332
Nicolás Marinez Burbano
Problema 3
a. Genere por simulación un gran número (al menos 1000) de los tiempos de vida de los sistemas
n = 1000
rnorm_log = function(n, mu, sigma) rlnorm(n, meanlog=mu, sdlog = sigma)
R1 = rnorm_log(n, 2, 1)
R2 = rnorm_log(n, 1, 0.1)
R3 = rnorm_log(n, 2, 1)
R4 = rnorm_log(n, 1, 0.1)Sistema 1: paralelo entre R1-R2 y R3-R4, luego en serie
sistema1 = pmin(pmax(R1, R2), pmax(R3, R4))
sistema1## [1] 9.348545 5.308260 4.163530 2.062684 4.155874 4.084196 2.308105
## [8] 2.690727 2.862011 4.508830 6.211025 4.920456 11.753635 8.313144
## [15] 2.832385 2.330085 6.781166 5.159608 2.376171 10.635386 9.032841
## [22] 2.788856 3.140160 6.299203 7.838766 2.489298 2.607887 33.894003
## [29] 8.946339 2.384878 2.343877 2.548122 17.284910 2.653630 3.113854
## [36] 12.142703 2.824934 4.523185 3.078125 2.351288 3.105265 2.407971
## [43] 2.992838 3.642583 7.827088 7.597541 9.613079 7.965392 2.902023
## [50] 10.942838 8.950088 16.409234 3.000260 10.576403 4.122355 3.166834
## [57] 6.941313 4.206335 4.265565 3.340901 5.951072 2.414879 11.130731
## [64] 9.689812 4.424666 2.795480 2.760429 3.299599 3.166421 20.323650
## [71] 4.939252 11.690951 3.779795 8.664501 3.375594 3.044537 3.807214
## [78] 4.601416 2.818540 9.978035 3.032834 3.363719 11.356742 3.649107
## [85] 2.814106 11.203780 3.861448 2.631707 4.044150 10.526283 2.817352
## [92] 11.619888 3.006177 2.929659 7.491904 2.328771 12.593914 6.504684
## [99] 3.563038 3.241940 13.458619 2.478283 11.462644 9.068925 3.672302
## [106] 2.965055 2.713847 2.953221 18.891096 5.207758 7.884164 7.584860
## [113] 7.054917 5.067869 2.388999 6.504167 2.819830 2.571641 15.277115
## [120] 10.957143 9.009872 4.550744 3.075124 9.884595 35.350979 2.354922
## [127] 5.431171 11.906046 3.359344 7.697388 5.271959 3.235765 2.595360
## [134] 6.769393 2.485701 3.058873 2.519312 4.629665 3.544777 3.891681
## [141] 14.504322 5.617663 4.002942 11.188555 2.828275 7.547056 5.409146
## [148] 3.030342 6.520011 2.404432 3.452647 3.100564 3.030555 7.631903
## [155] 2.714861 5.223215 4.819548 11.507273 2.746320 2.489479 6.592836
## [162] 3.715977 19.008642 6.033475 11.843435 9.123357 12.452735 18.255252
## [169] 3.798926 3.051589 2.665187 6.641026 4.960443 5.246202 2.818829
## [176] 7.314939 3.700476 2.663552 4.479870 4.393396 2.352640 7.050526
## [183] 3.915738 5.943497 2.503464 5.598490 3.348231 4.011051 3.044842
## [190] 8.849891 16.455883 17.600339 3.351006 4.538389 2.914359 3.177675
## [197] 3.025528 5.166664 5.654987 2.645002 5.481070 4.081499 3.322303
## [204] 2.547535 2.941611 12.393388 3.458669 2.434454 16.759054 2.813182
## [211] 3.715597 35.895163 5.398567 7.903627 6.614591 34.870672 10.725787
## [218] 4.813048 4.903183 6.018295 9.856982 5.489315 3.726482 2.478482
## [225] 4.293983 7.915652 4.679377 2.589083 3.738028 5.779904 12.074640
## [232] 7.546999 8.157977 5.309951 2.575672 6.033223 5.128200 2.910538
## [239] 11.331940 18.446917 8.605785 3.961208 13.893850 7.669408 10.331956
## [246] 6.130575 4.345103 3.851140 3.820632 9.989658 2.805244 18.171137
## [253] 2.428030 4.336507 2.642244 4.160580 14.368664 4.792184 3.365912
## [260] 2.430119 6.668240 2.559432 3.073312 6.834128 8.015219 2.653937
## [267] 2.894023 3.131991 10.784707 3.137510 5.409438 5.385137 14.142788
## [274] 21.951010 5.461827 6.226991 3.547002 2.974696 4.248048 6.194886
## [281] 9.726196 3.375902 5.824030 4.068679 5.928650 2.972412 2.508523
## [288] 7.748023 6.276771 2.810404 3.716993 8.589845 4.454187 3.537261
## [295] 20.227203 4.060811 3.822050 4.412691 6.164433 2.496055 8.526090
## [302] 2.695505 2.860246 2.486057 6.300643 10.411759 3.332642 5.446706
## [309] 2.837648 18.885437 3.097506 2.381615 7.375901 3.674193 7.199901
## [316] 15.579456 3.232973 10.743531 2.513303 7.375571 8.862893 5.702870
## [323] 4.187031 2.858013 7.816468 2.596389 3.223681 9.818901 8.581259
## [330] 2.881094 10.653039 9.807863 3.057485 2.832081 4.840588 2.906600
## [337] 3.015958 21.903088 2.863429 3.469687 3.658318 5.229477 4.651513
## [344] 3.121758 2.494788 3.999250 2.952205 4.582333 4.099200 7.995234
## [351] 2.648233 3.757845 2.013765 2.843106 4.346453 3.338276 2.430099
## [358] 9.966390 6.268321 13.120141 2.827588 3.822637 4.833963 3.647428
## [365] 5.135559 8.356904 3.611917 5.073826 3.904470 5.230893 6.988158
## [372] 42.931164 2.445977 7.678747 5.668751 2.578426 4.853852 4.044881
## [379] 3.522582 3.360802 2.892571 2.986411 10.077929 11.166812 5.126206
## [386] 10.879193 3.692085 7.416498 2.366517 2.994964 3.316589 9.180144
## [393] 6.383813 3.226482 2.929673 3.155020 4.471993 3.009695 4.497654
## [400] 3.987727 5.013681 2.652832 7.501453 4.736841 2.319436 7.120759
## [407] 6.649884 5.242834 3.584338 8.252897 2.466099 2.932143 3.899639
## [414] 3.139444 5.886979 2.996238 8.501053 2.825954 2.931734 2.916884
## [421] 6.080351 2.356367 5.326356 6.513825 3.934561 5.078900 3.102368
## [428] 2.760820 2.615314 2.181360 2.553788 16.877177 2.868586 10.359671
## [435] 16.769049 2.787063 2.823334 2.502439 7.073163 7.114178 2.923456
## [442] 6.395121 8.052316 13.402206 2.926601 3.235329 3.579588 2.741550
## [449] 15.813111 4.036395 2.963085 8.270466 2.628131 2.494752 9.575070
## [456] 2.503343 3.195939 15.253024 2.869741 2.885334 3.003067 3.278558
## [463] 3.637875 5.285381 4.359409 2.618379 2.336728 11.161853 2.675622
## [470] 3.177121 4.432366 2.703001 7.139942 3.081105 12.348050 8.993722
## [477] 2.393959 6.188908 5.474993 3.489559 9.031598 2.889573 2.724219
## [484] 4.416687 5.803949 3.622291 2.700413 9.946720 2.583527 2.584306
## [491] 11.885608 7.140423 2.596676 2.861949 10.163598 8.855599 9.794603
## [498] 12.681948 4.810080 3.456098 2.264124 3.028338 7.868091 3.459805
## [505] 5.113712 5.796485 2.890416 2.617971 17.275107 3.307182 10.839167
## [512] 2.495745 2.892482 7.060951 2.703656 10.001069 7.147450 5.482423
## [519] 2.764409 13.481939 12.284394 3.348437 2.565594 7.850922 2.668774
## [526] 2.460787 5.466743 2.660189 2.655016 26.569667 5.643559 11.846878
## [533] 3.467513 6.362405 3.693574 3.600571 5.372952 6.517753 2.830084
## [540] 2.704809 8.676711 3.334973 8.112339 3.317487 3.412398 2.283125
## [547] 2.528015 4.215128 2.834600 5.686876 2.876344 4.856532 2.716095
## [554] 12.362566 6.550340 3.054347 3.677278 7.988496 10.603368 5.413195
## [561] 9.321252 11.679353 6.062516 10.222065 7.123472 4.764402 2.755576
## [568] 3.063413 4.588703 6.400982 7.241478 4.176405 3.128070 7.735184
## [575] 3.309611 2.867326 5.248201 3.129866 4.096727 8.320343 4.540060
## [582] 7.689229 6.360845 2.777197 2.713657 14.340884 13.627685 3.920413
## [589] 7.223708 3.496555 3.890004 3.589386 2.689799 6.351084 3.351274
## [596] 3.032631 8.697736 18.684922 4.732687 14.711498 2.721880 3.911525
## [603] 10.587027 2.730409 7.756054 5.842393 7.938323 2.873431 6.986797
## [610] 7.792727 3.752776 7.456306 12.715967 2.783957 2.740718 2.337413
## [617] 5.533761 12.293473 11.464980 9.225017 16.321421 5.203589 4.171581
## [624] 6.285546 17.041273 6.016508 2.819191 32.286198 3.029851 3.162580
## [631] 9.403118 27.732299 4.534433 3.850471 7.177511 2.656139 2.663832
## [638] 4.815967 4.222578 11.780004 16.861926 4.786163 2.785785 6.209666
## [645] 2.869194 3.342452 2.857486 2.918970 8.145724 2.699370 8.693118
## [652] 3.870654 9.653637 2.984065 3.113105 2.995299 3.601287 2.875552
## [659] 3.852693 7.950673 3.553687 2.420669 3.613344 5.731873 2.761472
## [666] 3.599209 7.163406 2.285578 9.329847 2.625888 15.697550 6.393887
## [673] 6.846476 5.585073 31.052443 6.688605 2.647651 2.685807 3.999201
## [680] 2.602460 3.584194 7.351810 8.154469 2.661507 14.619167 3.136915
## [687] 4.632141 3.209729 3.165712 4.502618 2.287955 3.189155 2.602916
## [694] 4.795273 8.375773 2.741879 22.963878 9.746341 6.118900 3.226919
## [701] 3.029675 2.256757 2.999515 2.598249 3.013114 12.971987 7.223987
## [708] 2.768083 3.647814 2.532142 12.155236 4.662848 4.131256 5.218896
## [715] 9.911197 3.317935 6.393047 5.353092 5.919901 6.637658 3.911746
## [722] 2.569796 7.403661 7.218989 5.496785 5.807962 2.667715 10.651158
## [729] 3.096708 4.117866 12.879973 20.581698 5.431407 7.576712 2.777771
## [736] 24.951019 3.087630 16.305966 2.986156 3.116111 13.348736 5.998403
## [743] 6.014536 2.608366 6.184895 8.845888 14.574390 3.612210 2.587608
## [750] 4.761228 2.665241 8.214417 2.775894 5.529032 2.558536 9.996132
## [757] 2.977876 3.119587 2.408234 3.512271 4.553298 7.134229 7.358468
## [764] 2.742673 7.922152 5.049328 4.019656 4.534508 15.617514 3.316189
## [771] 9.277802 2.682807 2.644712 2.796750 2.454783 12.906711 2.804329
## [778] 3.528444 10.402664 11.280995 3.002377 2.665576 4.195620 2.515184
## [785] 3.238648 4.850463 7.127832 8.394823 9.266556 9.386517 3.117795
## [792] 19.307384 7.801123 12.162025 16.879321 3.035090 5.304859 2.571989
## [799] 9.297132 9.792515 5.645733 15.231237 3.222081 3.638486 2.469452
## [806] 8.614720 4.230097 2.883716 4.360383 5.682051 3.332687 2.514574
## [813] 6.066962 18.981086 2.672643 2.893387 3.340701 3.234540 6.842432
## [820] 7.776736 2.874350 2.167008 2.619883 3.874722 2.496015 14.781187
## [827] 2.661926 2.530921 2.874355 4.537431 8.739133 26.915244 6.953591
## [834] 2.669575 3.430257 3.525090 5.248867 9.401206 3.446591 4.498758
## [841] 2.767553 2.435247 2.799144 2.662320 8.935275 4.953197 2.692631
## [848] 4.540442 3.028764 2.938349 4.453660 4.464830 8.738074 4.379691
## [855] 5.035462 3.019835 6.649204 15.342125 2.894349 6.747676 4.153087
## [862] 2.606776 3.907681 2.788561 4.318561 8.940711 11.310392 21.412422
## [869] 2.775907 2.676096 4.634783 2.953109 11.156576 11.358595 6.843910
## [876] 3.106525 3.807533 2.504728 8.570196 2.838105 2.671791 2.757454
## [883] 8.365744 6.604440 4.759211 3.046293 3.291939 2.651891 6.490267
## [890] 3.110458 9.570815 22.126530 4.295946 27.805129 3.799141 6.584887
## [897] 2.543297 2.793783 3.884309 2.927550 2.599868 7.203707 38.549037
## [904] 8.849065 4.324181 5.021534 6.407734 2.961231 2.457757 5.516444
## [911] 3.071713 2.740839 22.916787 5.166396 4.305127 13.576374 2.826546
## [918] 4.339895 7.867333 7.686976 2.839192 5.328052 3.612780 3.087408
## [925] 2.626053 3.301406 12.319725 6.564707 2.882145 4.201745 3.580509
## [932] 8.654080 5.363286 6.087540 3.575430 3.380997 7.017237 2.143953
## [939] 2.482648 3.722893 2.810095 6.806646 2.715602 7.192360 8.753768
## [946] 8.033116 16.333616 5.086034 2.389549 5.040705 3.101053 19.202683
## [953] 2.451034 2.910039 13.713618 8.498853 13.231755 2.828502 10.560387
## [960] 4.325002 3.970638 4.631055 2.788540 3.011281 4.139887 2.400905
## [967] 3.075237 7.386118 5.113298 35.443492 7.779346 11.910903 6.609605
## [974] 12.440289 2.668347 5.666979 5.937436 2.978523 18.410342 18.332163
## [981] 3.033126 2.930079 3.871116 4.550592 4.277099 2.436147 6.374112
## [988] 11.177740 2.826329 27.565976 11.805220 6.431304 3.221948 12.393215
## [995] 10.673604 2.994928 2.629003 13.250947 9.686889 4.189562Sistema 2: paralelo R1-R2
sistema2 = pmax(R1, R2)
sistema2## [1] 9.348545 5.308260 5.410688 2.062684 6.228428 8.501803
## [7] 2.308105 2.690727 2.862011 4.508830 6.211025 4.920456
## [13] 46.788445 10.957828 16.404054 2.330085 6.781166 5.159608
## [19] 2.376171 10.635386 10.608573 10.453788 8.932859 6.299203
## [25] 10.242536 13.440254 2.607887 111.950365 8.946339 2.384878
## [31] 2.343877 2.882456 29.971855 2.653630 3.113854 23.641262
## [37] 6.578751 10.321778 3.971492 2.351288 3.105265 2.407971
## [43] 2.992838 11.954701 15.517550 7.597541 10.292132 14.070975
## [49] 88.735635 52.456366 8.950088 34.902005 18.434839 10.576403
## [55] 8.803027 3.166834 19.653033 44.964274 8.355457 6.489776
## [61] 5.951072 31.389648 11.130731 18.373632 30.887704 5.046566
## [67] 9.045860 3.299599 9.920806 30.110775 20.568625 11.895094
## [73] 3.779795 8.664501 5.039388 18.835862 3.929325 6.697229
## [79] 20.738357 10.889602 3.590939 3.363719 11.356742 5.071232
## [85] 2.814106 20.682305 11.363392 2.631707 4.044150 14.297281
## [91] 57.440494 12.071028 3.006177 15.042562 7.491904 2.328771
## [97] 26.026719 6.504684 3.563038 3.241940 13.458619 2.478283
## [103] 11.462644 9.068925 3.672302 2.965055 2.713847 13.531050
## [109] 41.862906 5.207758 24.512557 20.571384 7.054917 29.562552
## [115] 2.388999 6.504167 2.819830 2.571641 17.804329 10.957143
## [121] 14.715855 77.766947 3.075124 9.884595 35.350979 3.167307
## [127] 27.873047 11.906046 8.892880 9.519048 98.714056 21.635749
## [133] 2.595360 6.769393 10.599084 3.064977 2.519312 4.629665
## [139] 11.376391 4.039054 14.504322 13.956154 4.002942 11.188555
## [145] 17.767010 7.547056 45.167748 4.701607 6.520011 15.907655
## [151] 6.742830 3.100564 3.803182 9.055867 2.714861 6.727920
## [157] 4.819548 11.507273 2.746320 13.824266 10.608405 4.604525
## [163] 19.008642 18.290874 11.843435 10.908038 12.452735 18.255252
## [169] 40.317714 3.051589 17.400339 8.801679 4.960443 9.729890
## [175] 2.818829 7.314939 14.202269 8.154582 18.221768 4.393396
## [181] 2.352640 7.050526 3.915738 5.943497 2.503464 5.598490
## [187] 12.810847 4.011051 3.044842 14.868984 21.697477 17.600339
## [193] 3.351006 6.623804 2.914359 5.118589 3.025528 5.166664
## [199] 5.654987 5.409088 5.481070 4.081499 16.889698 2.547535
## [205] 2.941611 12.393388 9.363914 3.644149 16.759054 8.248498
## [211] 3.715597 35.895163 10.424451 40.873309 6.614591 34.870672
## [217] 12.788696 28.702506 4.903183 8.216902 9.856982 5.489315
## [223] 6.281355 2.478482 4.293983 7.915652 4.679377 2.589083
## [229] 3.738028 5.987303 12.074640 16.744445 8.157977 93.068344
## [235] 17.250771 6.033223 10.140548 16.766985 11.331940 18.446917
## [241] 19.098741 7.565455 42.367471 14.708255 10.331956 6.130575
## [247] 7.588929 3.851140 4.392872 12.481283 2.805244 18.392319
## [253] 8.107849 4.336507 2.642244 4.160580 15.564818 15.265412
## [259] 3.365912 2.430119 16.101511 3.279839 3.073312 6.834128
## [265] 24.696258 7.279753 2.894023 12.016937 10.784707 6.396763
## [271] 26.578861 101.613166 15.793615 21.951010 5.461827 100.950039
## [277] 15.178267 2.974696 21.966865 10.624844 10.968576 3.375902
## [283] 44.518259 4.068679 28.716579 2.972412 9.396390 11.824313
## [289] 6.276771 6.003061 3.716993 9.328046 6.860790 3.537261
## [295] 20.227203 4.060811 3.822050 4.412691 6.164433 7.492580
## [301] 8.526090 10.628859 6.054904 2.486057 6.300643 12.982649
## [307] 12.766567 7.078844 2.837648 18.885437 27.428569 2.381615
## [313] 8.898871 3.674193 7.199901 17.274476 5.065102 10.743531
## [319] 12.927478 7.375571 8.862893 5.702870 4.187031 2.858013
## [325] 8.347525 2.596389 5.892148 20.723682 8.581259 2.881094
## [331] 10.653039 9.807863 4.981769 3.586008 4.840588 8.671966
## [337] 36.247391 32.508356 7.532985 3.469687 3.658318 5.229477
## [343] 16.555839 5.977329 10.235148 14.975442 3.348740 12.207972
## [349] 4.099200 7.995234 2.648233 10.228137 2.013765 2.843106
## [355] 4.346453 16.902144 4.198883 11.970620 6.268321 13.120141
## [361] 3.087479 11.439460 4.833963 3.647428 16.618494 8.356904
## [367] 3.611917 5.073826 9.288330 29.769743 8.982841 137.830581
## [373] 2.445977 14.319357 67.260458 2.578426 4.853852 23.368176
## [379] 3.522582 20.315616 10.240645 48.242198 11.134384 11.166812
## [385] 5.126206 10.879193 17.279926 10.957978 10.403496 15.373601
## [391] 54.900893 13.184226 6.383813 3.226482 2.929673 31.138053
## [397] 4.471993 3.009695 9.461545 22.534866 5.013681 2.652832
## [403] 7.501453 4.736841 2.624333 7.120759 128.833117 5.242834
## [409] 3.584338 8.843477 2.750547 3.024672 21.382993 3.411173
## [415] 5.886979 19.821395 8.501053 24.278168 2.931734 2.916884
## [421] 6.080351 9.443646 24.588820 16.850739 3.934561 5.078900
## [427] 3.102368 2.760820 2.702321 20.136120 8.834647 31.972583
## [433] 3.585066 11.956863 21.291438 10.213209 7.244697 2.502439
## [439] 7.073163 10.063543 2.923456 24.285998 8.052316 13.402206
## [445] 7.152326 7.538765 3.579588 2.741550 15.813111 4.036395
## [451] 2.963085 8.270466 2.628131 2.494752 25.215450 15.832234
## [457] 3.195939 29.453755 2.869741 35.496180 3.003067 3.278558
## [463] 4.451483 5.285381 4.359409 19.300071 2.336728 11.161853
## [469] 2.675622 5.504569 13.990594 2.703001 7.139942 3.081105
## [475] 16.081975 9.291234 11.604074 6.188908 13.281000 3.489559
## [481] 11.292443 2.889573 2.724219 8.868698 52.635248 3.622291
## [487] 2.700413 9.946720 2.583527 2.584306 19.477710 7.140423
## [493] 6.869745 2.861949 17.897787 33.711510 11.835489 12.681948
## [499] 4.810080 5.199962 29.839146 3.028338 21.435088 16.457968
## [505] 5.113712 9.711365 2.890416 2.617971 17.275107 3.307182
## [511] 10.839167 2.495745 6.323737 50.501309 4.123672 13.674233
## [517] 7.147450 5.482423 2.764409 16.569768 12.284394 12.618473
## [523] 2.565594 7.850922 2.668774 17.629305 6.434116 4.768660
## [529] 2.655016 26.569667 5.643559 11.846878 15.314903 7.647109
## [535] 9.433491 11.973373 5.372952 6.517753 5.853898 2.704809
## [541] 19.108992 8.993788 8.806256 3.317487 3.412398 2.283125
## [547] 2.528015 12.006765 4.040180 5.686876 2.876344 4.856532
## [553] 2.716095 19.342103 6.550340 15.744531 3.677278 10.383316
## [559] 31.338238 18.047550 10.964791 11.679353 6.062516 38.494662
## [565] 7.123472 4.764402 119.965804 3.063413 4.588703 10.059038
## [571] 7.241478 7.087978 3.128070 13.406854 6.189833 2.867326
## [577] 14.655914 78.350960 4.096727 26.952634 12.594065 33.162661
## [583] 6.448290 4.810921 8.756197 14.340884 13.627685 3.920413
## [589] 7.223708 6.756119 3.890004 13.162662 2.689799 6.351084
## [595] 11.897581 6.762593 24.273798 18.684922 13.298520 15.918856
## [601] 2.721880 16.276151 17.497045 7.228650 21.740869 5.842393
## [607] 7.938323 3.308746 14.599198 7.792727 3.752776 7.456306
## [613] 12.715967 2.783957 9.470253 10.298794 34.973027 15.224515
## [619] 51.399814 9.225017 22.630860 18.201831 4.171581 6.285546
## [625] 17.041273 6.016508 2.819191 32.286198 37.955816 3.162580
## [631] 54.956114 27.732299 4.534433 3.850471 45.887623 2.702866
## [637] 2.663832 59.101247 4.222578 22.127429 60.183344 4.786163
## [643] 3.264333 6.209666 5.278316 13.961646 11.026833 2.918970
## [649] 8.145724 2.699370 8.693118 8.600029 23.478016 3.984601
## [655] 3.113105 2.995299 3.601287 2.875552 34.521984 8.134850
## [661] 41.292190 2.420669 3.613344 7.078239 9.563572 3.599209
## [667] 31.005531 3.601369 17.940446 18.414958 15.697550 6.393887
## [673] 16.150421 5.585073 31.052443 6.688605 3.652894 2.685807
## [679] 32.283574 2.602460 3.584194 7.351810 8.154469 15.811561
## [685] 33.459747 39.903534 6.533041 3.209729 3.165712 8.743821
## [691] 2.287955 3.189155 10.613060 11.202250 8.375773 2.741879
## [697] 24.798896 9.746341 52.456665 3.226919 4.767163 2.256757
## [703] 2.999515 5.750538 3.013114 12.971987 7.223987 7.758755
## [709] 5.941828 2.532142 12.155236 4.662848 4.131256 7.361863
## [715] 11.571135 3.458523 6.393047 5.353092 5.919901 6.637658
## [721] 3.911746 5.667813 18.449706 7.218989 10.450326 5.807962
## [727] 2.667715 13.196572 5.887473 4.946144 14.570991 22.978655
## [733] 5.431407 12.907562 12.554691 27.491330 3.087630 16.305966
## [739] 10.725934 3.116111 21.352491 5.998403 10.449915 2.608366
## [745] 21.133603 8.845888 18.975805 5.517943 6.778640 9.329697
## [751] 44.122006 24.405609 8.655454 37.118568 15.064801 9.996132
## [757] 3.198666 3.119587 18.567738 3.512271 4.553298 7.134229
## [763] 7.358468 2.742673 18.152892 5.049328 5.078871 14.593894
## [769] 15.617514 7.241845 9.277802 9.376841 3.780195 19.035683
## [775] 2.454783 12.906711 2.804329 3.528444 10.402664 11.280995
## [781] 19.251315 2.665576 13.798133 2.515184 3.238648 10.241621
## [787] 7.127832 43.441775 9.266556 9.386517 3.117795 19.307384
## [793] 7.801123 45.484419 18.817522 19.412318 5.304859 2.571989
## [799] 11.591335 22.766418 5.645733 102.013854 5.187941 3.638486
## [805] 3.349786 15.816448 4.230097 9.897622 4.360383 5.682051
## [811] 87.812302 5.551074 6.066962 18.981086 2.672643 4.149180
## [817] 8.859158 25.160784 6.842432 7.776736 2.874350 2.765364
## [823] 2.619883 10.172714 9.467242 14.781187 2.661926 21.617379
## [829] 24.318918 4.537431 8.739133 26.915244 17.488110 54.349530
## [835] 3.430257 3.525090 10.226722 9.401206 4.085451 9.615688
## [841] 2.767553 2.435247 2.799144 2.662320 8.935275 4.953197
## [847] 4.940130 4.540442 3.028764 2.938349 9.252868 29.713368
## [853] 8.738074 4.379691 5.035462 3.019835 10.954870 41.116880
## [859] 5.644253 30.496955 9.383328 2.606776 3.907681 2.788561
## [865] 5.098444 8.940711 11.310392 28.411167 2.798735 2.823655
## [871] 4.634783 8.552294 11.156576 16.128966 6.843910 8.651466
## [877] 3.807533 2.504728 29.389138 2.838105 2.671791 2.757454
## [883] 8.365744 6.604440 14.396193 3.046293 7.482015 2.651891
## [889] 9.591082 3.110458 9.570815 22.126530 4.295946 27.805129
## [895] 15.461192 6.584887 5.778947 11.802114 13.503071 15.360812
## [901] 5.519043 7.203707 38.549037 8.849065 4.324181 8.611224
## [907] 22.818325 85.751625 3.044878 14.317452 21.293056 2.740839
## [913] 22.916787 7.409847 29.333386 35.096737 2.826546 58.693568
## [919] 18.545295 22.570276 2.839192 5.328052 10.016785 4.316897
## [925] 2.626053 3.301406 12.319725 6.564707 14.199187 4.201745
## [931] 3.580509 8.654080 9.379166 10.317442 3.735779 21.026129
## [937] 18.749128 2.143953 2.482648 3.722893 11.982351 6.806646
## [943] 10.912646 7.192360 8.770202 16.230359 16.333616 18.212893
## [949] 2.675659 6.293888 3.101053 20.556908 8.208700 2.910039
## [955] 24.890863 8.498853 44.290488 2.828502 15.415374 19.519862
## [961] 4.613643 4.631055 6.946729 12.663410 4.139887 2.400905
## [967] 3.075237 7.386118 5.113298 39.191624 8.973611 11.910903
## [973] 6.609605 19.450642 5.409968 6.342415 34.699559 2.978523
## [979] 18.410342 30.953172 9.123764 2.930079 3.871116 4.550592
## [985] 5.915649 20.667384 36.998831 18.873625 63.213613 27.565976
## [991] 11.805220 15.131751 3.221948 12.393215 11.418206 2.994928
## [997] 9.370219 16.387265 9.686889 6.327425Sistema 3: serie R1-R2
sistema3 = pmin(R1, R2)
sistema3## [1] 2.5442107 2.8922977 2.6506534 0.7390826 2.8654280 2.7785018 1.6529695
## [8] 2.6086478 2.4414000 2.8580140 2.9395705 2.6539815 2.5919620 3.0651961
## [15] 2.6539362 1.5423923 2.7258693 2.1284255 2.2398100 2.8243583 2.7502670
## [22] 2.6218444 2.6709350 2.5705302 2.5867084 3.4937707 1.1717117 2.8541736
## [29] 4.0790288 2.0111444 0.3285004 2.5694482 2.5683833 1.4615974 0.7664422
## [36] 2.7242474 2.8136678 2.7501234 2.5929556 1.9940248 2.2802246 2.2728147
## [43] 1.8928725 2.6521149 2.6257827 2.3632392 2.8459437 2.7229196 2.6693170
## [50] 2.8837123 2.8706592 2.1966510 2.7125385 2.8591653 3.0526245 2.9260337
## [57] 2.9171450 2.9108390 2.6152931 2.8483451 2.1481132 2.6220424 2.8363654
## [64] 2.9695569 3.8136005 2.9356222 2.3914744 2.9727005 2.2678208 2.6407515
## [71] 2.8827723 2.6608478 2.6868422 2.9469198 3.2768140 2.5574584 2.8537089
## [78] 2.8622776 3.3051719 2.9858092 2.1040639 2.7953484 2.4772458 2.4185378
## [85] 2.1897140 2.6712994 2.6859363 2.1263906 2.5043958 2.4830675 2.8607926
## [92] 2.6562654 1.3080279 3.1050766 2.6847527 1.8202219 2.9148732 3.4599558
## [99] 2.3841602 2.2003989 2.9507896 2.3156038 3.2678947 2.5242955 2.4928452
## [106] 2.9252335 2.6818789 2.3953104 2.7946189 2.6859382 3.2197755 2.8365028
## [113] 3.0227665 2.6268820 0.8226103 3.1819544 1.9798145 1.7736949 2.5636561
## [120] 2.6889696 2.7139245 2.4313303 2.6775504 2.9673295 2.7240924 2.6988360
## [127] 2.7799562 2.2921642 2.4271732 2.5712917 2.7312876 3.3945121 1.4964537
## [134] 2.3911641 2.5424344 2.4792482 0.2662459 2.0976866 2.5912785 2.8450306
## [141] 2.6562488 3.0844672 2.9303876 3.2123794 2.3272112 2.8852166 3.1716238
## [148] 2.6102926 2.6216635 2.2426551 2.7325318 1.1339353 2.2927756 2.7653572
## [155] 0.5518697 2.1793376 2.7277837 2.4256570 2.2528410 2.8573462 2.9831561
## [162] 2.9218363 2.5518953 2.2898984 2.6279930 3.0652363 2.9741596 2.7894811
## [169] 2.7533458 2.7322029 2.3165678 2.8657073 2.8319665 2.3206863 2.0777409
## [176] 2.5364236 2.7941325 2.9921254 2.7768433 2.6876915 2.0269030 2.9237926
## [183] 2.5418696 2.9277116 1.5298326 2.6031956 2.8469575 2.5889840 0.8738335
## [190] 2.8893386 2.4921880 2.8234392 2.7375512 2.6375518 2.7835172 2.4669925
## [197] 2.5403603 2.8766439 2.6470171 2.9042142 2.8191658 2.4134117 2.6901656
## [204] 0.8509462 2.6198465 3.4639314 2.6991472 2.5893301 2.8772147 2.7885708
## [211] 2.6335869 2.4056321 2.9567427 2.8415333 2.7898936 2.7824414 2.8891001
## [218] 2.7406707 2.2956300 2.8851523 2.7822180 3.1135956 2.9026579 1.3914644
## [225] 3.1606666 2.5740260 3.1082267 2.4929873 2.4298085 2.8033249 2.3588979
## [232] 2.5116911 2.3386991 2.6460017 2.8189755 2.8923433 2.7783282 2.5867235
## [239] 2.6454000 2.6139306 2.6622909 2.4554288 2.8297936 2.2835010 2.6471142
## [246] 2.5983821 2.7275098 2.6760667 2.5361291 2.4887611 2.1247635 2.7509826
## [253] 3.0459834 2.7993584 1.3952791 2.5597836 2.7351590 3.2054028 2.5277721
## [260] 1.5953739 2.8830651 2.4199742 2.9954756 3.1609748 2.2690768 2.8303405
## [267] 2.7859088 2.7831474 2.7637999 2.8030033 2.5549012 2.7005726 2.6378920
## [274] 2.0991520 2.4243434 2.5636051 3.0122986 2.4262549 2.9270764 2.9673637
## [281] 2.5757726 2.0149220 2.8861920 2.5899955 2.5003739 2.7893441 2.9047108
## [288] 2.8678154 2.6156238 2.8177225 2.6090880 2.7867362 2.7201772 2.6400366
## [295] 2.3747825 2.3605945 2.7233596 2.7189265 3.2571310 2.8567090 2.1999578
## [302] 2.6643785 3.0191025 1.1617793 2.5627838 2.5498735 2.0878292 3.1215004
## [309] 1.5940372 2.7202643 2.5846015 0.7472830 2.5383672 2.7297736 3.1808921
## [316] 2.1546579 2.5457762 2.7112073 2.3540829 2.8930552 2.8038704 3.0725117
## [323] 2.8345647 1.1185942 3.0396650 1.1454186 3.0028428 2.7650500 2.5896645
## [330] 1.8975121 2.6245964 2.3451373 3.0399728 2.7491879 2.3807264 2.9568323
## [337] 3.0058671 2.6235575 3.2952385 2.7715394 2.6898556 2.6053553 3.2464799
## [344] 2.5171298 2.7833524 2.6222138 2.9895356 2.5474588 2.6865561 3.2283987
## [351] 2.5847212 2.2238722 0.9004401 2.0318120 2.5837183 2.2747594 3.0586421
## [358] 2.6697748 2.6516142 3.1309462 2.7559641 2.7728507 2.9791051 2.5878905
## [365] 2.6323441 2.5351197 2.3154801 2.6484912 2.8431957 3.1378234 2.5414208
## [372] 2.8673988 0.8243916 2.8215030 2.5647491 1.6451000 2.4903048 2.6276765
## [379] 2.8553372 2.4367283 2.5461827 2.6158131 2.9917104 3.1621696 2.5605452
## [386] 2.9087297 2.6862710 2.5755191 2.8173874 2.6983674 2.9774549 2.7255843
## [393] 2.8561927 2.5608287 2.0588764 3.0026409 2.7417680 2.8228391 2.7134582
## [400] 2.2364142 2.7740620 1.7898431 2.5670914 2.7396939 2.1271396 2.5515531
## [407] 2.7388954 2.2969153 2.5480886 2.3740482 1.6465843 2.6564407 2.9505414
## [414] 2.6241981 2.7415420 2.6659642 3.1474923 2.5552344 1.5264853 0.4479105
## [421] 2.9331349 2.8183343 2.6627112 2.8330671 2.4208771 2.8613755 2.2627689
## [428] 2.3899891 1.4940434 2.6408230 2.7705047 2.7977017 2.8492519 2.6113782
## [435] 2.9600459 2.9736420 2.6613925 0.2994017 2.6448017 2.9577066 1.5609126
## [442] 2.4692811 2.5343232 2.8286806 2.2052527 2.6985260 2.8097033 2.1083981
## [449] 2.3796403 2.5084991 2.5147478 2.8508629 0.6978683 1.5381828 3.1678138
## [456] 2.3878830 2.7620314 2.5499047 1.7757297 2.6043020 2.2731755 2.5914372
## [463] 2.4887892 2.9560013 2.6779741 3.2066883 1.7582273 2.7668285 2.5066954
## [470] 2.8263426 2.0877937 2.3852814 2.5857794 2.4233301 2.5616622 2.6463181
## [477] 2.8299294 2.6017029 2.2016758 3.0771417 2.8238053 2.4405007 0.6511119
## [484] 2.9978332 2.3631042 2.6532991 2.3810295 2.8579840 2.4556031 1.7801114
## [491] 2.8754365 2.5434785 2.7664331 1.2276138 2.2371962 2.6396451 2.6691520
## [498] 2.9127895 2.4911897 2.6180068 3.1522641 3.0213525 2.4064201 2.7780646
## [505] 2.9159224 2.6978610 2.3176644 2.1389210 2.8013834 2.6405732 3.1236654
## [512] 2.2973483 2.7188006 3.1169798 2.6113913 2.6096200 2.8487462 2.1705802
## [519] 2.3313880 2.9107429 2.5983596 2.6748199 2.3484630 2.8555789 1.7018745
## [526] 2.5468105 3.2355554 2.6172947 0.8428949 2.8055916 3.2202828 3.1268059
## [533] 2.9301274 2.5010440 2.6885094 2.7216927 2.3797249 2.4671309 2.3503069
## [540] 2.4889030 2.5872885 2.7360335 2.6192029 2.8253231 2.7049492 1.5248275
## [547] 1.9607694 2.3123568 2.6623484 2.7015786 2.3523790 2.2769741 1.3949968
## [554] 2.9449087 2.6890082 2.6046902 2.5053404 2.5646110 2.6416400 2.9187837
## [561] 2.8027643 3.4762740 2.6717686 2.8938336 2.7947816 2.5708252 2.9639090
## [568] 2.4920031 2.6278031 2.5082731 2.5571975 2.9369534 2.6655279 2.7368912
## [575] 2.5005959 0.7540082 2.5843457 2.8834126 2.6136082 2.5733889 2.3660322
## [582] 2.7212289 2.7541497 2.4444006 2.9428939 2.6874174 2.9694377 3.0101211
## [589] 2.2800312 2.5973455 2.1378840 2.2229610 0.9218067 2.9768663 2.4516675
## [596] 2.7894379 3.3172200 2.1554063 2.8494551 2.4622793 1.2897666 2.7572509
## [603] 2.8786826 2.8022193 2.6725676 3.1962032 2.3768894 0.8269830 2.5951722
## [610] 2.8813783 2.5610865 3.0561017 2.6462122 1.9023799 2.6681021 3.0105990
## [617] 2.7208096 2.7477562 2.4065158 2.5891402 2.7970537 3.4780140 2.4619202
## [624] 3.0179355 3.0036324 2.8449755 1.1685298 2.3210209 2.8117046 1.2077876
## [631] 2.6276254 2.6976592 2.9558848 2.8271514 2.0283307 2.5633111 0.7635777
## [638] 2.9739550 3.1450415 2.7207526 2.9431542 3.0980386 3.2124710 2.6662012
## [645] 2.3353719 2.9934622 2.2087053 2.2636535 3.0744328 1.9721584 3.0870771
## [652] 2.9121349 2.5823903 2.7695790 2.6532081 1.9368605 3.1244890 1.4368094
## [659] 2.3888408 2.1654934 2.6697197 0.7349075 2.9457305 2.7016783 2.9753361
## [666] 2.7021664 2.6321729 2.5214977 2.2069265 2.6988784 2.7189057 2.7255038
## [673] 2.6159356 3.1306383 2.3977020 2.5314104 2.7457843 1.8768669 2.8147229
## [680] 1.3287017 2.6748391 2.8691414 2.7619695 2.7782507 2.6932338 2.9842179
## [687] 2.5784061 2.6851271 2.4153975 3.0063406 2.1364302 3.0377878 2.7526461
## [694] 3.1237521 2.7347394 0.9312194 3.0155256 2.6718490 3.1039676 2.7297428
## [701] 3.0535096 1.5782556 2.1250436 2.7336911 1.1795045 2.6617851 2.8579776
## [708] 3.0848208 2.4772201 2.2881190 2.7580071 3.0128054 2.9318292 2.7384679
## [715] 2.3008752 2.9143236 2.2629553 2.7942883 2.5638483 2.6431107 2.6605181
## [722] 3.3857733 2.5721997 2.3593384 2.5488898 2.8837372 1.5948828 2.5098384
## [729] 2.5882158 2.5819885 2.5762024 2.7080617 3.1625014 2.7834096 2.4813397
## [736] 2.8138545 2.9954038 2.6526861 3.0255937 2.4906359 2.8331501 3.1267991
## [743] 2.2892709 2.5654328 2.6187603 3.0852707 2.9546764 3.1839490 2.5888190
## [750] 2.5957389 2.7754082 2.7540146 2.3952753 2.8798295 2.3868878 2.5284271
## [757] 2.6027355 2.7516683 2.5280274 3.0516071 2.2523573 2.2852751 2.7448797
## [764] 1.1891933 2.9759751 2.8770387 3.2470813 2.3429890 2.5114444 2.4966166
## [771] 3.0427506 2.3477973 2.6065345 2.6498555 1.4210015 2.9635995 1.6933058
## [778] 2.7494374 2.5683152 2.4554480 2.5300839 2.2902803 2.5968769 2.3009661
## [785] 2.8247414 2.8585043 2.4727359 2.7047848 2.5028993 2.3912312 3.0692922
## [792] 2.7360226 2.1257959 2.5481487 2.9126961 2.7265154 2.2586742 1.0508409
## [799] 3.1107599 2.7347806 2.9712718 2.1028422 2.7189163 2.6752537 2.9432639
## [806] 2.3514186 2.7969564 2.7665213 2.5573796 2.7434311 2.8895963 2.7648219
## [813] 2.6902035 2.6503729 1.9060432 2.5834700 2.9913651 2.3870389 2.4427244
## [820] 2.6565703 2.4583805 2.0715310 0.9322305 2.7818162 2.8647647 3.2912164
## [827] 2.3878966 3.2397650 2.9290201 2.7384860 2.9889286 2.6731914 2.6165199
## [834] 2.4672488 2.6840460 2.1352047 2.8465160 2.6781382 3.0289620 2.6386565
## [841] 1.0473572 1.2365831 2.6275695 1.9329025 2.8525425 2.8855582 2.6011948
## [848] 2.7852246 2.6388133 1.8064397 2.8715200 3.3560939 2.4029134 2.4999762
## [855] 2.7705406 1.4924028 2.5206811 2.9011749 2.5267927 2.6660427 2.5403145
## [862] 2.1317665 2.6658884 1.5629946 2.8437241 2.6696906 2.5526735 2.6148395
## [869] 1.0725078 2.2581231 2.4945626 2.7341463 2.8133983 2.8203839 2.3584277
## [876] 2.8003390 2.1982448 1.7619512 2.4138726 2.1783076 2.6360270 2.2810843
## [883] 2.8651066 2.3647663 3.5188823 2.3039604 2.7838573 2.5102367 3.0498112
## [890] 2.7026519 2.9661477 2.7312034 3.1193863 2.5752927 2.7575777 2.6460214
## [897] 2.3475779 2.6973558 2.6136935 2.7655795 2.5137145 2.6554911 2.4837282
## [904] 2.3943870 2.4813011 2.6797356 3.0162229 2.5680999 0.9748053 2.9473815
## [911] 2.2432282 2.7072756 2.3105557 2.7029607 2.6099940 3.1185319 2.8102494
## [918] 2.3756668 2.5144744 3.4051801 2.3533756 2.9762436 2.9922090 2.6393593
## [925] 1.6688154 2.7761475 2.2194424 3.0253411 2.5206876 2.8553751 2.8175596
## [932] 2.5420613 2.8548858 2.6736763 2.5940666 3.0635059 3.1922849 1.1953501
## [939] 0.8324442 3.0400903 2.6709645 2.6055636 2.7184968 2.5768416 2.8288800
## [946] 2.7421998 2.6493677 2.8648754 0.9571451 2.9255014 2.5715815 2.5257829
## [953] 2.9399979 2.9077040 2.6859109 3.0170872 2.4634954 2.5873823 2.9383817
## [960] 2.0996461 2.5206924 3.2603629 2.5394285 2.7477860 2.6439900 1.7407910
## [967] 1.2850810 2.5875304 3.0717761 3.0533197 2.9977710 2.2653132 2.6934431
## [974] 2.9979213 2.9170325 2.7312128 2.7684095 2.1991931 2.4802760 2.7985298
## [981] 2.4796483 1.9898357 2.4140847 2.7575020 2.9133189 2.8790914 2.7878062
## [988] 2.6643147 2.9413436 2.1722138 2.6590601 2.9584943 2.2492778 2.8209011
## [995] 2.8799726 2.4465868 2.4641345 2.5565973 2.5261531 2.9850302b. Estime la media del tiempo de vida para cada sistema.
mean(sistema1)## [1] 6.19694mean(sistema2)## [1] 12.25605mean(sistema3)## [1] 2.56589c. Estime la probabilidad de que los sistemas fallen en un tiempo inferior a dos meses.
mean(sistema1 < 2)## [1] 0mean(sistema2 < 2)## [1] 0mean(sistema3 < 2)## [1] 0.092d. Estime el 20o percentil (P20) de los tiempos de vida del primer sistema .
quantile(sistema1, probs=0.20)## 20%
## 2.829767e. Construya una gráfica de probabilidad normal de los tiempo de vida para cada sistema.
qqnorm(sistema1); qqline(sistema1)
qqnorm(sistema2); qqline(sistema2)
qqnorm(sistema3); qqline(sistema3)
f. Construya un histograma de los tiempos de vida de los sistemas.
hist(sistema1, main="Sistema 1", col="skyblue", breaks=30)
hist(sistema2, main="Sistema 2", col="salmon", breaks=30)
hist(sistema3, main="Sistema 3", col="lightgreen", breaks=30)
A partir de las gráficas es posible visualizar que en el caso del sistema 1 y del sistema 2 hay un sesgo a la derecha, mientras que en el sistema 3, hay un sesgo a la izquierda.
Problema 4
n = 1000
x = runif(n)
y = runif(n)
dist_centro = (x-0.5)^2+(y-0.5)^2
dentro_circulo = dist_centro<=0.25
estimacion_pi = 4 * mean(dentro_circulo)
sum(dentro_circulo)## [1] 783estimacion_pi## [1] 3.132plot(x, y, col = ifelse(dentro_circulo, "blue", "red"), asp = 1, pch = 16,
main = "Estimación de pi con 1000 puntos")
symbols(0.5, 0.5, circles = 0.5, inches = FALSE, add = TRUE)
Problema 6
solicitudes = rpois(10000, lambda = 30)
# Probabilidad de más de 40 solicitudes en un minuto
mean(solicitudes > 40)## [1] 0.0316# Proporción de sobrecarga (>35 solicitudes)
mean(solicitudes > 35)## [1] 0.1571# Histograma
hist(solicitudes, main = "Solicitudes por minuto (λ = 30)", col = "orange", breaks = 30)
Comentario: La distribución es aproximadamente simétrica pero ligeramente sesgada a la derecha. La demanda es algo dispersa alrededor del valor medio (30).
Mejoras sugeridas: Escalar horizontalmente con más servidores, balanceo de carga, priorización de peticiones críticas o uso de colas de procesamiento asincrónicas.
Problema 8
# Tiempos de vida para 4 componentes
c1 = rexp(5000, rate = 1/5000)
c2 = rexp(5000, rate = 1/4000)
c3 = rexp(5000, rate = 1/6000)
c4 = rexp(5000, rate = 1/5500)
# Vida útil de la turbina: mínimo de los 4 componentes
vida_turbina = pmin(c1, c2, c3, c4)
# Vida media
mean(vida_turbina)## [1] 1255.309# Probabilidad de falla antes de 4000 horas
mean(vida_turbina < 4000)## [1] 0.9564# Histograma
hist(vida_turbina, col = "cyan", main = "Vida útil de la turbina", breaks = 30)
Comentario: La distribución de los tiempos de vida es asimétrica y sesgada a la derecha, como es típico de las distribuciones exponenciales.
Estrategias de mantenimiento: - Reemplazo periódico de componentes críticos. - Monitoreo predictivo basado en sensores. - Redundancia o diseño tolerante a fallos.