MIL-STD 105E TABLA II-C

Tamao de lote o carga

S-3 S-4 I II III

2 a 8 B B B B C

9 a 15 B B B B D

16 a 25 B B B C E

26 a 50 B B C D F

51 a 90 B B D E G

91 a 150 B C E F H

151 a 280 B D F G I

281 a 400 C E G H J

401 a 500 C E G I J

501 a 1 200 D F H J K

1 201 a 3 200 E G I K L

3 201 a 10 000 F H J L M

10 001 a 35 000 G I K M N

35001 a 150 000 H J L N P

150 001 a 500 000 I K M P P

500 001 en adelante J L N P P

IND 214 MIL-STD 414 TABLA A-2

Niveles de inspeccin

0.10 0.15 0.25 0.4 0.65 1 1.5 2.5 4 6.5 10

k k k k k k k k k k k

B 3 1.12 0.958 0.765 0.566

C 4 1.45 1.34 1.17 1.01 0.814 0.617

D 5 1.65 1.53 1.40 1.24 1.07 0.874 0.675

E 7 2.00 1.88 1.75 1.62 1.50 1.33 1.15 0.955 0.755

F 10 2.24 2.11 1.98 1.84 1.72 1.58 1.41 1.23 1.03 0.828

G 15 2.42 2.32 2.20 2.06 1.91 1.79 1.65 1.47 1.30 1.09 0.886

H 20 2.47 2.36 2.24 2.11 1.96 1.82 1.69 1.51 1.33 1.12 0.917

I 25 2.50 2.40 2.26 2.14 1.98 1.85 1.72 1.53 1.35 1.14 0.936

J 35 2.54 2.45 2.31 2.18 2.03 1.89 1.76 1.57 1.39 1.18 0.969

K 50 2.60 2.50 2.35 2.22 2.08 1.93 1.80 1.61 1.42 1.21 1.00

L 75 2.66 2.55 2.41 2.27 2.12 1.98 1.84 1.65 1.46 1.24 1.03

M 100 2.69 2.58 2.43 2.29 2.14 2.00 1.86 1.67 1.48 1.26 1.05

N 150 2.73 2.61 2.47 2.33 2.18 2.03 1.89 1.70 1.51 1.29 1.07

P 200 2.73 2.62 2.47 2.33 2.18 2.04 1.89 1.70 1.51 1.29 1.07

No existe un plan de muestreo adecuado en esta rea; use el primer plan de muestreo al final de la flecha

Este se refiere a ambos, el tamao de la muestra y la constante k

El plan dado en esta rea ofrece un alto grado de seguridad pero a expensas de una muestra grande

A discrecin de la autoridad responsable debe ser utilizado el plan al final de la flecha

Las linas gruesas indican de los limites de los planes de muestreo por atributos equivalentes en ISO 2859

Grado("nivel") aceptable de calidad AQL, para inspeccin NORMAL

muestraLetra clave

IND 214 MIL-STD 414 TABLA B-1

0.10 0.15 0.25 0.4 0.65 1 1.5 2.5 4 6.5 10


B 3 1.12 0.958 0.765

C 4 1.45 1.34 1.17 1.01 0.814

D 5 1.65 1.53 1.40 1.24 1.07 0.874

E 7 2.00 1.88 1.75 1.62 1.50 1.33 1.15 0.955

F 10 2.24 2.11 1.98 1.84 1.72 1.58 1.41 1.23 1.03

G 15 2.53 2.42 2.32 2.20 2.06 1.91 1.79 1.65 1.47 1.3 1.09

H 20 2.58 2.47 2.36 2.24 2.11 1.96 1.82 1.69 1.51 1.33 1.12

I 25 2.61 2.50 2.40 2.26 2.14 1.98 1.85 1.72 1.53 1.35 1.14

J 35 2.65 2.54 2.45 2.31 2.18 2.03 1.89 1.76 1.57 1.39 1.18

K 50 2.71 2.60 2.50 2.35 2.22 2.08 1.93 1.80 1.61 1.42 1.21

L 75 2.77 2.66 2.55 2.41 2.27 2.12 1.95 1.84 1.65 1.46 1.24

M 100 2.80 2.69 2.58 2.43 2.29 2.14 2.00 1.86 1.67 1.48 1.26

N 150 2.84 2.73 2.61 2.47 2.33 2.18 2.03 1.89 1.70 1.51 1.29

P 200 2.85 2.73 2.62 2.47 2.33 2.18 2.04 1.89 1.70 1.51 1.29







Letra clave muestra

Grado("nivel") aceptable de calidad AQL, para inspeccin RIGUROSA

0.10 0.15 0.25 0.4 0.65 1 1.5 2.5 4 6.5 10


B 3 0.12 0.958 0.765 0.566 0.341

C 3 0.12 0.958 0.765 0.566 0.341

D 3 1.12 0.958 0.765 0.566 0.341

E 3 1.12 0.958 0.765 0.566 0.341

F 4 1.45 1.34 1.17 1.01 0.81 0.62 0.393

G 5 1.65 1.53 1.40 1.24 1.07 0.87 0.68 0.455

H 7 2.00 1.88 1.75 1.62 1.50 1.33 1.15 0.96 0.76 0.536

I 10 2.24 2.11 1.98 1.84 1.72 1.58 1.41 1.23 1.03 0.83 0.611

J 15 2.32 2.20 2.06 1.91 1.79 1.65 1.47 1.30 1.09 0.89 0.664

K 20 2.36 2.24 2.11 1.96 1.82 1.69 1.51 1.33 1.12 0.92 0.695

L 25 2.40 2.26 2.14 1.98 1.85 1.72 1.53 1.35 1.14 0.94 0.712

M 35 2.45 2.31 2.18 2.03 1.89 1.76 1.57 1.39 1.18 0.97 0.745

N 50 2.50 2.35 2.22 2.08 1.93 1.80 1.61 1.42 1.21 1.00 0.774

P 75 2.55 2.41 2.27 2.12 1.98 1.84 1.65 1.46 1.24 1.03 0.804







Letra clave muestra

Grado("nivel") aceptable de calidad AQL, para inspeccin REDUCIDA

0.10 0.15 0.25 0.40 0.65 1.0 1.5 2.5 4.0 6.5 10.0

B 3 0.436 0.453 0.475 0.502 0.538

C 4 0.339 0.353 0.374 0.399 0.432 0.472 0.528

D 5 0.294 0.308 0.323 0.346 0.372 0.408 0.452 0.511

E 7 0.242 0.253 0.266 0.280 0.295 0.318 0.345 0.381 0.425 0.485

F 10 0.214 0.224 0.235 0.248 0.261 0.276 0.298 0.324 0.359 0.403 0.460

G 15 0.188 0.195 0.202 0.211 0.222 0.235 0.248 0.262 0.284 0.309 0.344 0.386 0.442

H 20 0.183 0.190 0.197 0.206 0.216 0.229 0.242 0.255 0.277 0.302 0.336 0.377 0.432

I 25 0.180 0.187 0.193 0.203 0.212 0.225 0.238 0.251 0.273 0.297 0.331 0.372 0.426

J 35 0.176 0.183 0.189 0.198 0.208 0.22 0.232 0.245 0.266 0.291 0.323 0.364 0.416

K 50 0.172 0.178 0.184 0.194 0.230 0.214 0.227 0.241 0.261 0.284 0.317 0.356 0.408

L 75 0.168 0.174 0.181 0.189 0.199 0.211 0.223 0.235 0.255 0.276 0.310 0.348 0.399

M 100 0.166 0.172 0.179 0.187 0.197 0.208 0.220 0.233 0.253 0.276 0.307 0.345 0.395

N 150 0.163 0.170 0.175 0.185 0.193 0.206 0.216 0.230 0.249 0.271 0.302 0.341 0.388

P 200 0.163 0.168 0.175 0.183 0.193 0.203 0.215 0.228 0.248 0.269 0.302 0.338 0.386

0.10 0.15 0.25 0.40 0.65 1.0 1.5 2.5 4.0 6.5 10.0

0.10 0.15 0.25 0.40 0.65 1.0 1.5 2.5 4.0 6.5 10.0

El valor de MSSD indica el mximo valor permitido para la desviacin estndar de la muestra cuando se usa un plan de muestreo con doble

limite de especificacin y variabilidad desconocida. Si la desviacin estndar de la muestra es menor que el MSSD existe la posibilidad, pero no

la certeza, de que el lote vaya a ser aceptado.


Grado ("nivel") aceptable de calidad AQL, para inspeccin NORMALmuestraLetra clave

Grado ("nivel") aceptable de calidad AQL, para inspeccin REDUCIDA

Grado ("nivel") aceptable de calidad AQL, para inspeccin RIGUROSA

alfa = 0.05

1 2 3 4 5 6 7 8 9 10

1 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88

2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40

3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 8.79

4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96

5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74

6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 4.06

7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 3.64

8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.35

9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.14

10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.98

11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.85

12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.75

13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.67

14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.60

15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.54

16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49

17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45

18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41

19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38

20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35

25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24

30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16

35 4.12 3.27 2.87 2.64 2.49 2.37 2.29 2.22 2.16 2.11

40 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08

45 4.06 3.20 2.81 2.58 2.42 2.31 2.22 2.15 2.10 2.05

50 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.07 2.03

alfa = 0.10

1 2 3 4 5 6 7 8 9 10

1 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 59.86 60.19

2 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38 9.39

3 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24 5.23

4 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 3.92

5 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32 3.30

6 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96 2.94

7 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72 2.70

8 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56 2.54

9 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44 2.42

10 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35 2.32

11 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27 2.25

12 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21 2.19

13 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16 2.14

14 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12 2.10

15 3.07 2.70 2.49 2.36 2.27 2.21 2.16 2.12 2.09 2.06

16 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06 2.03

17 3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03 2.00

18 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00 1.98

19 2.99 2.61 2.40 2.27 2.18 2.11 2.06 2.02 1.98 1.96

20 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96 1.94

25 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89 1.87

30 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85 1.82

35 2.85 2.46 2.25 2.11 2.02 1.95 1.90 1.85 1.82 1.79

40 2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79 1.76

45 2.82 2.42 2.21 2.07 1.98 1.91 1.85 1.81 1.77 1.74

50 2.81 2.41 2.20 2.06 1.97 1.90 1.84 1.80 1.76 1.73

IND 214 Tabla N 7 - Valores de F

Grados de libertad del numerador

Gra

do

s d

e lib

erta

d d

el d

eno

min

ado

r

Grados de libertad del numerador

Gra

do

s d

e lib

erta

d d

el d

eno

min

ado

r

Grados de libertad del Numerador 1 Grados de libertad del Denominador 8

F 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 1.00000 0.75992 0.66658 0.59883 0.54474 0.49958 0.46086 0.42707 0.39720 0.37056

1 0.34659 0.32492 0.30520 0.28720 0.27069 0.25551 0.24150 0.22855 0.21655 0.20540

2 0.19502 0.18534 0.17630 0.16785 0.15993 0.15250 0.14553 0.13897 0.13280 0.12699

3 0.12150 0.11633 0.11143 0.10681 0.10243 0.09828 0.09435 0.09062 0.08708 0.08371

4 0.08052 0.07747 0.07458 0.07182 0.06919 0.06669 0.06430 0.06202 0.05984 0.05776

5 0.05577 0.05386 0.05204 0.05030 0.04863 0.04703 0.04550 0.04403 0.04262 0.04127

6 0.03997 0.03872 0.03752 0.03637 0.03527 0.03420 0.03318 0.03219 0.03124 0.03033

7 0.02945 0.02860 0.02778 0.02700 0.02624 0.02550 0.02480 0.02411 0.02346 0.02282

8 0.02220 0.02161 0.02104 0.02048 0.01994 0.01943 0.01892 0.01844 0.01797 0.01751

9 0.01707 0.01664 0.01623 0.01583 0.01544 0.01507 0.01470 0.01435 0.01400 0.01367

10 0.01335 0.01304 0.01273 0.01244 0.01215 0.01187 0.01160 0.01134 0.01108 0.01083


F 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 1.00000 0.75726 0.66269 0.59392 0.53895 0.49300 0.45357 0.41913 0.38868 0.36150

1 0.33705 0.31493 0.29482 0.27646 0.25963 0.24417 0.22992 0.21675 0.20455 0.19323

2 0.18272 0.17292 0.16379 0.15527 0.14729 0.13983 0.13284 0.12627 0.12011 0.11432

3 0.10886 0.10373 0.09889 0.09433 0.09002 0.08595 0.08210 0.07846 0.07501 0.07175

4 0.06866 0.06572 0.06294 0.06030 0.05779 0.05540 0.05314 0.05098 0.04893 0.04698

5 0.04512 0.04334 0.04165 0.04004 0.03850 0.03703 0.03563 0.03429 0.03301 0.03179

6 0.03062 0.02950 0.02843 0.02741 0.02643 0.02549 0.02459 0.02373 0.02290 0.02211

7 0.02135 0.02062 0.01992 0.01924 0.01860 0.01798 0.01738 0.01681 0.01626 0.01573

8 0.01522 0.01473 0.01426 0.01381 0.01337 0.01295 0.01254 0.01215 0.01178 0.01142

9 0.01107 0.01073 0.01041 0.01009 0.00979 0.00950 0.00922 0.00895 0.00868 0.00843

10 0.00819 0.00795 0.00772 0.00750 0.00729 0.00708 0.00688 0.00669 0.00650 0.00632


F 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0 1.00000 0.90493 0.81906 0.74150 0.67141 0.60807 0.55082 0.49905 0.45224 0.40990

1 0.37160 0.33695 0.30558 0.27719 0.25148 0.22821 0.20713 0.18803 0.17072 0.15504

2 0.14082 0.12793 0.11625 0.10565 0.09603 0.08731 0.07939 0.07221 0.06568 0.05976

3 0.05438 0.04949 0.04506 0.04102 0.03736 0.03403 0.03100 0.02824 0.02574 0.02346

4 0.02138 0.01950 0.01778 0.01622 0.01479 0.01350 0.01232 0.01124 0.01026 0.00937

5 0.00856 0.00782 0.00714 0.00652 0.00596 0.00545 0.00498 0.00455 0.00416 0.00381

6 0.00348 0.00319 0.00291 0.00267 0.00244 0.00223 0.00205 0.00187 0.00172 0.00157

7 0.00144 0.00132 0.00121 0.00111 0.00102 0.00093 0.00085 0.00078 0.00072 0.00066

8 0.00060 0.00056 0.00051 0.00047 0.00043 0.00039 0.00036 0.00033 0.00031 0.00028

9 0.00026 0.00024 0.00022 0.00020 0.00018 0.00017 0.00016 0.00014 0.00013 0.00012

10 0.00011 0.00010 0.00009 0.00009 0.00008 0.00007 0.00007 0.00006 0.00006 0.00005

IND 214 Tabla N 8 - Probabilidad (F>f) o p-value

v 0.4 0.75 0.9 0.95 0.975

1 -0.325 1.000 3.078 6.314 12.706

2 -0.289 0.816 1.886 2.920 4.303

3 -0.277 0.765 1.638 2.353 3.182

4 -0.271 0.741 1.533 2.132 2.776

5 -0.267 0.727 1.476 2.015 2.571

6 -0.265 0.718 1.440 1.943 2.447

7 -0.263 0.711 1.415 1.895 2.365

8 -0.262 0.706 1.397 1.860 2.306

9 -0.261 0.703 1.383 1.833 2.262

10 -0.260 0.700 1.372 1.812 2.228

11 -0.260 0.697 1.363 1.796 2.201

12 -0.259 0.695 1.356 1.782 2.179

13 -0.259 0.694 1.350 1.771 2.160

14 -0.258 0.692 1.345 1.761 2.145

15 -0.258 0.691 1.341 1.753 2.131

16 -0.258 0.690 1.337 1.746 2.120

17 -0.257 0.689 1.333 1.740 2.110

18 -0.257 0.688 1.330 1.734 2.101

19 -0.257 0.688 1.328 1.729 2.093

20 -0.257 0.687 1.325 1.725 2.086

21 -0.257 0.686 1.323 1.721 2.080

22 -0.256 0.686 1.321 1.717 2.074

23 -0.256 0.685 1.319 1.714 2.069

24 -0.256 0.685 1.318 1.711 2.064

25 -0.256 0.684 1.316 1.708 2.060

26 -0.256 0.684 1.315 1.706 2.056

27 -0.256 0.684 1.314 1.703 2.052

28 -0.256 0.683 1.313 1.701 2.048

29 -0.256 0.683 1.311 1.699 2.045

30 -0.256 0.683 1.310 1.697 2.042

35 -0.255 0.682 1.306 1.690 2.030

40 -0.255 0.681 1.303 1.684 2.021

60 -0.254 0.679 1.296 1.671 2.000

120 -0.254 0.677 1.289 1.658 1.980

0.99 0.995 0.999 0.9995

31.821 63.657 318.309 636.619

6.965 9.925 22.327 31.599

4.541 5.841 10.215 12.924

3.747 4.604 7.173 8.610

3.365 4.032 5.893 6.869

3.143 3.707 5.208 5.959

2.998 3.499 4.785 5.408

2.896 3.355 4.501 5.041

2.821 3.250 4.297 4.781

2.764 3.169 4.144 4.587

2.718 3.106 4.025 4.437

2.681 3.055 3.930 4.318

2.650 3.012 3.852 4.221

2.624 2.977 3.787 4.140

2.602 2.947 3.733 4.073

2.583 2.921 3.686 4.015

2.567 2.898 3.646 3.965

2.552 2.878 3.610 3.922

2.539 2.861 3.579 3.883

2.528 2.845 3.552 3.850

2.518 2.831 3.527 3.819

2.508 2.819 3.505 3.792

2.500 2.807 3.485 3.768

2.492 2.797 3.467 3.745

2.485 2.787 3.450 3.725

2.479 2.779 3.435 3.707

2.473 2.771 3.421 3.690

2.467 2.763 3.408 3.674

2.462 2.756 3.396 3.659

2.457 2.750 3.385 3.646

2.438 2.724 3.340 3.591

2.423 2.704 3.307 3.551

2.390 2.660 3.232 3.460

2.358 2.617 3.160 3.373

2 3 4 5 6

1 2 2.9 3.8 4.7

1.41421 1.91155 2.23887 2.48124 2.67253

1.9 3.8 5.7 7.5 9.2

1.27931 1.80538 2.15069 2.40484 2.60438

2.8 5.7 8.4 11.1 13.6

1.23105 1.76858 2.12049 2.37883 2.58127

3.7 7.5 11.2 14.7 18.1

1.20621 1.74989 2.10522 2.36571 2.56964

4.6 9.3 13.9 18.4 22.6

1.19105 1.73857 2.09601 2.35781 2.56263

5.5 11.1 16.7 22 27

1.18083 1.73099 2.08985 2.35253 2.55795

6.4 12.9 19.4 25.6 31.5

1.17348 1.72555 2.08543 2.34875 2.5546

7.2 14.8 22.1 29.2 36

1.16794 1.72147 2.08212 2.34591 2.55208

8.1 16.6 24.9 32.9 40.4

1.16361 1.71828 2.07953 2.3437 2.55013

9 18.4 27.6 36.5 44.9

1.16014 1.71573 2.07746 2.34192 2.54856

9.9 20.2 30.4 40.1 49.4

1.15729 1.71363 2.07577 2.34048 2.54728

10.7 22 33.1 43.7 53.8

1.1549 1.71189 2.07436 2.33927 2.54621

11.6 23.8 35.8 47.3 58.3

1.15289 1.71041 2.07316 2.33824 2.5453

12.5 25.7 38.6 51 62.8

1.15115 1.70914 2.07213 2.33737 2.54452

13.4 27.5 41.3 54.6 67.2

1.14965 1.70804 2.07125 2.33661 2.54385

14.3 29.3 44.1 58.2 71.7

1.14833 1.70708 2.07047 2.33594 2.54326

15.1 31.1 46.8 61.8 76.2

1.14717 1.70623 2.06978 2.33535 2.54274

16 32.9 49.5 65.5 80.6

1.14613 1.70547 2.06917 2.33483 2.54228

16.9 34.7 52.3 69.1 85.1

1.1452 1.7048 2.06862 2.33436 2.54187

17.8 36.5 55 72.7 89.6

1.14437 1.70419 2.06813 2.33394 2.54149

1.12838 1.69257 2.05875 2.32593 2.53441

20

d2

14

15

16

17

18

19

8

9

10

11

12

13

Subgoup Size (m)

Nu

mb

er o

f Su

bgr

ou

ps

(g)

1

2

3

4

5

6

7

0.876 1.815 2.7378 3.623 4.4658

Table entries: 1st line of each cell is the degrees of freedom () and the 2nd line of each cell is d2* ; d2 is the infinity value of d2

* : Additional values of can be built up from the constant difference cd.

Note: The notation used in this table follows that of Acheson Duncan Quality Control and Industrial Statistics, 5th edition, McGraw-Hill, 1986.

( * )2 2

2 R d is distributed approximately as a 2 distribution with of freedom where R is the average range of g subgroups of size m

cd

7 8 9 10 11 12 13

5.5 6.3 7 7.7 8.3 9 9.6

2.82981 2.96288 3.07794 3.17905 3.26909 3.35016 3.42378

10.8 12.3 13.8 15.1 16.5 17.8 19

2.76779 2.90562 3.02446 3.12869 3.22134 3.30463 3.38017

16 18.3 20.5 22.6 24.6 26.5 28.4

2.74681 2.88628 3.00643 3.11173 3.20526 3.28931 3.3655

21.3 24.4 27.3 30.1 32.7 35.3 37.7

2.73626 2.87656 2.99737 3.10321 3.1972 3.28163 3.35815

26.6 30.4 34 37.5 40.8 44 47.1

2.72991 2.87071 2.99192 3.09808 3.19235 3.27701 3.35372

31.8 36.4 40.8 45 49 52.8 56.5

2.72567 2.8668 2.98829 3.09467 3.18911 3.27392 3.35077

37.1 42.5 47.6 52.4 57.1 61.6 65.9

2.72263 2.86401 2.98568 3.09222 3.18679 3.27172 3.34866

42.4 48.5 54.3 59.9 65.2 70.3 75.2

2.72036 2.86192 2.98373 3.09039 3.18506 3.27006 3.34708

47.7 54.5 61.1 67.3 73.3 79.1 84.6

2.71858 2.86028 2.98221 3.08896 3.1837 3.26878 3.34585

52.9 60.6 67.8 74.8 81.5 87.9 94

2.71717 2.85898 2.981 3.08781 3.18262 3.26775 3.34486

58.2 66.6 74.6 82.2 89.6 96.6 103.4

2.716 2.85791 2.98 3.08688 3.18174 3.2669 3.34406

63.5 72.6 81.3 89.7 97.7 105.4 112.7

2.71504 2.85702 2.97917 3.0861 3.181 3.2662 3.34339

68.7 78.6 88.1 97.1 105.8 114.1 122.1

2.71422 2.85627 2.97847 3.08544 3.18037 3.26561 3.34282

74 84.7 94.9 104.6 113.9 122.9 131.5

2.71351 2.85562 2.97787 3.08487 3.17984 3.2651 3.34233

79.3 90.7 101.6 112.1 122.1 131.7 140.9

2.7129 2.85506 2.97735 3.08438 3.17938 3.26465 3.34191

84.5 96.7 108.4 119.5 130.2 140.4 150.2

2.71237 2.85457 2.97689 3.08395 3.17897 3.26427 3.34154

89.8 102.8 115.1 127 138.3 149.2 159.6

2.7119 2.85413 2.97649 3.08358 3.17861 3.26393 3.34121

95.1 108.8 121.9 134.4 146.4 157.9 169

2.71148 2.85375 2.97613 3.08324 3.17829 3.26362 3.34092

100.3 114.8 128.7 141.9 154.5 166.7 178.4

2.71111 2.85341 2.97581 3.08294 3.17801 3.26335 3.34066

105.6 120.9 135.4 149.3 162.7 175.5 187.8

2.71077 2.8531 2.97552 3.08267 3.17775 3.26311 3.34042

2.70436 2.8472 2.97003 3.07751 3.17287 3.25846 3.33598

Subgoup Size (m)

5.2673 6.0305 6.7582 7.4539 8.1207 8.7602 9.3751



Note: The notation used in this table follows that of Acheson Duncan Quality Control and Industrial Statistics, 5th edition, McGraw-Hill, 1986.

2 R d is distributed approximately as a 2 distribution with of freedom where R is the average range of g subgroups of size m

14 15 16 17 18 19 20

10.2 10.8 11.3 11.9 12.4 12.9 13.4

3.49116 3.55333 3.61071 3.66422 3.71424 3.76118 3.80537

20.2 21.3 22.4 23.5 24.5 25.5 26.5

3.44922 3.51287 3.57156 3.62625 3.67734 3.72524 3.77032

30.1 31.9 33.5 35.1 36.7 38.2 39.7

3.43512 3.49927 3.55842 3.61351 3.66495 3.71319 3.75857

40.1 42.4 44.6 46.7 48.8 50.8 52.8

3.42805 3.49246 3.55183 3.60712 3.65875 3.70715 3.75268

50.1 52.9 55.7 58.4 61 63.5 65.9

3.42381 3.48836 3.54787 3.60328 3.65502 3.70352 3.74914

60.1 63.5 66.8 70 73.1 76.1 79.1

3.42097 3.48563 3.54522 3.60072 3.65253 3.70109 3.74678

70 74 77.9 81.6 85.3 88.8 92.2

3.41894 3.48368 3.54333 3.59888 3.65075 3.69936 3.74509

80 84.6 89 93.3 97.4 101.4 105.3

3.41742 3.48221 3.54192 3.59751 3.64941 3.69806 3.74382

90 95.1 100.1 104.9 109.5 114.1 118.5

3.41624 3.48107 3.54081 3.59644 3.64838 3.69705 3.74284

99.9 105.6 111.2 116.5 121.7 126.7 131.6

3.41529 3.48016 3.53993 3.59559 3.64755 3.69625 3.74205

109.9 116.2 122.3 128.1 133.8 139.4 144.7

3.41452 3.47941 3.53921 3.59489 3.64687 3.69558 3.74141

119.9 126.7 133.3 139.8 146 152 157.9

3.41387 3.47879 3.53861 3.5943 3.6463 3.69503 3.74087

129.8 137.3 144.4 151.4 158.1 164.7 171

3.41333 3.47826 3.5381 3.59381 3.64582 3.69457 3.74041

139.8 147.8 155.5 163 170.3 177.3 184.2

3.41286 3.47781 3.53766 3.59339 3.64541 3.69417 3.74002

149.8 158.3 166.6 174.6 182.4 190 197.3

3.41245 3.47742 3.53728 3.59302 3.64505 3.69382 3.73969

159.7 168.9 177.7 186.3 194.6 202.6 210.4

3.4121 3.47707 3.53695 3.5927 3.64474 3.69351 3.73939

169.7 179.4 188.8 197.9 206.7 215.2 223.6

3.41178 3.47677 3.53666 3.59242 3.64447 3.69325 3.73913

179.7 190 199.9 209.5 218.8 227.9 236.7

3.4115 3.4765 3.5364 3.59216 3.64422 3.69301 3.7389

189.6 200.5 211 221.1 231 240.5 249.8

3.41125 3.47626 3.53617 3.59194 3.644 3.6928 3.73869

199.6 211 222.1 232.8 243.1 253.2 263

3.41103 3.47605 3.53596 3.59174 3.6438 3.6926 3.7385

3.40676 3.47193 3.53198 3.58788 3.64006 3.68896 3.735

Subgoup Size (m)

9.9679 10.5396 11.0913 11.6259 12.144 12.6468 13.1362



tablas estadisticas rev. 5

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