GALVEZ MURILLOS SUSANCHOCANO LANDERAS MACARENAGUILLERMO VASQUEZ MARITE

PROVEEDOR A PROVEEDOR Bn 50 100c 2 4

p Pa, n=50 y c = 2 Pa, n=100 y c = 40.001 0.9999810783449 0.999999930439010.003 0.999523786387 0.999985565270690.005 0.9979444558904 0.999841400761170.007 0.9947399145326 0.999270852823980.009 0.989571673868 0.997808960257450.01 0.9861827291694 0.996567678412240.02 0.921572251649 0.94916955463050.03 0.8107980753697 0.817854806075640.04 0.6767140040966 0.62886406644530.05 0.5405331227195 0.435981300685710.06 0.4162464724119 0.276775219015070.07 0.3107885610019 0.16316424363440.08 0.2259742754335 0.09033655854240.09 0.1605404907245 0.047386679246510.1 0.1117287563463 0.02371108266348

0.11 0.0763268798536 0.011377254050520.12 0.0512641757519 0.005256593675570.13 0.0338941013933 0.002346191135480.14 0.0220824629381 0.001014226390530.15 0.0141885166011 0.000425513817040.16 0.0089965551212 0.00017354680523 La línea roja, ya que hay menor cantidad de lotes rechazados. Por lo tanto se elige al proveedor B.0.17 0.0056323936404 6.8899953192E-050.18 0.0034831258111 2.66551486E-050.19 0.0021283773214 1.0057032367E-050.2 0.0012854149532 3.7031730573E-06

0.21 0.0007674289189 1.3314262512E-060.22 0.0004529961736 4.6759210076E-070.23 0.000264395224 1.604517193E-070.24 0.0001525944008 5.3805583489E-08

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

Pa, n=50 y c = 2Pa, n=100 y c = 4

0.25 8.7087685833E-05 1.763429044E-08

La línea roja, ya que hay menor cantidad de lotes rechazados. Por lo tanto se elige al proveedor B.

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

Pa, n=50 y c = 2Pa, n=100 y c = 4

A)N = 3000

AQL = 1%Nivel de inspección general = II

Código = K

n AceptaciónN 125 3S 125 2R 50 1

B)

n=125 y c = 1 n=125 y c = 1n 125 125c 1 1

p Pa, n=125 y c = 1 Pa, n=125 y c = 10.001 0.992857341017304 0.992857341017304

0.003 0.945265357599377 0.9452653575993770.005 0.87011574419731 0.870115744197310.007 0.781778432973472 0.7817784329734720.009 0.689681885732556 0.6896818857325560.01 0.644187284981776 0.6441872849817760.02 0.284192511352813 0.2841925113528130.03 0.108053054349012 0.1080530543490120.04 0.0377467145284197 0.03774671452841970.05 0.0124468527644245 0.01244685276442450.06 0.00392822443683542 0.003928224436835420.07 0.00119608206422952 0.001196082064229520.08 0.000353112611864154 0.0003531126118641540.09 0.000101406600230404 0.0001014066002304040.1 2.83906913862787E-05 2.83906913862787E-05

0.11 7.76071796175032E-06 7.76071796175032E-060.12 2.07348952025317E-06 2.07348952025317E-060.13 5.4186498124125E-07 5.4186498124125E-070.14 1.38573641936251E-07 1.38573641936251E-070.15 3.46898849847024E-08 3.46898849847024E-080.16 8.50215829122094E-09 8.50215829122094E-090.17 2.04024594652285E-09 2.04024594652285E-090.18 4.79342836710342E-10 4.79342836710342E-100.19 1.10247995865007E-10 1.10247995865007E-100.2 2.48186464811271E-11 2.48186464811271E-11

0.21 5.46721316564439E-12 5.46721316564439E-120.22 1.17817591057761E-12 1.17817591057761E-120.23 2.48294028323298E-13 2.48294028323298E-130.24 5.11530783063876E-14 5.11530783063876E-140.25 1.02978518341177E-14 1.02978518341177E-14

C)

p Pa, n=125 y c = 3 Pa, n=125 y c = 20.001 0.999991201398333 0.999709962671773

0.0015 0.999957553235877 0.9990646101484250.002 0.99987215002397 0.9978810110037870.003 0.999412002140748 0.9934655402848650.005 0.996251672630265 0.9747034515229680.007 0.988086432827913 0.941828310985550.009 0.973024226207765 0.8961467823582410.01 0.962550937836635 0.8693158680719980.02 0.758669804503146 0.542519037623550.03 0.481405046713336 0.2726673418914640.04 0.259303708419306 0.1195523738112080.05 0.123784697783227 0.04770383702037850.06 0.0538949925051814 0.01774256619690760.07 0.0218119252800698 0.00624153843021149

0.08 0.0083118816738016 0.00209646202543140.09 0.00300940669432783 0.0006766848797148950.1 0.00104197028528558 0.000210835018288152

0.11 0.000346652972715571 6.36151821711763E-050.12 0.000111212042278859 1.86324423525933E-050.13 3.44988338190279E-05 5.3067944794468E-060.14 1.03694482319496E-05 1.47168760366527E-060.15 3.02482764781588E-06 3.97778041899917E-070.16 8.57382130090649E-07 1.04861506441426E-070.17 2.36366752457451E-07 2.69749895880703E-080.18 6.34227946513188E-08 6.77368801817119E-090.19 1.65721366118787E-08 1.66072820272211E-090.2 4.21837628228204E-09 3.97579325218986E-10

0.21 1.04628159114024E-09 9.29399108890411E-110.22 2.52896405221971E-10 2.12128921210763E-110.23 5.95716917842669E-11 4.72662895695825E-120.24 1.36746409500352E-11 1.02793145401525E-120.25 3.05853350759293E-12 2.181321010904E-13

Rechazo434

n=50 y c = 150

1

Pa, n=50 y c = 10.998813517496182

0.9899794398995330.973868475930110.95189531414549

0.9252797350315920.9105646869039690.7357713944617260.5552798733073160.4004811966929520.2794317523206950.1900032581375240.126493498821593

0.08271202292681480.05323846054627890.03378585969243190.02116465452349950.01309903714262760.00801513545288120.0048511718214151 Se selecciona la curva azul y rojo, en este caso son las mismas, porque hay menor cantidad de lotes rechazados.0.00290545287294240.00172241294986070.00101089993861850.00058747616962930.00033808397843340.00019267843851530.00010874803421196.078281679722E-053.364264215559E-051.843812250466E-051.000501593021E-05

Pa, n=50 y c = 10.9988135174961820.997372615781201 n=125 y c = 10.995402811792015 n 1250.989979439899533 c 3

0.973868475930110.95189531414549

0.9252797350315920.9105646869039690.7357713944617260.5552798733073160.4004811966929520.2794317523206950.1900032581375240.126493498821593

Estas son las probabilidades de

aceptación para 1.5 % y 2 %.

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

Pa, n=125 y c = 1Pa, n=125 y c = 1Pa, n=50 y c = 1

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

Pa, n=125 y c = 3Pa, n=125 y c = 2Pa, n=50 y c = 1

0.08271202292681480.05323846054627890.03378585969243190.02116465452349950.01309903714262760.00801513545288120.00485117182141510.00290545287294240.00172241294986070.00101089993861850.00058747616962930.00033808397843340.00019267843851530.00010874803421196.078281679722E-053.364264215559E-051.843812250466E-051.000501593021E-05

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

Pa, n=125 y c = 3Pa, n=125 y c = 2Pa, n=50 y c = 1

Se selecciona la curva azul y rojo, en este caso son las mismas, porque hay menor cantidad de lotes rechazados.

n=125 y c = 1 n=50 y c = 1125 50

2 1

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

Pa, n=125 y c = 1Pa, n=125 y c = 1Pa, n=50 y c = 1

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

Pa, n=125 y c = 3Pa, n=125 y c = 2Pa, n=50 y c = 1

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

Pa, n=125 y c = 3Pa, n=125 y c = 2Pa, n=50 y c = 1

N= 12000AQL= 1.50%

codigo= M

Normal Rigurosan= 315 n= 315

Ac= 10 Ac= 8R= 11 R= 9

p Pa, n=315 y c=10 Pa,n=315 y c=8 Pa, n=125 y c=50.001 1 0.99999999994 0.999999995760.003 0.999999995109 0.99999935241 0.999997480450.005 0.999999225733 0.99996277911 0.999955914190.007 0.9999819646 0.99955328962 0.999728845240.009 0.999835047917 0.99750070927 0.998998799750.01 0.999600651076 0.99506870109 0.99829627996

0.011 0.999133872965 0.99110302593 0.997269978220.012 0.998284351131 0.98508816412 0.995837144160.013 0.996850337856 0.97650080028 0.993911044810.014 0.994579428714 0.96485391419 0.991403585970.015 0.991175187074 0.94973854239 0.988227908110.016 0.986309448392 0.9308583398 0.984300840380.017 0.979639278471 0.90805366467 0.979545123610.018 0.97082696046 0.88131366059 0.973891339060.019 0.959561065112 0.85077640866 0.967279503260.02 0.945576625596 0.81671848347 0.95966030935

0.021 0.928672652793 0.77953608535 0.950996012510.022 0.908725621064 0.73972034126 0.941260970580.023 0.885698048977 0.6978294258 0.9304418614 Como cliente se aceptaría el plan de muestreo riguroso con una muestra de 315 y una aceptacón de 8.0.024 0.859641818304 0.65445993752 0.918537606060.025 0.830696355455 0.61021956953 0.905559032220.026 0.799082197756 0.56570262301 0.891528314680.027 0.765090757637 0.52146940143 0.876478231310.028 0.729071272966 0.47803004392 0.860451272320.029 0.691415997533 0.43583294391 0.843498639130.03 0.652544657785 0.39525757165 0.82567916708

0.031 0.612889101404 0.35661128154 0.807058203040.032 0.572878913315 0.3201295329 0.78770646584

3. En una empresa se ha venido aplicando un muestreo de aceptación con base en el MIL STD 105D, usando un AQL de 1.5%.

a) Suponiendo lotes de 12,000 piezas y usando nivel de inspección general II, encuentre los planes de muestreo normal, reducido y severo que aplicarán.

0 0.01 0.02 0.03 0.04 0.05 0.060

0.2

0.4

0.6

0.8

1

1.2

Pa

Pa, n=315 y c=10Pa,n=315 y c=8Pa, n=125 y c=5

0.033 0.532928597344 0.28597887544 0.767698913980.034 0.4934267363626 0.25426203383 0.747113641330.035 0.454727365829 0.22502445563 0.726030818370.036 0.41714363651 0.19826174807 0.704531692810.037 0.380943708806 0.17392751003 0.682697660440.038 0.346348717084 0.15194115525 0.660609414370.039 0.313532568197 0.13219541338 0.638346177640.04 0.282623292047 0.11456328096 0.61598502267

0.041 0.253705640516 0.09890427102 0.593600278140.042 0.22682462998 0.08506987566 0.571263022850.043 0.201989737524 0.07290820953 0.549040664280.044 0.179179487405 0.06226784437 0.526996598530.045 0.15834619816 0.05300087544 0.505189947340.046 0.139420698511 0.04496528256 0.483675367250.047 0.12231685896 0.03802666116 0.462502925340.048 0.106935823418 0.03205940558 0.441718035750.049 0.093169859821 0.02694742801 0.421361451010.05 0.080905779307 0.02258449384 0.40146930205

Reducidon= 125

Ac= 5R= 8

Como cliente se aceptaría el plan de muestreo riguroso con una muestra de 315 y una aceptacón de 8.

0 0.01 0.02 0.03 0.04 0.05 0.060

0.2

0.4

0.6

0.8

1

1.2

Pa

Pa, n=315 y c=10Pa,n=315 y c=8Pa, n=125 y c=5

Normal Rigurosan= 125 n= 200

AC= 0 AC= 0R= 1 R= 1

p Pa, n=125 y c=0 Pa,n=200 y c=0 Pa, n=50 y c=00.001 0.882441711456 0.81864882948 0.95120562820.003 0.686902012774 0.54831693863 0.86051395080.005 0.534422941652 0.36695782173 0.77831255710.007 0.415581361854 0.24538595354 0.70382133060.009 0.323003189396 0.16395735255 0.6363304770.01 0.284707773273 0.13397967486 0.6050060671

0.011 0.250920676437 0.10946072478 0.57519430820.012 0.221114932898 0.08941058111 0.54682357440.013 0.194824730298 0.073018101 0.51982556410.014 0.171638364523 0.05961876676 0.49413514860.015 0.151192000066 0.04866829138 0.46969022820.016 0.133164144675 0.03972095543 0.44643159350.017 0.117270757114 0.03241183105 0.4243027940.018 0.103260916031 0.02644219827 0.40325001230.019 0.090912986056 0.0215675829 0.38322194340.02 0.080031224461 0.01758794661 0.3641696801

0.021 0.070442778131 0.01433964371 0.34604660290.022 0.061995026282 0.01168882772 0.32880827550.023 0.054553229417 0.00952604752 0.31241234440.024 0.047998449478 0.0077618194 0.29681844350.025 0.042225710157 0.00632299939 0.28198810230.026 0.037142369816 0.00514981201 0.26788465930.027 0.032666682656 0.00419341702 0.25447317790.028 0.028726526488 0.00341391721 0.24172036780.029 0.025258277976 0.00277872764 0.2295945080.03 0.022205818373 0.00226124101 0.2180653753

0.031 0.019519654725 0.00183973559 0.20710417440.032 0.017156143238 0.00149648188 0.19668347170.033 0.015076803006 0.00121701188 0.18677713270.034 0.013247709675 0.00098952161 0.17736026160.035 0.011638959795 0.0008043826 0.16840914350.036 0.010224197682 0.00065374259 0.1599011898

4. Un producto se surte en lotes de tamaño N= 10 000. El AQL se ha especificado en 0.10%. Encontrar los planes de muestreo, para atributos, con inspección normal, rigurosa y reducida, suponiendo que se usa el

nivel II de inspección general.

0.037 0.00898019755 0.00053119922 0.15181488550.038 0.007886494499 0.00043153339 0.14412973960.039 0.006925058693 0.00035049154 0.13682623710.04 0.006080007709 0.00028460768 0.1298857935

0.041 0.005337352623 0.00023105823 0.12329071140.042 0.004684773893 0.00018754341 0.11702413880.043 0.004111423578 0.0001521905 0.11107002990.044 0.003607750824 0.00012347484 0.10541310690.045 0.003165347887 0.00010015539 0.10003882430.046 0.002776814305 8.1222236E-05 0.09493333440.047 0.002435637095 6.5853692E-05 0.09008345450.048 0.002136085087 5.3381365E-05 0.08547663550.049 0.001873115757 4.3261681E-05 0.08110093230.05 0.001642293073 3.5052666E-05 0.0769449753

0.051 0.001439715079 2.839504E-05 0.07299794280.052 0.001261950056 2.2996803E-05 0.06924953590.053 0.00110598026 1.8620691E-05 0.06568995290.054 0.000969152343 1.5073957E-05 0.06230986640.055 0.000849133673 1.2200053E-05 0.05910040070.056 0.000743873842 9.8718571E-06 0.05605311020.057 0.000651570768 7.9861699E-06 0.05315995890.058 0.000570640838 6.4592272E-06 0.05041330150.059 0.000499692612 5.223056E-06 0.0478058640.06 0.00043750367 4.2225103E-06 0.0453307266

0.061 0.000383000229 3.4128598E-06 0.04298130660.062 0.000335239201 2.7578312E-06 0.04075134230.063 0.000293392401 2.2280153E-06 0.03863487790.064 0.000256732643 1.7995742E-06 0.03662624840.065 0.000224621519 1.4531892E-06 0.03472006610.066 0.000196498631 1.1732086E-06 0.03291120710.067 0.000171872134 9.4695371E-07 0.03119479870.068 0.000150310405 7.6415678E-07 0.02956620730.069 0.000131434726 6.1650442E-07 0.0280210270.07 0.000114912843 4.9726708E-07 0.0265550686

N= 10000AQL= 0.10%

codigo: L

Reducidan= 50

AC= 0R= 1

Como cliente se aceptaría el plan de muestreo riguroso con tamaño de muestra 200 y aceptación 0

4. Un producto se surte en lotes de tamaño N= 10 000. El AQL se ha especificado en 0.10%. Encontrar los planes de muestreo, para atributos, con inspección normal, rigurosa y reducida, suponiendo que se usa el

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pa

Pa, n=125 y c=0Pa,n=200 y c=0Pa, n=50 y c=0

n 62c 1

p Pa, n=62 y c=10.001 0.99818299204460.002 0.99301515242810.003 0.9848937957055 las probabilidades de aceptación de lotes con 1%,2% y 3% respectivamente son :0.998182992,0.993015152 y 0.984893796.0.005 0.96121034704520.007 0.92966853284670.009 0.89236872556670.01 0.87211297230660.02 0.6473566172410.03 0.44143038713110.04 0.28516988335560.05 0.17725355160230.06 0.10695103365410.07 0.06298983590980.08 0.03634417325780.09 0.02059537141490.1 0.0114828958165

0.11 0.00630731880960.12 0.00341638123250.13 0.00182610551730.14 0.00096372672060.15 0.00050236631470.16 0.00025873115130.17 0.00013168129830.18 6.6237176807E-050.19 3.2931527967E-050.2 1.6183152912E-05

0.21 7.8604289646E-060.22 3.7734276245E-060.23 1.7901656358E-060.24 8.3920077808E-070.25 3.886784232E-07

5.   Una clínica evalúa los lotes de unos aplicadores de algodón usando el plan de muestreo simple N= 8,000, n= 62 y c= 1. Construya la curva CO e indique la probabilidad de aceptación de lotes con 1%, 2% y 3% de defectos en los aplicadores.curva

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

pa

Column C

Axis Title

Axis Title

las probabilidades de aceptación de lotes con 1%,2% y 3% respectivamente son :0.998182992,0.993015152 y 0.984893796.

Una clínica evalúa los lotes de unos aplicadores de algodón usando el plan de muestreo simple N= 8,000, n= 62 y c= 1. Construya la curva CO e indique la probabilidad de aceptación de lotes con 1%, 2% y 3% de defectos en los aplicadores.curva

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

pa

Column C

Axis Title

Axis Title

las probabilidades de aceptación de lotes con 1%,2% y 3% respectivamente son :0.998182992,0.993015152 y 0.984893796.

Una clínica evalúa los lotes de unos aplicadores de algodón usando el plan de muestreo simple N= 8,000, n= 62 y c= 1. Construya la curva CO e indique la probabilidad de aceptación de lotes con 1%, 2% y 3% de defectos en los aplicadores.curva

a ) Encontrar los planes de muestreo, para atributos, con inspección normal, rigurosa y reducida, suponiendo que se usa el nivel II de inspección general.b) Calcular la probabilidad de aceptación de los lotes para cada plan, en caso de tener 1%, 2% y 3% de artículos defectuosos.tablade artículos defectuosos.tabla

a) N= 2000AQL= 1.5INSP= III

CODIGO= Ln Aceptación Rechazo

inspeccion normal 200 7 8insp.rigurosa 200 5 6insp. reducida 80 3 6

inspeccion normal insp.rigurosa insp. reducidab) p Pa, n=200 y c=7 Pa, n=200y c=5 Pa, n=80 y c=3

0.001 0.99999999995354 0.99999993020076 0.99999851163760.002 0.99999998996924 0.99999621466278 0.99997758740110.003 0.99999978313515 0.99996344631199 0.99989320080980.005 0.99999080490607 0.999436056356 0.99926965092160.007 0.99990325435597 0.99693694396269 0.99751221496390.009 0.99948434319892 0.98999546639606 0.9939692228260.01 0.99898744284948 0.98397709309082 0.99134081110710.02 0.95066494505517 0.78672246570266 0.92314500893760.03 0.74610319127415 0.44322921232841 0.78066670530760.04 0.45010429213966 0.18564969483659 0.60163088181760.05 0.2133047027847 0.06234249504229 0.42844863722040.06 0.0828846325728 0.01772085472348 0.2857875544190.07 0.02741711291436 0.00442113501898 0.18050675871710.08 0.0079438962826 0.00099209146416 0.10886261271420.09 0.00205908036121 0.00020365942953 0.06309004922460.1 0.00048499671645 3.87119324627E-05 0.0353062584811

0.11 0.0001050349608 6.8740014314E-06 0.01915055139110.12 2.11029559342E-05 1.14777629545E-06 0.01009765002280.13 3.96060636826E-06 1.81113139377E-07 0.0051876219080.14 6.98107340942E-07 2.71107394414E-08 0.00260146092280.15 1.1605329716E-07 3.86104291251E-09 0.00127525834820.16 1.82563799948E-08 5.24350990506E-10 0.00061180758230.17 2.72482754816E-09 6.80219895894E-11 0.00028752116880.18 3.86665653551E-10 8.44037643352E-12 0.00013245957770.19 5.22534975386E-11 1.00274263294E-12 5.985607926E-050.2 6.73333462868E-12 1.14141262245E-13 2.654246003E-05

0.21 8.28132234171E-13 1.24546608799E-14 1.155397521E-050.22 9.72818737534E-14 1.30311593002E-15 4.93842014E-06

6.    Un producto se embarca en lotes de tamaño N= 2 000. El AQL se ha especificado en 1.5%.

0.23 1.09204297202E-14 1.3075222624E-16 2.072932259E-060.24 1.17179977769E-15 1.25811196551E-17 8.546066825E-070.25 1.20207315411E-16 1.16071715821E-18 3.460574251E-07

) Encontrar los planes de muestreo, para atributos, con inspección normal, rigurosa y reducida,

b) Calcular la probabilidad de aceptación de los lotes para cada plan, en caso de tener 1%, 2% y 3% de artículos defectuosos.tabla

estas son las probabilidades de aceptación de los lotes para cada plan(1%,2% y 3%)

como cliente aceptaría el plan de muestreo rigurosa con tamaño de muestra 200 y aceptación 5

0 0.05 0.1 0.15 0.2 0.250

0.2

0.4

0.6

0.8

1

1.2

pa

Column CColumn DColumn E

Axis Title

Axis Title

como cliente aceptaría el plan de muestreo rigurosa con tamaño de muestra 200 y aceptación 5