6.3 Calculo MTBF Funcion Exponencial

Taller # 7

Caculo del MTBF

CalcularCalcular el MTBF y la rata de falla

Cual es la probabilidad que falle antes de las 200 horas.

Cual es la confiabilidad en 300 horas.

Datos de falla del siguiente Equipo son: 30, 31, 14, 2, 26, 25, 22, 7 en dias.

Si el costo de la falla es de Col$ 26’670.000 y el costos del mantto preventivo es de $ 1’590.000, cual es el tiempo óptimo para hacer el mantenimiento?.

Confiabilidad Distribucion exponencial

MTBF = 1

Rata de falla 1.0000

Tiempo Exponencial1 #NAME?2 0.143 0.054 0.025 0.016 0.007 0.008 0.009 0.00

10 0.0011 0.0012 0.0013 0.0014 0.0015 0.0016 0.0017 0.0018 0.0019 0.0020 0.0021 0.0022 0.0023 0.0024 0.0025 0.0026 0.0027 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 0.0037 0.0038 0.0039 0.0040 0.0041 0.0042 0.0043 0.0044 0.0045 0.0046 0.0047 0.0048 0.0049 0.0050 0.0051 0.0052 0.0053 0.0054 0.0055 0.0056 0.0057 0.0058 0.0059 0.0060 0.0061 0.0062 0.0063 0.0064 0.0065 0.0066 0.0067 0.0068 0.00

69 0.0070 0.0071 0.0072 0.0073 0.0074 0.0075 0.0076 0.0077 0.0078 0.0079 0.0080 0.0081 0.0082 0.0083 0.0084 0.0085 0.0086 0.0087 0.0088 0.0089 0.0090 0.0091 0.0092 0.0093 0.0094 0.0095 0.0096 0.0097 0.0098 0.0099 0.00100 0.00

Simulación por Monte Carlo de Confiabilidad Exponencial

A : distribucion exponencial con MTTF=137 dias

landa = 1/137 = 0.0073Landa= 0.0037

s Aleatorio Exponencial1 0.490 192.562 0.074 704.073 0.872 37.114 0.504 185.085 0.624 127.286 0.685 102.437 0.620 129.148 0.765 72.409 0.220 409.51

10 0.296 329.2411 0.107 605.2012 0.893 30.6313 0.280 343.8414 0.859 40.9615 0.617 130.3616 0.123 567.0917 0.547 163.0818 0.587 144.0119 0.600 138.2720 0.631 124.3621 0.129 553.8422 0.347 285.9423 0.006 1372.8624 0.546 163.6625 0.326 302.7626 0.251 373.3227 0.724 87.2428 0.757 75.3229 0.833 49.2530 0.307 319.4531 0.281 343.1432 0.151 511.4533 0.335 295.8734 0.081 679.3235 0.972 7.7436 0.003 1594.8937 0.934 18.3138 0.329 300.0639 0.798 61.0440 0.498 188.5241 0.877 35.3642 0.270 354.0943 0.048 821.3844 0.453 213.9345 0.238 387.8546 0.455 212.7447 0.759 74.6448 0.613 132.3049 0.389 254.8650 0.739 81.7551 0.617 130.6152 0.888 32.2553 0.585 144.8954 0.521 176.1855 0.493 191.3956 0.166 484.8257 0.372 267.2858 0.361 275.3359 0.694 98.7060 0.426 230.6361 0.528 172.6262 0.603 136.6263 0.703 95.2264 0.222 406.9565 0.940 16.6066 0.438 222.8367 0.684 102.8468 0.853 42.9469 0.797 61.2170 0.372 266.9071 0.538 167.5672 0.780 67.05

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Exponencial

Exponencial

X= (-1/landa)*{ln (aleatorio)}Aleatorios

s Aleatorio Exponencial

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Exponencial

Exponencial

73 0.242 383.4074 0.602 137.2375 0.233 393.3676 0.098 626.5577 0.208 424.3378 0.480 198.5679 0.491 192.2780 0.636 122.4781 0.984 4.4682 0.135 541.2583 0.016 1114.1984 0.541 165.9085 0.646 118.0886 0.466 206.5287 0.885 33.1088 0.393 252.2789 0.489 193.3690 0.033 922.1091 0.086 662.2892 0.914 24.1693 0.490 192.5994 0.085 664.8595 0.713 91.4396 0.648 117.3997 0.177 467.5598 0.232 395.2599 0.318 309.26100 0.220 409.09Prob 0.0901226268622

0.83092364470540.5100690039632

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 17000.000

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Exponencial

Exponencial

Figure 6: Weibull Reliability Calculator

Calculo de la Confiabilidad Distribucion exponencial

CALCULO DE CONFIABILIDAD TIEMPO RELIABILITY

MTBF (dias)= 365.00 0 1.0000

Rata de falla = 0.002740 40 .8962

Tiempo Probabilidad falla Reliability 80 .80320 1.0000 .0000 120 .71985 .9864 .0136 160 .6451

10 .9730 .0270 200 .578115 .9597 .0403 240 .518120 .9467 .0533 280 .464325 .9338 .0662 320 .416130 .9211 .0789 360 .373035 .9086 .0914 400 .334240 .8962 .1038 440 .2995

1,000 .0646 .9354 480 .2685Reliability Dias FFI 520 .2406

0.01 1,681 722.70 560 .21560.1 840 657.00 600 .19320.5 253 365.00 640 .17320.6 186 292.00 680 .15520.7 130 219.00 720 .13910.8 81 146.00 760 .12470.9 38 73.00 800 .1117

0.99 4 7.30 840 .1001

0.999 0 0.73 880 .0897920 .0804

CALCULOS DE CONFIABILIDAD - METODO DE DISTRIBUCION EXPONENCIAL960 .0721

R=1 - EXP^(-t/MTBF) 1,000 .06461,040 .0579


CALCULOS DE MANTENIBILIDAD, FAILURE-FINDING TASK 1,080 .0519FFI=2*(1-R)*MTBF 1,120 .0465

1,160 .04171,200 .03731,240 .03351,280 .0300

CONFIABILIDAD DESEADA 98%

TIEMPO PARA ENCONTRAR FALLA RONDA OPERATIVA 14.6

TIEMPO PARA MANTENIMIENTO PREDICTIVO R=80% 81

TIEMPO PARA MANTENIMIENTO PREVENTIVO R=50% 253


Calculo de la Confiabilidad Distribucion exponencial

.0000

.1038

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.9421

PROBABILIDA DE FALLA

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Figure 6: Weibull Reliability Calculator0 40 80 120 160 200 240 280 320 360 400 440 480 520 560 600 640 680 720 760 800 840 880 920 960 1,000

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6.3 Calculo MTBF Funcion Exponencial

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