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Problema 9 Genere en una hoja de cálculo 100 números con la función 𝑋𝑋 = −3𝑋𝑋(1 − 𝑋𝑋 ) donde r es un número pseudo aleatorio entre cero y uno obtenido a partir de la función ALEATORO de la hoja de cálculo. Suponga que estos valores son tempos de proceso de cierta pieza. Determina el promedio móvil de estos valores conforme se va realzando el procesamiento de las piezas y grafique ese promedio ¿El tiempo promedio de proceso es estable? ¿Y si ahora se generan 200 números? Desarrollo:
N°
VALORES
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
0,311085709 14,84298148 1,936501581 2,765417738 0,028636239 8,789833599 0,015640701 1,422998962 0,555376452 0,524489073 3,427692529 7,676305495 6,741451158 1,853006158 3,694032003 3,432398412 4,591880196 3,499067822 1,874223444 8,055932142 3,938016664 6,020804553 0,300787266 0,857451438 0,252101987 0,559711713 1,934214124 1,00264436 1,650779079 2,211924229
TIEMPO DE ERROR PROCESO PROMEDIO TIPICO 100 MÓVIL VALORES 4,3599 4,7266 #N/A #N/A 2,6990 #N/A #N/A 1,9537 #N/A #N/A 2,9035 #N/A #N/A 0,8072 #N/A #N/A 2,6954 #N/A #N/A 8,8523 #N/A #N/A 0,1243 #N/A #N/A 4,9197 #N/A #N/A 1,7620 3,4042 #N/A 1,9245 3,1444 #N/A 0,4243 2,8642 #N/A 2,4952 2,6367 #N/A 2,7474 2,6908 #N/A 0,5270 2,6752 #N/A 10,2156 2,6472 #N/A 1,7486 3,3992 #N/A 7,8314 2,6889 #N/A 1,5783 3,4596 2,84577122 1,5395 3,1254 2,84746968 1,2077 3,1032 2,85683625 4,3805 3,0315 2,89928256 7,3187 3,4271 2,82971336 0,4306 3,9095 3,02749197 0,4271 3,6778 3,19681458 0,9536 3,6678 3,2894214 2,5564 2,7416 2,54826976 3,8806 2,8224 2,53225934 0,3886 2,4273 2,17077166
N°
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
TIEMPO DE ERROR PROCESO PROMEDIO TIPICO 200 MÓVIL VALORES 1,5225 2,9666 #N/A #N/A 6,5411 #N/A #N/A 0,3631 #N/A #N/A 0,9482 #N/A #N/A 5,7316 #N/A #N/A 0,7224 #N/A #N/A 3,0733 #N/A #N/A 2,5882 #N/A #N/A 6,9379 #N/A #N/A 4,7836 3,1395 #N/A 6,8191 3,4656 #N/A 3,8082 3,8509 #N/A 1,3109 3,5776 #N/A 0,1319 3,6724 #N/A 2,6384 3,5907 #N/A 1,4535 3,2814 #N/A 6,2144 3,3545 #N/A 2,7414 3,6686 #N/A 4,7251 3,6839 2,32304743 4,1830 3,4627 2,0280882 1,2877 3,4026 2,00008071 0,9855 2,8495 1,8339001 2,3955 2,5672 1,89948379 0,1069 2,6756 1,74877805 0,6882 2,6731 1,58758576 0,6657 2,4781 1,67315855 1,3342 2,3993 1,65488536 1,3530 1,9113 1,45734159 2,3558 1,7725 1,43269132
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
1,923372457 2,3211 0,555015463 5,6854 2,791929714 1,2185 2,888575103 6,5812 6,974492106 0,2384 1,206362121 4,1243 1,218045778 2,4284 7,595994772 1,3332 1,397078801 0,1561 0,55718205 10,5498 1,104941527 1,0131 2,976277336 1,3899 0,323089726 0,2961 0,392034971 7,1384 0,631792746 0,1416 0,045950112 2,1163 0,407459169 7,8355 3,285355198 3,5970 2,343968614 6,9592 0,724686411 1,1263 0,318415788 3,5126 4,683372156 3,5476 3,069957914 3,3506 2,086048812 4,7792 0,867850061 0,0298 5,294768446 2,8387 3,414555191 0,8932 1,575280787 6,1438 0,426419301 1,6357 5,220348708 0,9249 9,906772301 3,4732 2,051373257 2,1242 0,310420225 0,2698 3,087538542 1,4952 0,482267337 4,9399 0,333800437 15,2984 2,639153255 4,5410 1,867507023 0,7643 0,067657213 1,4399 12,44323602 2,7220 1,585441677 7,6187 4,598819824 7,9016 7,170972022 4,2183 4,085390669 3,7912 2,630488989 0,5381
2,3083 2,3865 2,8343 2,5181 2,4443 2,4251 2,7948 2,9423 2,8200 2,4475 3,4636 3,3328 2,9033 2,8111 2,8668 2,8571 2,6563 3,1970 3,4234 4,1037 3,1613 3,4113 3,6271 3,9325 3,6966 3,6854 3,7577 3,0634 3,3181 2,7858 2,7656 2,7617 2,6193 2,3113 1,9829 2,4739 3,7198 4,0846 3,5467 3,5271 3,7068 4,1213 4,6991 5,0939 5,3235
2,20032316 2,14413977 2,25335265 2,2705935 2,38845448 2,26460369 2,06275964 1,99040132 2,04344346 2,118848 3,02363842 3,11128024 3,01599278 3,09189373 3,1101602 3,15156233 3,12806001 3,45107234 3,41933861 3,46153149 2,7156865 2,61493338 2,57089006 2,45170396 2,07446228 2,21411488 2,22656407 1,81025473 2,01803843 1,84101794 1,82044737 1,83401874 1,84051966 1,94175685 1,91754765 1,71720638 4,03369484 3,97750404 3,9744462 4,01242893 3,98217689 4,12677614 4,24633767 4,20610252 4,23111458
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
1,7181 0,5231 0,6359 2,4835 1,2739 0,5338 4,1709 2,9909 5,8138 1,0064 6,4367 6,2144 2,3822 0,9033 4,2939 5,4605 11,5897 1,0700 3,0483 11,3168 5,3159 2,4290 5,2461 4,4221 5,2118 1,3766 4,1830 8,2466 8,5941 2,8713 5,4054 2,1339 2,1217 1,1526 0,3631 0,9318 7,1907 0,0211 2,6457 3,9841 6,4625 4,8737 0,3699 6,3859 0,3429
1,5355 1,2891 1,2126 1,1776 1,1864 1,3031 1,2877 1,6382 1,8039 2,2500 2,1150 2,5869 3,1560 3,3307 3,1726 3,4746 3,9673 4,7092 4,5171 4,2406 5,2716 5,1595 4,7810 5,0674 5,4192 5,5110 5,1026 4,3620 5,0796 5,6342 4,7897 4,7986 4,7691 4,4567 4,1297 3,6448 3,6004 3,9011 3,0786 2,4837 2,5950 2,7007 2,9747 2,7995 3,3228
1,40017992 1,38492239 1,3121206 1,22508893 1,28888641 1,00136906 0,85976971 1,03927967 1,08981164 1,56211433 1,57981741 1,98986245 2,20167761 2,21539799 2,29232248 2,30689659 2,34262506 3,09525102 3,26004848 3,08219776 3,609914 3,39879197 3,3420896 3,32908452 3,26607476 3,25715863 3,43139381 2,65396365 2,61883055 2,75540228 2,07504199 2,08330909 2,11693998 2,24130062 2,41046359 2,6226621 2,49040753 2,69834017 2,68568276 2,5178179 2,48281332 2,74638581 2,68492639 2,69331446 2,70293194 2
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101
3,176156175 0,2928 1,096282263 0,3523 7,264105887 2,0277 3,655229556 8,4653 2,420291722 2,6406 2,443911234 1,4987 3,537840575 7,4237 0,632903926 3,9966 0,374649546 3,2863 6,869006603 0,3061 13,75610268 3,2577 3,543699952 0,0280 2,601787502 4,1963 0,148201051 15,5019 3,26212697 0,7631 0,762355067 3,5970 0,358040273 4,0725 1,236562962 3,3653 1,894463401 1,0098 0,51913416 3,0392 1,049523613 2,3710 2,967390834 12,1711 10,67355358 3,4418 0,486850989 3,0725 4,132598566 17,7435 3,515485053 2,962554723 1,774480581 12,91519678 5,32647749 2,234584849 5,333569692 1,985526992 3,677632919 1,041022616 7,554769888 2,157857515 0,95030296 10,96053693 3,028509341 3,846884313 3,190025024 3,152896906 0,40025134 0,855056865
4,8833 3,3828 2,9639 3,0903 3,7928 3,7847 3,1727 3,1249 3,1027 3,0522 3,0290 3,3255 3,2931 3,5099 4,2136 4,0258 4,2357 3,9005 3,8374 3,6098 3,8831 3,7944 5,0087 4,9333 3,6903 5,3884
4,37976388 2,59437293 2,71882257 2,59436849 2,91176677 2,91758341 2,7512445 2,89684436 2,89740015 2,85755031 2,64931945 2,46263507 2,53940074 2,5264133 4,11607351 4,22796565 4,19955512 3,97381923 3,9665636 4,05020329 3,96660249 3,99200431 4,47214543 4,49170477 2,73331919 4,65526063
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
5,3693 2,5459 1,8264 0,3869 1,3530 3,3626 3,2898 2,3822 2,1278 6,9991 5,8770 1,3342 0,5266 2,3101 0,9565 1,6445 1,2877 5,2983 0,6359 0,0302 1,2739 1,8990 2,5180 1,1526 1,4293 1,2557 9,1728 2,3624 6,9379 0,9277 3,5722 1,5325 1,4487 7,8519 0,4075 0,7997 0,5917 0,4665 2,0024 4,3702 1,5475 0,1476 0,2371 0,2145 1,0444
3,3208 3,7646 3,3001 3,4806 3,2547 2,9916 2,6816 2,5233 2,7245 2,2987 2,9643 3,0151 2,8939 2,7639 2,9562 2,9166 2,7448 2,5446 2,8362 2,6870 1,9901 1,5298 1,5863 1,7854 1,6697 1,7169 1,6780 2,4666 2,1730 2,8032 2,8929 3,1227 3,0861 2,9792 3,6491 3,5469 3,5013 2,6432 2,4536 1,9601 2,3043 2,1018 1,9634 1,8422 1,0785
2,66752381 2,58090831 2,37399527 2,23039318 2,40717168 2,42281859 2,1216319 2,0492637 1,90286485 1,63877459 1,85114772 1,99706944 2,04320383 2,09799737 1,90286659 1,93302363 1,9522468 1,97749032 2,12248445 2,21872307 1,91804262 1,69303888 1,62261654 1,47851425 1,47342765 1,33979876 1,30071037 2,45586777 2,32995433 2,59183012 2,59222713 2,5948593 2,63910786 2,67310079 2,98078442 3,14044895 3,25183702 2,54909973 2,62472925 2,27591215 2,28480827 2,28711131 2,3063415 2,31140467 1,91073075 3
1,180016785 6,925809496 6,533148333 1,101474822 0,905748697 3,962643668 2,180732432 4,700572395 3,753193236 1,796785516 1,393257753 3,626956038 0,396482711 5,860012995 2,500678003 0,610390442 0,048388146 4,228074902 4,002244469 0,369215993 11,39608296 1,342613654 0,533076865 3,080829006 15,83554422 0,08427264 0,793068741 1,544500935 2,159089547 3,24969356 1,461815612 2,249787584 0,455959071 4,69339364 2,624726682 1,165381528 3,753193236 4,31402639 1,035509857 5,3406787 1,756108765 0,602312101 2,642046913 7,731065816 12,95997373
121 2,4698 122 5,6914 123 2,5459 124 1,0657 125 1,7448 126 7,8933 127 3,8730 128 0,3061 129 7,2574 130 4,6253 131 1,1132 132 11,7361 133 9,5103 134 2,1157 135 1,8541 136 0,5735 137 1,4927 138 5,1278 139 1,2923 140 0,7415 141 1,9618 142 9,4397 143 0,2081 144 3,8839 145 2,6240 146 0,1287 147 1,3483 148 11,8899 149 1,4196 150 2,5319 151 3,0401 152 0,3228 153 2,5459 154 1,5325 155 4,2939 156 20,7233 157 4,2441 158 0,2306 159 1,3861 160 0,9524 161 1,4780 162 1,8990 163 1,9217 164 0,2048 165 0,3564
1,1422 1,3092 1,8191 2,0271 1,9334 1,6709 2,3054 2,6780 2,6849 3,3892 3,7473 3,6116 4,2161 4,9125 5,0175 5,0284 4,2965 4,0584 4,5406 3,9441 3,5557 3,6406 3,4109 2,4807 2,6575 2,7345 2,6901 2,6756 3,3518 3,3645 3,5436 3,6514 2,7397 2,9735 2,7384 2,9054 4,9648 5,2544 4,0885 4,0851 3,9272 3,7709 3,9286 3,8661 3,7334
1,63285899 1,43911874 1,77471376 1,66782638 1,69019201 1,5590148 2,3499306 2,3098185 2,37560445 2,65803309 2,67231861 2,76238885 3,43313406 3,72470408 3,8262521 3,95566477 3,72973992 3,79821555 3,72760757 3,61966118 3,71709626 3,67075402 3,38436965 3,13951114 3,02735093 2,85629999 2,72551628 2,63559265 3,76853239 3,72517527 3,63143491 3,5976185 3,14523035 3,06500537 3,06419367 3,0952966 5,81013985 5,80375837 5,28033333 5,31338957 5,38652926 5,43167494 5,41579565 5,44891341 5,54890096 4
1,47061901 2,914617618 5,963323059 2,524941567 6,630017735 4,056258569 1,875344311 0,276016937 3,998829557 6,833677441 8,536768845 2,281709571 2,87681192 6,047710563 0,394429088 1,040173839 1,111017918 3,700204845 1,700601044 0,445500025 0,829237441 3,955907138 0,146625503 1,175574314 0,864646644 1,06274795 0,174158794 2,562766023 0,93019207 7,786844315 1,357198486 0,408834055 0,096949804 11,47753593
166 10,7267 167 1,6969 168 0,7377 169 2,2587 170 0,4665 171 3,3903 172 2,3955 173 2,7265 174 2,7265 175 0,9648 176 0,0945 177 0,6100 178 2,3166 179 1,0872 180 2,4089 181 0,3462 182 5,3159 183 1,4148 184 1,1394 185 0,0976 186 0,3028 187 1,3909 188 0,5990 189 0,4665 190 1,4682 191 1,3577 192 8,3906 193 0,2862 194 3,3903 195 1,4780 196 1,6084 197 3,1581 198 1,3109 199 4,4352 200 2,0573 201
3,3396 2,3400 2,0852 2,1360 2,2232 2,1746 2,3659 2,4155 2,4960 2,7481 2,8090 1,7458 1,6371 1,7950 1,6778 1,8721 1,5677 1,8597 1,7285 1,5698 1,4831 1,5039 1,5820 1,4103 1,3482 1,2541 1,3553 1,6627 1,5499 1,7750 1,9130 2,0436 2,2203 2,2915 2,6884 2,7473
5,61137201 3,6997626 3,68798757 3,5083456 3,40296259 3,31466444 3,25056617 3,18658097 3,12754057 2,92172823 2,82606157 1,10709124 1,1471945 1,07133151 1,08743134 0,95892717 0,98172235 1,46909999 1,47064098 1,4769106 1,42587308 1,38011338 1,34271415 1,35701415 1,37271674 1,36386055 1,30802446 2,24563672 2,27875481 2,33133609 2,29392303 2,26643777 2,28495621 2,29158728 2,34067998 2,34985189
5
Solución 9 Cuando se tiene 100 tiempos de proceso, podemos observar en la gráfica de promedios o medias móviles son relativamente estables, mediante la observación, lo mismo sucede cuando se tiene 200 tiempos de proceso, sin embargo, se observa que sí es menos inestable que los 100 promedios iniciales Gráficas tomadas con un intervalo de 10, cabe resaltar que las gráficas son hechos con un intervalo de 10.
Problema 10 Genere en una hoja de cálculo 100 números con la función 𝑋𝑋 = 5 + 10 𝑋𝑋 donde r es un número pseudo aleatorio entre cero y uno obtenido a partir de la función ALEATORO de la hoja de cálculo. Suponga que estos valores son tempos de proceso de cierta pieza. Determina el promedio móvil de estos valores conforme se va realzando la atención de los clientes y grafique ese promedio ¿El tiempo promedio de proceso es estable? ¿Y si ahora se generan 200 números? Desarrollo:
N°
VALORES
1
12,445
TIEMPO DE ATC PROMED 100 IO VALORES MÓVIL 7,7250
ERROR TIPICO
N° 1
TIEMPO DE ATC 200 VALORES 12,8310
PROMEDIO MÓVIL
ERROR TIPICO
6
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
11,579 12,806 13,66 5,55 8,07 9,631 14,444 5,837 6,436 8,45 8,868 5,663 11,352 10,414 14,34 7,567 9,049 11,268 10,23 8,599 5,705 14,865 10,091 9,712 6,99 8,26 7,464 11,664 5,531 10,653 7,937 5,792 14,608 6,538 7,029 5,998 12,531 5,62 10,082 11,689 10,628 11,849 14,616 7,019 14,073
14,1680 6,7160 12,4630 7,5030 5,5030 14,0760 10,6340 8,9490 7,1660 8,3640 12,5110 11,3060 11,7060 10,1810 11,9220 5,6170 10,6580 12,4110 13,5830 6,2490 6,5280 8,2490 8,5690 12,2850 14,7040 11,1080 13,0180 9,2640 14,5870 6,7800 9,8430 14,6070 14,3840 6,1210 11,6840 11,0070 9,4480 8,3670 14,5090 11,8590 8,7080 5,5360 11,1540 10,3120 11,6090
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A 9,4903 9,5542 9,3885 9,8475 9,7718 10,0396 10,6815 9,8356 9,838 10,1842 10,8259 10,6144 10,0161 9,7104 9,3967 9,6071 9,8853 10,4344 10,6704 10,3557 10,4561 10,5092 10,8407 11,4765 12,058 11,4416 11,1396 11,1295 10,7725 10,6828 10,675 11,1829 11,0694 10,1623 9,8393 10,2584
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A 2,17769977 2,22762189 2,59351372 2,63969637 2,63985676 2,58132514 2,71631275 3,08973427 2,79502647 2,88028741 2,81413799 2,97752348 2,88975217 2,68952114 2,8284197 2,91075194 3,25365033 2,87991157 2,87228438 2,80612277 2,87948556 2,838126 2,59036234 2,67732283 2,88588282 2,82137124 2,26484978
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
14,0750 13,3490 11,2430 9,8620 14,8670 11,9980 13,0090 13,6160 11,7780 8,4020 10,9100 8,5330 5,9060 5,9480 13,1360 11,6870 12,9980 10,1580 13,5260 6,5490 6,5660 12,8040 14,4160 7,8530 11,3440 14,5310 6,2910 11,0270 11,5750 14,3010 13,8190 14,5770 11,2870 10,9290 11,1360 6,0320 12,4600 12,1570 14,1170 13,2260 5,1530 14,0620 6,0020 10,3440 14,5890
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A 12,6628 12,2199 11,9034 11,4218 10,8881 10,4967 10,3236 10,2925 10,2914 9,9456 10,1204 9,9351 9,5007 9,9278 10,7788 10,9693 10,7901 11,0745 10,4038 10,4907 10,2956 11,0708 11,7961 11,9734 11,6605 11,9681 11,9473 11,0974 11,7143 11,8273 12,0815 11,974 11,1074 11,0559 10,5274 10,4689
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A 2,95682691 3,13438182 3,08436066 3,20559554 3,20446233 3,01817316 2,83044777 2,69279701 2,87253058 3,03486012 3,0388528 2,87027902 2,85225412 2,77188015 2,7448024 2,49498859 2,3155579 2,32313336 2,60154514 2,26542084 2,26146856 2,31622098 2,11617835 2,75943587 2,80004942 3,1423321 3,12535408 7
47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
11,067 6,9 13,786 8,529 12,627 12,094 11,004 13,346 14,825 11,953 14,239 9,872 8,302 7,77 8,616 14,254 11,029 14,618 13,934 12,003 9,411 12,731 12,214 12,652 9,808 10,481 6,065 11,324 12,92 5,913 11,709 13,531 6,658 10,105 11,221 13,277 14,08 7,729 10,04 14,047 10,612 10,34 10,656 11,505 6,186
7,0380 14,4340 7,5190 14,8430 7,0060 9,7780 8,9250 11,1880 12,7270 10,7460 12,6690 9,0020 7,4530 10,7500 14,1540 11,8490 14,4400 14,3930 8,2530 14,1760 5,4540 13,4740 7,7720 5,9450 11,9220 10,4800 14,0070 5,3870 10,7110 11,1320 12,9730 9,8430 11,1520 6,0800 14,1250 6,5910 11,9000 10,6840 13,1550 12,4460 13,3100 14,4250 11,4500 9,7960 12,7600
10,2509 9,854 10,3526 10,2678 10,3012 9,8159 9,9229 10,2618 10,2652 10,5067 10,4204 10,9835 10,4403 10,4337 10,0244 10,7392 10,9463 11,4978 11,8183 11,3709 11,7139 10,9924 11,4396 11,4715 10,991 10,7678 10,6309 10,5876 9,687 9,9328 9,6284 10,3803 10,0172 10,3552 10,3687 10,589 10,2001 9,9894 10,5191 10,7635 10,8949 10,9286 11,3868 11,4166 11,7882
2,29877162 2,46492108 2,75067056 2,79024832 2,89453361 3,02029262 2,92688334 2,57003587 2,55291926 2,64765607 2,61462055 2,51542164 2,20645284 2,23635893 1,7294959 1,8351262 1,85663009 2,03323042 2,17066303 2,27836231 2,40552009 2,92742606 2,96257168 3,04253246 3,42790983 3,2737895 3,26166952 3,30787902 3,48255015 3,34911706 3,29187982 2,90539061 2,83380501 2,59332023 2,45324132 2,67123657 2,90444281 2,76253464 2,40526856 2,50931953 2,51220906 2,49120285 2,66947991 2,65758264 2,37072496
47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
10,6290 6,4450 6,5960 12,5850 7,0300 5,8450 10,7500 10,8920 13,8620 8,7080 7,0260 5,4850 7,7860 12,7490 13,6250 13,2010 6,2550 14,4790 14,1230 11,0290 11,5250 5,2740 8,7480 6,6300 14,9530 7,0970 6,3300 6,4070 13,0130 13,5550 15,0000 5,9010 10,4330 6,2220 10,0520 9,4080 5,4460 12,9240 10,0510 7,6440 8,2770 9,2990 13,7280 5,5130 11,9130
10,8142 11,2739 10,6724 10,1163 9,9631 9,3435 9,4127 9,0815 9,5705 9,9223 9,3342 8,9739 8,8779 8,9969 9,0133 9,6728 10,4084 9,9589 10,3176 10,3437 10,5758 11,0257 11,0046 11,1008 10,4889 10,6217 10,0113 10,0188 9,2116 9,1006 9,3532 9,7007 9,7634 9,9319 9,8911 9,401 9,6321 9,5437 10,1954 9,8992 9,3081 8,6358 8,9756 9,3051 9,2342
3,33570515 2,93303439 3,21468116 3,40037586 3,44030027 3,49487392 3,15301509 3,05224993 2,72817546 2,9989173 2,75822517 2,81880257 2,70365196 2,49341344 2,63158129 2,81992559 2,73111579 2,92446436 3,17955666 3,16002655 3,1570705 3,10041816 3,42715529 3,48601954 3,49941391 3,54399848 3,55378365 3,55221272 3,41658724 3,43153681 3,67701213 4,03778976 3,80940703 3,73940172 3,72024781 3,46505526 3,34100517 3,38831899 3,38210781 3,14805816 2,90201322 2,37198154 2,03591302 2,46496169 2,47275951 8
92 93 94 95 96 97 98 99 10 0 10 1
10,719 8,053 14,295 11,811 8,705 11,968 6,446 5,957
8,4480 13,7510 9,7070 10,1980 9,2520 11,6090 11,8770 11,0910
11,6517 11,8374 12,0225 11,9248 11,6291 11,3097 11,1396 10,8848
2,11963207 2,08304658 2,06707887 2,18219145 2,09638666 2,13954641 2,00812995 1,79107958
92 93 94 95 96 97 98 99
13,4280 12,7800 13,0460 8,6970 11,0280 7,3850 13,1910 11,6520
9,4203 9,8223 10,5557 10,5679 10,4325 10,7709 10,6817 11,0709
2,5871828 2,82641115 2,60849315 2,58337157 2,64058713 2,58889697 2,78860841 2,86624502
9,25
6,8810
10,8489
1,79268395
100
6,3130
10,8633
2,51423166
10,5574
2,04167121
101
6,0360
10,9433
2,66093888
102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134
9,8710 8,0140 13,7480 14,2760 10,5570 7,1530 11,8530 5,9350 5,2620 7,6990 11,2610 12,3040 6,5700 7,9490 14,8240 13,9000 8,2350 12,6300 12,6290 12,8500 6,8230 11,7530 5,4070 6,1400 5,9330 7,1100 11,6870 5,8830 11,0140 10,3300 13,6890 14,7040 10,4370
10,3556 9,9999 9,5233 9,5935 10,1514 10,1043 10,0811 9,9473 9,3756 9,2705 9,4368 9,5758 10,0048 9,287 8,6543 9,081 9,7557 9,3939 10,0634 10,8001 11,3152 10,8714 10,8163 10,7 10,5191 9,63 8,951 9,2962 8,6215 8,46 8,208 8,8946 9,1897
2,88533097 2,65079027 2,59994936 2,80564177 3,04494043 3,04721938 3,00933544 2,99496021 3,17668927 3,09098595 2,82671091 2,87621678 2,92804651 2,75421101 2,43601941 3,03511149 3,17364885 3,13738469 3,05256505 2,83651788 2,82478316 3,05521919 2,98219263 3,31011313 3,58116682 3,30050478 3,08459683 3,15468305 3,16910395 3,21885444 3,25203801 3,35192841 3,76675376
6,044 5,384 6,837 10,506 11,771 12,234 14,376 13,406 7,455 8,408 14,874 8,819 6,77 14,451 5,618 8,881 6,003 6,327 7,793 14,537 6,974 12,44 8,551 14,245 5,394 12,896 7,075 6,484 10,189 9,136 8,629 13,095 11,689 8,715
9
12,428 7,029 13,559 6,78 7,512 13,546 13 7,066 11,385 13,038 14,057 12,859 12,771 11,653 12,627 13,176 13,926 5 6,436 12,561 8,756 8,544 14,903 10,797 14,958 7,371 14,609 5,13 7,455 8,315 8,41 11,912 5,717 10,886 7,557 10,004 10,726 10,665 11,641 12,237 12,228 12,537 9,196 9,606 6,369
135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179
10,1880 14,9580 6,1880 12,3210 14,0440 7,5190 12,3740 10,3280 14,5260 11,2020 11,1220 10,9000 13,9550 8,5350 9,6650 6,1110 7,8920 12,3130 13,0500 10,4000 13,6410 11,1670 10,1810 11,0260 14,3980 11,4340 12,8920 10,4840 14,4510 7,8670 12,7260 6,4500 5,6300 10,3760 11,4350 7,6930 13,4270 12,6210 9,9210 13,0350 11,5740 12,2120 12,8780 7,3090 7,0350
9,6927 10,0975 11 10,9078 10,9712 11,7873 11,4378 11,6422 11,3061 11,2883 11,3648 11,4582 11,0524 11,8291 11,4505 11,0126 10,8718 10,4236 10,6221 10,4745 10,3943 10,6462 10,6729 10,2955 10,5446 11,0179 11,5502 12,0502 11,8673 12,0074 11,7541 11,6626 11,1909 10,7358 10,6708 10,3745 10,0004 10,0539 10,2676 9,8146 10,3314 10,2162 10,7924 11,5172 11,2105
3,38263909 3,08632703 3,1185269 3,40792212 3,35030397 3,3141919 3,44489125 3,38681863 3,04427023 2,6972395 2,68744359 2,68939344 2,38087867 1,97303754 2,13557841 2,05743244 2,22797005 2,3560979 2,39613097 2,31440997 2,31383802 2,49788431 2,50230233 2,41057729 2,23249713 2,4382265 1,9182745 1,76344547 1,73642666 1,71725817 2,11185393 1,91732268 2,42885283 2,91632207 2,91383776 2,73137491 2,82691849 3,00971523 3,06934571 2,97067283 2,83635113 2,84888888 2,46375343 1,91006264 2,27196364 10
8,1 7,72 14,562 11,009 8,718 10,141 13,459 8,037 13,225 11,112 9,781 13,612 5,173 11,861 5,916 11,097 5,708 8,349 10,227 6,783 5,785
180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201
6,0310 7,0350 6,5370 12,1830 14,4870 5,2280 5,4270 13,2330 9,9510 8,6970 12,9130 5,4480 7,1910 7,4550 14,9520 6,1530 8,3430 5,2570 7,3660 13,9920 8,4500
10,7705 10,6043 9,9651 9,3567 9,5829 9,7281 9,0935 8,415 8,4505 8,7147 8,8809 9,5691 9,4104 9,4758 9,003 9,0495 9,142 9,4336 8,636 8,3775 8,907 8,4607
2,53865098 2,82910703 2,77931913 2,82238135 2,93951636 3,18975297 3,38885983 3,48936369 3,77858597 3,59282416 3,39357796 3,24700336 3,35477921 3,31383522 3,24731924 3,42991545 3,34118587 3,22329792 3,0404248 3,03210363 3,43161667 3,26463439
11
Solución 10 Cuando se tiene 100 tiempos de atención al cliente, podemos observar en la gráfica de promedios o medias móviles que estas si son estables, mediante la observación, caso contrario sucede cuando se tiene 200 tiempos de atención al cliente, los promedios en esta gráfica tienen menor estabilidad, cabe resaltar que las gráficas son elaboradas con un intervalo de 10.
12
N°
VALORES
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
0,311085709 14,84298148 1,936501581 2,765417738 0,028636239 8,789833599 0,015640701 1,422998962 0,555376452 0,524489073 3,427692529 7,676305495 6,741451158 1,853006158 3,694032003 3,432398412 4,591880196 3,499067822 1,874223444 8,055932142 3,938016664 6,020804553 0,300787266 0,857451438 0,252101987 0,559711713 1,934214124 1,00264436 1,650779079 2,211924229
TIEMPO DE ERROR PROCESO PROMEDIO TIPICO 100 MÓVIL VALORES 4,3599 4,7266 #N/A #N/A 2,6990 #N/A #N/A 1,9537 #N/A #N/A 2,9035 #N/A #N/A 0,8072 #N/A #N/A 2,6954 #N/A #N/A 8,8523 #N/A #N/A 0,1243 #N/A #N/A 4,9197 #N/A #N/A 1,7620 3,4042 #N/A 1,9245 3,1444 #N/A 0,4243 2,8642 #N/A 2,4952 2,6367 #N/A 2,7474 2,6908 #N/A 0,5270 2,6752 #N/A 10,2156 2,6472 #N/A 1,7486 3,3992 #N/A 7,8314 2,6889 #N/A 1,5783 3,4596 2,84577122 1,5395 3,1254 2,84746968 1,2077 3,1032 2,85683625 4,3805 3,0315 2,89928256 7,3187 3,4271 2,82971336 0,4306 3,9095 3,02749197 0,4271 3,6778 3,19681458 0,9536 3,6678 3,2894214 2,5564 2,7416 2,54826976 3,8806 2,8224 2,53225934 0,3886 2,4273 2,17077166
N°
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
TIEMPO DE ERROR PROCESO PROMEDIO TIPICO 200 MÓVIL VALORES 1,5225 2,9666 #N/A #N/A 6,5411 #N/A #N/A 0,3631 #N/A #N/A 0,9482 #N/A #N/A 5,7316 #N/A #N/A 0,7224 #N/A #N/A 3,0733 #N/A #N/A 2,5882 #N/A #N/A 6,9379 #N/A #N/A 4,7836 3,1395 #N/A 6,8191 3,4656 #N/A 3,8082 3,8509 #N/A 1,3109 3,5776 #N/A 0,1319 3,6724 #N/A 2,6384 3,5907 #N/A 1,4535 3,2814 #N/A 6,2144 3,3545 #N/A 2,7414 3,6686 #N/A 4,7251 3,6839 2,32304743 4,1830 3,4627 2,0280882 1,2877 3,4026 2,00008071 0,9855 2,8495 1,8339001 2,3955 2,5672 1,89948379 0,1069 2,6756 1,74877805 0,6882 2,6731 1,58758576 0,6657 2,4781 1,67315855 1,3342 2,3993 1,65488536 1,3530 1,9113 1,45734159 2,3558 1,7725 1,43269132
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
1,923372457 2,3211 0,555015463 5,6854 2,791929714 1,2185 2,888575103 6,5812 6,974492106 0,2384 1,206362121 4,1243 1,218045778 2,4284 7,595994772 1,3332 1,397078801 0,1561 0,55718205 10,5498 1,104941527 1,0131 2,976277336 1,3899 0,323089726 0,2961 0,392034971 7,1384 0,631792746 0,1416 0,045950112 2,1163 0,407459169 7,8355 3,285355198 3,5970 2,343968614 6,9592 0,724686411 1,1263 0,318415788 3,5126 4,683372156 3,5476 3,069957914 3,3506 2,086048812 4,7792 0,867850061 0,0298 5,294768446 2,8387 3,414555191 0,8932 1,575280787 6,1438 0,426419301 1,6357 5,220348708 0,9249 9,906772301 3,4732 2,051373257 2,1242 0,310420225 0,2698 3,087538542 1,4952 0,482267337 4,9399 0,333800437 15,2984 2,639153255 4,5410 1,867507023 0,7643 0,067657213 1,4399 12,44323602 2,7220 1,585441677 7,6187 4,598819824 7,9016 7,170972022 4,2183 4,085390669 3,7912 2,630488989 0,5381
2,3083 2,3865 2,8343 2,5181 2,4443 2,4251 2,7948 2,9423 2,8200 2,4475 3,4636 3,3328 2,9033 2,8111 2,8668 2,8571 2,6563 3,1970 3,4234 4,1037 3,1613 3,4113 3,6271 3,9325 3,6966 3,6854 3,7577 3,0634 3,3181 2,7858 2,7656 2,7617 2,6193 2,3113 1,9829 2,4739 3,7198 4,0846 3,5467 3,5271 3,7068 4,1213 4,6991 5,0939 5,3235
2,20032316 2,14413977 2,25335265 2,2705935 2,38845448 2,26460369 2,06275964 1,99040132 2,04344346 2,118848 3,02363842 3,11128024 3,01599278 3,09189373 3,1101602 3,15156233 3,12806001 3,45107234 3,41933861 3,46153149 2,7156865 2,61493338 2,57089006 2,45170396 2,07446228 2,21411488 2,22656407 1,81025473 2,01803843 1,84101794 1,82044737 1,83401874 1,84051966 1,94175685 1,91754765 1,71720638 4,03369484 3,97750404 3,9744462 4,01242893 3,98217689 4,12677614 4,24633767 4,20610252 4,23111458
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
1,7181 0,5231 0,6359 2,4835 1,2739 0,5338 4,1709 2,9909 5,8138 1,0064 6,4367 6,2144 2,3822 0,9033 4,2939 5,4605 11,5897 1,0700 3,0483 11,3168 5,3159 2,4290 5,2461 4,4221 5,2118 1,3766 4,1830 8,2466 8,5941 2,8713 5,4054 2,1339 2,1217 1,1526 0,3631 0,9318 7,1907 0,0211 2,6457 3,9841 6,4625 4,8737 0,3699 6,3859 0,3429
1,5355 1,2891 1,2126 1,1776 1,1864 1,3031 1,2877 1,6382 1,8039 2,2500 2,1150 2,5869 3,1560 3,3307 3,1726 3,4746 3,9673 4,7092 4,5171 4,2406 5,2716 5,1595 4,7810 5,0674 5,4192 5,5110 5,1026 4,3620 5,0796 5,6342 4,7897 4,7986 4,7691 4,4567 4,1297 3,6448 3,6004 3,9011 3,0786 2,4837 2,5950 2,7007 2,9747 2,7995 3,3228
1,40017992 1,38492239 1,3121206 1,22508893 1,28888641 1,00136906 0,85976971 1,03927967 1,08981164 1,56211433 1,57981741 1,98986245 2,20167761 2,21539799 2,29232248 2,30689659 2,34262506 3,09525102 3,26004848 3,08219776 3,609914 3,39879197 3,3420896 3,32908452 3,26607476 3,25715863 3,43139381 2,65396365 2,61883055 2,75540228 2,07504199 2,08330909 2,11693998 2,24130062 2,41046359 2,6226621 2,49040753 2,69834017 2,68568276 2,5178179 2,48281332 2,74638581 2,68492639 2,69331446 2,70293194 2
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101
3,176156175 0,2928 1,096282263 0,3523 7,264105887 2,0277 3,655229556 8,4653 2,420291722 2,6406 2,443911234 1,4987 3,537840575 7,4237 0,632903926 3,9966 0,374649546 3,2863 6,869006603 0,3061 13,75610268 3,2577 3,543699952 0,0280 2,601787502 4,1963 0,148201051 15,5019 3,26212697 0,7631 0,762355067 3,5970 0,358040273 4,0725 1,236562962 3,3653 1,894463401 1,0098 0,51913416 3,0392 1,049523613 2,3710 2,967390834 12,1711 10,67355358 3,4418 0,486850989 3,0725 4,132598566 17,7435 3,515485053 2,962554723 1,774480581 12,91519678 5,32647749 2,234584849 5,333569692 1,985526992 3,677632919 1,041022616 7,554769888 2,157857515 0,95030296 10,96053693 3,028509341 3,846884313 3,190025024 3,152896906 0,40025134 0,855056865
4,8833 3,3828 2,9639 3,0903 3,7928 3,7847 3,1727 3,1249 3,1027 3,0522 3,0290 3,3255 3,2931 3,5099 4,2136 4,0258 4,2357 3,9005 3,8374 3,6098 3,8831 3,7944 5,0087 4,9333 3,6903 5,3884
4,37976388 2,59437293 2,71882257 2,59436849 2,91176677 2,91758341 2,7512445 2,89684436 2,89740015 2,85755031 2,64931945 2,46263507 2,53940074 2,5264133 4,11607351 4,22796565 4,19955512 3,97381923 3,9665636 4,05020329 3,96660249 3,99200431 4,47214543 4,49170477 2,73331919 4,65526063
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
5,3693 2,5459 1,8264 0,3869 1,3530 3,3626 3,2898 2,3822 2,1278 6,9991 5,8770 1,3342 0,5266 2,3101 0,9565 1,6445 1,2877 5,2983 0,6359 0,0302 1,2739 1,8990 2,5180 1,1526 1,4293 1,2557 9,1728 2,3624 6,9379 0,9277 3,5722 1,5325 1,4487 7,8519 0,4075 0,7997 0,5917 0,4665 2,0024 4,3702 1,5475 0,1476 0,2371 0,2145 1,0444
3,3208 3,7646 3,3001 3,4806 3,2547 2,9916 2,6816 2,5233 2,7245 2,2987 2,9643 3,0151 2,8939 2,7639 2,9562 2,9166 2,7448 2,5446 2,8362 2,6870 1,9901 1,5298 1,5863 1,7854 1,6697 1,7169 1,6780 2,4666 2,1730 2,8032 2,8929 3,1227 3,0861 2,9792 3,6491 3,5469 3,5013 2,6432 2,4536 1,9601 2,3043 2,1018 1,9634 1,8422 1,0785
2,66752381 2,58090831 2,37399527 2,23039318 2,40717168 2,42281859 2,1216319 2,0492637 1,90286485 1,63877459 1,85114772 1,99706944 2,04320383 2,09799737 1,90286659 1,93302363 1,9522468 1,97749032 2,12248445 2,21872307 1,91804262 1,69303888 1,62261654 1,47851425 1,47342765 1,33979876 1,30071037 2,45586777 2,32995433 2,59183012 2,59222713 2,5948593 2,63910786 2,67310079 2,98078442 3,14044895 3,25183702 2,54909973 2,62472925 2,27591215 2,28480827 2,28711131 2,3063415 2,31140467 1,91073075 3
1,180016785 6,925809496 6,533148333 1,101474822 0,905748697 3,962643668 2,180732432 4,700572395 3,753193236 1,796785516 1,393257753 3,626956038 0,396482711 5,860012995 2,500678003 0,610390442 0,048388146 4,228074902 4,002244469 0,369215993 11,39608296 1,342613654 0,533076865 3,080829006 15,83554422 0,08427264 0,793068741 1,544500935 2,159089547 3,24969356 1,461815612 2,249787584 0,455959071 4,69339364 2,624726682 1,165381528 3,753193236 4,31402639 1,035509857 5,3406787 1,756108765 0,602312101 2,642046913 7,731065816 12,95997373
121 2,4698 122 5,6914 123 2,5459 124 1,0657 125 1,7448 126 7,8933 127 3,8730 128 0,3061 129 7,2574 130 4,6253 131 1,1132 132 11,7361 133 9,5103 134 2,1157 135 1,8541 136 0,5735 137 1,4927 138 5,1278 139 1,2923 140 0,7415 141 1,9618 142 9,4397 143 0,2081 144 3,8839 145 2,6240 146 0,1287 147 1,3483 148 11,8899 149 1,4196 150 2,5319 151 3,0401 152 0,3228 153 2,5459 154 1,5325 155 4,2939 156 20,7233 157 4,2441 158 0,2306 159 1,3861 160 0,9524 161 1,4780 162 1,8990 163 1,9217 164 0,2048 165 0,3564
1,1422 1,3092 1,8191 2,0271 1,9334 1,6709 2,3054 2,6780 2,6849 3,3892 3,7473 3,6116 4,2161 4,9125 5,0175 5,0284 4,2965 4,0584 4,5406 3,9441 3,5557 3,6406 3,4109 2,4807 2,6575 2,7345 2,6901 2,6756 3,3518 3,3645 3,5436 3,6514 2,7397 2,9735 2,7384 2,9054 4,9648 5,2544 4,0885 4,0851 3,9272 3,7709 3,9286 3,8661 3,7334
1,63285899 1,43911874 1,77471376 1,66782638 1,69019201 1,5590148 2,3499306 2,3098185 2,37560445 2,65803309 2,67231861 2,76238885 3,43313406 3,72470408 3,8262521 3,95566477 3,72973992 3,79821555 3,72760757 3,61966118 3,71709626 3,67075402 3,38436965 3,13951114 3,02735093 2,85629999 2,72551628 2,63559265 3,76853239 3,72517527 3,63143491 3,5976185 3,14523035 3,06500537 3,06419367 3,0952966 5,81013985 5,80375837 5,28033333 5,31338957 5,38652926 5,43167494 5,41579565 5,44891341 5,54890096 4
1,47061901 2,914617618 5,963323059 2,524941567 6,630017735 4,056258569 1,875344311 0,276016937 3,998829557 6,833677441 8,536768845 2,281709571 2,87681192 6,047710563 0,394429088 1,040173839 1,111017918 3,700204845 1,700601044 0,445500025 0,829237441 3,955907138 0,146625503 1,175574314 0,864646644 1,06274795 0,174158794 2,562766023 0,93019207 7,786844315 1,357198486 0,408834055 0,096949804 11,47753593
166 10,7267 167 1,6969 168 0,7377 169 2,2587 170 0,4665 171 3,3903 172 2,3955 173 2,7265 174 2,7265 175 0,9648 176 0,0945 177 0,6100 178 2,3166 179 1,0872 180 2,4089 181 0,3462 182 5,3159 183 1,4148 184 1,1394 185 0,0976 186 0,3028 187 1,3909 188 0,5990 189 0,4665 190 1,4682 191 1,3577 192 8,3906 193 0,2862 194 3,3903 195 1,4780 196 1,6084 197 3,1581 198 1,3109 199 4,4352 200 2,0573 201
3,3396 2,3400 2,0852 2,1360 2,2232 2,1746 2,3659 2,4155 2,4960 2,7481 2,8090 1,7458 1,6371 1,7950 1,6778 1,8721 1,5677 1,8597 1,7285 1,5698 1,4831 1,5039 1,5820 1,4103 1,3482 1,2541 1,3553 1,6627 1,5499 1,7750 1,9130 2,0436 2,2203 2,2915 2,6884 2,7473
5,61137201 3,6997626 3,68798757 3,5083456 3,40296259 3,31466444 3,25056617 3,18658097 3,12754057 2,92172823 2,82606157 1,10709124 1,1471945 1,07133151 1,08743134 0,95892717 0,98172235 1,46909999 1,47064098 1,4769106 1,42587308 1,38011338 1,34271415 1,35701415 1,37271674 1,36386055 1,30802446 2,24563672 2,27875481 2,33133609 2,29392303 2,26643777 2,28495621 2,29158728 2,34067998 2,34985189
5
Solución 9 Cuando se tiene 100 tiempos de proceso, podemos observar en la gráfica de promedios o medias móviles son relativamente estables, mediante la observación, lo mismo sucede cuando se tiene 200 tiempos de proceso, sin embargo, se observa que sí es menos inestable que los 100 promedios iniciales Gráficas tomadas con un intervalo de 10, cabe resaltar que las gráficas son hechos con un intervalo de 10.
Problema 10 Genere en una hoja de cálculo 100 números con la función 𝑋𝑋 = 5 + 10 𝑋𝑋 donde r es un número pseudo aleatorio entre cero y uno obtenido a partir de la función ALEATORO de la hoja de cálculo. Suponga que estos valores son tempos de proceso de cierta pieza. Determina el promedio móvil de estos valores conforme se va realzando la atención de los clientes y grafique ese promedio ¿El tiempo promedio de proceso es estable? ¿Y si ahora se generan 200 números? Desarrollo:
N°
VALORES
1
12,445
TIEMPO DE ATC PROMED 100 IO VALORES MÓVIL 7,7250
ERROR TIPICO
N° 1
TIEMPO DE ATC 200 VALORES 12,8310
PROMEDIO MÓVIL
ERROR TIPICO
6
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
11,579 12,806 13,66 5,55 8,07 9,631 14,444 5,837 6,436 8,45 8,868 5,663 11,352 10,414 14,34 7,567 9,049 11,268 10,23 8,599 5,705 14,865 10,091 9,712 6,99 8,26 7,464 11,664 5,531 10,653 7,937 5,792 14,608 6,538 7,029 5,998 12,531 5,62 10,082 11,689 10,628 11,849 14,616 7,019 14,073
14,1680 6,7160 12,4630 7,5030 5,5030 14,0760 10,6340 8,9490 7,1660 8,3640 12,5110 11,3060 11,7060 10,1810 11,9220 5,6170 10,6580 12,4110 13,5830 6,2490 6,5280 8,2490 8,5690 12,2850 14,7040 11,1080 13,0180 9,2640 14,5870 6,7800 9,8430 14,6070 14,3840 6,1210 11,6840 11,0070 9,4480 8,3670 14,5090 11,8590 8,7080 5,5360 11,1540 10,3120 11,6090
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A 9,4903 9,5542 9,3885 9,8475 9,7718 10,0396 10,6815 9,8356 9,838 10,1842 10,8259 10,6144 10,0161 9,7104 9,3967 9,6071 9,8853 10,4344 10,6704 10,3557 10,4561 10,5092 10,8407 11,4765 12,058 11,4416 11,1396 11,1295 10,7725 10,6828 10,675 11,1829 11,0694 10,1623 9,8393 10,2584
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A 2,17769977 2,22762189 2,59351372 2,63969637 2,63985676 2,58132514 2,71631275 3,08973427 2,79502647 2,88028741 2,81413799 2,97752348 2,88975217 2,68952114 2,8284197 2,91075194 3,25365033 2,87991157 2,87228438 2,80612277 2,87948556 2,838126 2,59036234 2,67732283 2,88588282 2,82137124 2,26484978
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
14,0750 13,3490 11,2430 9,8620 14,8670 11,9980 13,0090 13,6160 11,7780 8,4020 10,9100 8,5330 5,9060 5,9480 13,1360 11,6870 12,9980 10,1580 13,5260 6,5490 6,5660 12,8040 14,4160 7,8530 11,3440 14,5310 6,2910 11,0270 11,5750 14,3010 13,8190 14,5770 11,2870 10,9290 11,1360 6,0320 12,4600 12,1570 14,1170 13,2260 5,1530 14,0620 6,0020 10,3440 14,5890
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A 12,6628 12,2199 11,9034 11,4218 10,8881 10,4967 10,3236 10,2925 10,2914 9,9456 10,1204 9,9351 9,5007 9,9278 10,7788 10,9693 10,7901 11,0745 10,4038 10,4907 10,2956 11,0708 11,7961 11,9734 11,6605 11,9681 11,9473 11,0974 11,7143 11,8273 12,0815 11,974 11,1074 11,0559 10,5274 10,4689
#N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A 2,95682691 3,13438182 3,08436066 3,20559554 3,20446233 3,01817316 2,83044777 2,69279701 2,87253058 3,03486012 3,0388528 2,87027902 2,85225412 2,77188015 2,7448024 2,49498859 2,3155579 2,32313336 2,60154514 2,26542084 2,26146856 2,31622098 2,11617835 2,75943587 2,80004942 3,1423321 3,12535408 7
47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
11,067 6,9 13,786 8,529 12,627 12,094 11,004 13,346 14,825 11,953 14,239 9,872 8,302 7,77 8,616 14,254 11,029 14,618 13,934 12,003 9,411 12,731 12,214 12,652 9,808 10,481 6,065 11,324 12,92 5,913 11,709 13,531 6,658 10,105 11,221 13,277 14,08 7,729 10,04 14,047 10,612 10,34 10,656 11,505 6,186
7,0380 14,4340 7,5190 14,8430 7,0060 9,7780 8,9250 11,1880 12,7270 10,7460 12,6690 9,0020 7,4530 10,7500 14,1540 11,8490 14,4400 14,3930 8,2530 14,1760 5,4540 13,4740 7,7720 5,9450 11,9220 10,4800 14,0070 5,3870 10,7110 11,1320 12,9730 9,8430 11,1520 6,0800 14,1250 6,5910 11,9000 10,6840 13,1550 12,4460 13,3100 14,4250 11,4500 9,7960 12,7600
10,2509 9,854 10,3526 10,2678 10,3012 9,8159 9,9229 10,2618 10,2652 10,5067 10,4204 10,9835 10,4403 10,4337 10,0244 10,7392 10,9463 11,4978 11,8183 11,3709 11,7139 10,9924 11,4396 11,4715 10,991 10,7678 10,6309 10,5876 9,687 9,9328 9,6284 10,3803 10,0172 10,3552 10,3687 10,589 10,2001 9,9894 10,5191 10,7635 10,8949 10,9286 11,3868 11,4166 11,7882
2,29877162 2,46492108 2,75067056 2,79024832 2,89453361 3,02029262 2,92688334 2,57003587 2,55291926 2,64765607 2,61462055 2,51542164 2,20645284 2,23635893 1,7294959 1,8351262 1,85663009 2,03323042 2,17066303 2,27836231 2,40552009 2,92742606 2,96257168 3,04253246 3,42790983 3,2737895 3,26166952 3,30787902 3,48255015 3,34911706 3,29187982 2,90539061 2,83380501 2,59332023 2,45324132 2,67123657 2,90444281 2,76253464 2,40526856 2,50931953 2,51220906 2,49120285 2,66947991 2,65758264 2,37072496
47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
10,6290 6,4450 6,5960 12,5850 7,0300 5,8450 10,7500 10,8920 13,8620 8,7080 7,0260 5,4850 7,7860 12,7490 13,6250 13,2010 6,2550 14,4790 14,1230 11,0290 11,5250 5,2740 8,7480 6,6300 14,9530 7,0970 6,3300 6,4070 13,0130 13,5550 15,0000 5,9010 10,4330 6,2220 10,0520 9,4080 5,4460 12,9240 10,0510 7,6440 8,2770 9,2990 13,7280 5,5130 11,9130
10,8142 11,2739 10,6724 10,1163 9,9631 9,3435 9,4127 9,0815 9,5705 9,9223 9,3342 8,9739 8,8779 8,9969 9,0133 9,6728 10,4084 9,9589 10,3176 10,3437 10,5758 11,0257 11,0046 11,1008 10,4889 10,6217 10,0113 10,0188 9,2116 9,1006 9,3532 9,7007 9,7634 9,9319 9,8911 9,401 9,6321 9,5437 10,1954 9,8992 9,3081 8,6358 8,9756 9,3051 9,2342
3,33570515 2,93303439 3,21468116 3,40037586 3,44030027 3,49487392 3,15301509 3,05224993 2,72817546 2,9989173 2,75822517 2,81880257 2,70365196 2,49341344 2,63158129 2,81992559 2,73111579 2,92446436 3,17955666 3,16002655 3,1570705 3,10041816 3,42715529 3,48601954 3,49941391 3,54399848 3,55378365 3,55221272 3,41658724 3,43153681 3,67701213 4,03778976 3,80940703 3,73940172 3,72024781 3,46505526 3,34100517 3,38831899 3,38210781 3,14805816 2,90201322 2,37198154 2,03591302 2,46496169 2,47275951 8
92 93 94 95 96 97 98 99 10 0 10 1
10,719 8,053 14,295 11,811 8,705 11,968 6,446 5,957
8,4480 13,7510 9,7070 10,1980 9,2520 11,6090 11,8770 11,0910
11,6517 11,8374 12,0225 11,9248 11,6291 11,3097 11,1396 10,8848
2,11963207 2,08304658 2,06707887 2,18219145 2,09638666 2,13954641 2,00812995 1,79107958
92 93 94 95 96 97 98 99
13,4280 12,7800 13,0460 8,6970 11,0280 7,3850 13,1910 11,6520
9,4203 9,8223 10,5557 10,5679 10,4325 10,7709 10,6817 11,0709
2,5871828 2,82641115 2,60849315 2,58337157 2,64058713 2,58889697 2,78860841 2,86624502
9,25
6,8810
10,8489
1,79268395
100
6,3130
10,8633
2,51423166
10,5574
2,04167121
101
6,0360
10,9433
2,66093888
102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134
9,8710 8,0140 13,7480 14,2760 10,5570 7,1530 11,8530 5,9350 5,2620 7,6990 11,2610 12,3040 6,5700 7,9490 14,8240 13,9000 8,2350 12,6300 12,6290 12,8500 6,8230 11,7530 5,4070 6,1400 5,9330 7,1100 11,6870 5,8830 11,0140 10,3300 13,6890 14,7040 10,4370
10,3556 9,9999 9,5233 9,5935 10,1514 10,1043 10,0811 9,9473 9,3756 9,2705 9,4368 9,5758 10,0048 9,287 8,6543 9,081 9,7557 9,3939 10,0634 10,8001 11,3152 10,8714 10,8163 10,7 10,5191 9,63 8,951 9,2962 8,6215 8,46 8,208 8,8946 9,1897
2,88533097 2,65079027 2,59994936 2,80564177 3,04494043 3,04721938 3,00933544 2,99496021 3,17668927 3,09098595 2,82671091 2,87621678 2,92804651 2,75421101 2,43601941 3,03511149 3,17364885 3,13738469 3,05256505 2,83651788 2,82478316 3,05521919 2,98219263 3,31011313 3,58116682 3,30050478 3,08459683 3,15468305 3,16910395 3,21885444 3,25203801 3,35192841 3,76675376
6,044 5,384 6,837 10,506 11,771 12,234 14,376 13,406 7,455 8,408 14,874 8,819 6,77 14,451 5,618 8,881 6,003 6,327 7,793 14,537 6,974 12,44 8,551 14,245 5,394 12,896 7,075 6,484 10,189 9,136 8,629 13,095 11,689 8,715
9
12,428 7,029 13,559 6,78 7,512 13,546 13 7,066 11,385 13,038 14,057 12,859 12,771 11,653 12,627 13,176 13,926 5 6,436 12,561 8,756 8,544 14,903 10,797 14,958 7,371 14,609 5,13 7,455 8,315 8,41 11,912 5,717 10,886 7,557 10,004 10,726 10,665 11,641 12,237 12,228 12,537 9,196 9,606 6,369
135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179
10,1880 14,9580 6,1880 12,3210 14,0440 7,5190 12,3740 10,3280 14,5260 11,2020 11,1220 10,9000 13,9550 8,5350 9,6650 6,1110 7,8920 12,3130 13,0500 10,4000 13,6410 11,1670 10,1810 11,0260 14,3980 11,4340 12,8920 10,4840 14,4510 7,8670 12,7260 6,4500 5,6300 10,3760 11,4350 7,6930 13,4270 12,6210 9,9210 13,0350 11,5740 12,2120 12,8780 7,3090 7,0350
9,6927 10,0975 11 10,9078 10,9712 11,7873 11,4378 11,6422 11,3061 11,2883 11,3648 11,4582 11,0524 11,8291 11,4505 11,0126 10,8718 10,4236 10,6221 10,4745 10,3943 10,6462 10,6729 10,2955 10,5446 11,0179 11,5502 12,0502 11,8673 12,0074 11,7541 11,6626 11,1909 10,7358 10,6708 10,3745 10,0004 10,0539 10,2676 9,8146 10,3314 10,2162 10,7924 11,5172 11,2105
3,38263909 3,08632703 3,1185269 3,40792212 3,35030397 3,3141919 3,44489125 3,38681863 3,04427023 2,6972395 2,68744359 2,68939344 2,38087867 1,97303754 2,13557841 2,05743244 2,22797005 2,3560979 2,39613097 2,31440997 2,31383802 2,49788431 2,50230233 2,41057729 2,23249713 2,4382265 1,9182745 1,76344547 1,73642666 1,71725817 2,11185393 1,91732268 2,42885283 2,91632207 2,91383776 2,73137491 2,82691849 3,00971523 3,06934571 2,97067283 2,83635113 2,84888888 2,46375343 1,91006264 2,27196364 10
8,1 7,72 14,562 11,009 8,718 10,141 13,459 8,037 13,225 11,112 9,781 13,612 5,173 11,861 5,916 11,097 5,708 8,349 10,227 6,783 5,785
180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201
6,0310 7,0350 6,5370 12,1830 14,4870 5,2280 5,4270 13,2330 9,9510 8,6970 12,9130 5,4480 7,1910 7,4550 14,9520 6,1530 8,3430 5,2570 7,3660 13,9920 8,4500
10,7705 10,6043 9,9651 9,3567 9,5829 9,7281 9,0935 8,415 8,4505 8,7147 8,8809 9,5691 9,4104 9,4758 9,003 9,0495 9,142 9,4336 8,636 8,3775 8,907 8,4607
2,53865098 2,82910703 2,77931913 2,82238135 2,93951636 3,18975297 3,38885983 3,48936369 3,77858597 3,59282416 3,39357796 3,24700336 3,35477921 3,31383522 3,24731924 3,42991545 3,34118587 3,22329792 3,0404248 3,03210363 3,43161667 3,26463439
11
Solución 10 Cuando se tiene 100 tiempos de atención al cliente, podemos observar en la gráfica de promedios o medias móviles que estas si son estables, mediante la observación, caso contrario sucede cuando se tiene 200 tiempos de atención al cliente, los promedios en esta gráfica tienen menor estabilidad, cabe resaltar que las gráficas son elaboradas con un intervalo de 10.
12
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