Согласно схеме изображенной на рис. 3. сначала работают элементы 1 и 2, а элемент 3 находиться в резерве. При отказе элемента 1 или 2 в работу включается элемент 3. Система откажет если откажут элементы 1 и 3 или элементы 2 и 3.
Составим таблицу для получения случайных чисел (см. табл. 3.1.1.):
· РРСЧ – равномерно распределенные случайные числа ξ из промежутка (0;1).
· X1 имеет логнормальное распределение с параметрами (1,5;1) и определяется как:
.
· X2 имеет логнормальное распределение с параметрами (1,5;1) и определяется так же.
· X3 имеет экспоненциальное распределение с параметром (0,08) и определяется как:
.
· G – дискретная случайная величина, имеющая геометрическое распределение G(0,7), определяется как:
· .
· Y – случайная величина.
Элемент 1 имеет последовательное соединение с элементом 2. Время до отказа этой пары равно самому минимальному времени до отказа составляющих ее частей – min(X1;X2). Считая пару элементов 1 и 2 одним элементом, имеем параллельное соединение с элементом 3. Время до отказа этой пары равно сумме .
· Z –случайная величина.
Таблица 3.1.1. Получение случайных чисел
РРСЧ | РРСЧ | Х1 | Х2 | Х3 | V | Y | Z | |
0.8711 | 0.1330 | 17.9011 | 17.9011 | 1.7255 | 1.7255 | 1.5687 | ||
0.3975 | 0.0424 | 0.6000 | 0.6000 | 11.5321 | 11.5321 | 10.4837 | ||
0.6010 | 0.7264 | 2.3539 | 2.3539 | 6.3647 | 6.3647 | 5.7861 | ||
0.7026 | 0.5447 | 3.2443 | 3.2443 | 4.4112 | 6.4885 | 5.8987 | ||
0.2818 | 0.8096 | 3.9400 | 3.9400 | 15.8341 | 15.8341 | 13.1951 | ||
0.1132 | 0.2228 | 16.6534 | 16.6534 | 27.2292 | 33.3067 | 27.7556 | ||
0.7606 | 0.4937 | 4.8497 | 4.8497 | 3.4209 | 9.6993 | 8.8176 | ||
0.2033 | 0.4461 | 6.4742 | 6.4742 | 19.9163 | 19.9163 | 16.5969 | ||
0.7102 | 0.3931 | 3.1965 | 3.1965 | 4.2771 | 6.3930 | 5.8119 | ||
0.9132 | 0.5542 | 11.3476 | 11.3476 | 1.1346 | 22.6953 | 20.6321 | ||
0.0579 | 0.9661 | 5.7291 | 5.7291 | 35.6224 | 35.6224 | 27.4018 | ||
0.3903 | 0.5339 | 1.8881 | 1.8881 | 11.7615 | 11.7615 | 10.6923 | ||
0.2828 | 0.9899 | 4.3529 | 4.3529 | 15.7871 | 15.7871 | 13.1559 | ||
0.9497 | 0.7825 | 8.7200 | 8.7200 | 0.6456 | 17.4400 | 15.8546 | ||
0.2891 | 0.8539 | 3.9092 | 3.9092 | 15.5129 | 15.5129 | 12.9274 | ||
0.0840 | 0.5471 | 11.5763 | 11.5763 | 30.9681 | 30.9681 | 23.8216 | ||
0.3083 | 0.8151 | 3.5648 | 3.5648 | 14.7103 | 14.7103 | 13.3730 | ||
0.4260 | 0.0533 | 0.5146 | 0.5146 | 10.6670 | 10.6670 | 9.6972 | ||
0.6520 | 0.7245 | 2.8192 | 2.8192 | 5.3457 | 5.6385 | 5.1259 | ||
0.8742 | 0.8873 | 6.3218 | 6.3218 | 1.6812 | 12.6437 | 11.4942 | ||
0.6095 | 0.1721 | 1.0525 | 1.0525 | 6.1881 | 6.1881 | 5.6255 | ||
0.5159 | 0.7901 | 2.2638 | 2.2638 | 8.2721 | 8.2721 | 7.5200 | ||
0.5082 | 0.0471 | 0.3796 | 0.3796 | 8.4618 | 8.4618 | 7.6926 | ||
0.0928 | 0.7821 | 8.0467 | 8.0467 | 29.7207 | 29.7207 | 24.7672 | ||
0.0136 | 0.9541 | 6.0816 | 6.0816 | 53.6986 | 53.6986 | 38.3561 | ||
0.2819 | 0.2058 | 3.1445 | 3.1445 | 15.8262 | 15.8262 | 13.1885 | ||
0.9571 | 0.9264 | 6.5328 | 6.5328 | 0.5478 | 13.0657 | 11.8779 | ||
0.3613 | 0.0003 | 0.3269 | 0.3269 | 12.7244 | 12.7244 | 11.5677 | ||
0.7252 | 0.8722 | 4.1319 | 4.1319 | 4.0168 | 8.2639 | 7.5126 | ||
0.4015 | 0.6533 | 2.1140 | 2.1140 | 11.4081 | 11.4081 | 10.3710 | ||
0.4260 | 0.6539 | 1.9661 | 1.9661 | 10.6664 | 10.6664 | 9.6967 | ||
0.7514 | 0.0173 | 4.5932 | 4.5932 | 3.5732 | 9.1863 | 8.3512 | ||
0.5355 | 0.9613 | 3.4081 | 3.4081 | 7.8080 | 7.8080 | 7.0982 | ||
0.9770 | 0.4447 | 15.7964 | 15.7964 | 0.2911 | 31.5928 | 28.7208 | ||
0.8971 | 0.1475 | 21.3678 | 21.3678 | 1.3570 | 42.7356 | 38.8506 | ||
0.8764 | 0.0977 | 20.8710 | 20.8710 | 1.6495 | 41.7419 | 37.9472 | ||
0.4143 | 0.8448 | 2.7225 | 2.7225 | 11.0157 | 11.0157 | 10.0143 | ||
0.3703 | 0.5647 | 2.1528 | 2.1528 | 12.4187 | 12.4187 | 11.2897 | ||
0.3362 | 0.3629 | 2.1512 | 2.1512 | 13.6258 | 13.6258 | 12.3870 | ||
0.6303 | 0.1659 | 1.2272 | 1.2272 | 5.7701 | 5.7701 | 5.2455 | ||
0.6947 | 0.6891 | 3.3408 | 3.3408 | 4.5532 | 6.6817 | 6.0742 | ||
0.8902 | 0.3454 | 13.7971 | 13.7971 | 1.4542 | 27.5942 | 25.0857 | ||
0.8275 | 0.5039 | 7.7510 | 7.7510 | 2.3669 | 15.5020 | 14.0928 | ||
0.6364 | 0.0660 | 0.9746 | 0.9746 | 5.6481 | 5.6481 | 5.1347 | ||
0.5721 | 0.8424 | 2.6466 | 2.6466 | 6.9811 | 6.9811 | 6.3465 | ||
0.3224 | 0.2377 | 2.1276 | 2.1276 | 14.1487 | 14.1487 | 12.8624 | ||
0.4023 | 0.1395 | 0.8846 | 0.8846 | 11.3811 | 11.3811 | 10.3465 | ||
0.9999 | 0.9620 | 5.9207 | 5.9207 | 0.0016 | 11.8414 | 10.7650 | ||
0.0036 | 0.0040 | 124.1835 | 124.1835 | 70.1842 | 248.3671 | 165.5780 | ||
0.4139 | 0.4623 | 1.5450 | 1.5450 | 11.0258 | 11.0258 | 10.0235 | ||
0.1583 | 0.8936 | 5.8028 | 5.8028 | 23.0396 | 23.0396 | 19.1997 | ||
0.1011 | 0.0054 | 60.5008 | 60.5008 | 28.6478 | 121.0016 | 100.8346 | ||
0.8280 | 0.4873 | 7.8803 | 7.8803 | 2.3594 | 15.7607 | 14.3279 | ||
0.1325 | 0.7445 | 7.5149 | 7.5149 | 25.2614 | 25.2614 | 21.0512 | ||
0.4188 | 0.7171 | 2.2001 | 2.2001 | 10.8807 | 10.8807 | 9.8916 | ||
0.0686 | 0.2588 | 19.9648 | 19.9648 | 33.4956 | 39.9297 | 30.7151 | ||
0.9737 | 0.3215 | 19.8064 | 19.8064 | 0.3336 | 39.6128 | 36.0116 | ||
0.4771 | 0.6324 | 1.7378 | 1.7378 | 9.2516 | 9.2516 | 8.4106 | ||
0.8030 | 0.3035 | 7.4251 | 7.4251 | 2.7425 | 14.8502 | 13.5002 | ||
0.8467 | 0.0377 | 19.3162 | 19.3162 | 2.0808 | 38.6325 | 35.1204 | ||
0.8824 | 0.5277 | 10.3399 | 10.3399 | 1.5634 | 20.6798 | 18.7999 | ||
0.6993 | 0.5667 | 3.2101 | 3.2101 | 4.4708 | 6.4201 | 5.8365 | ||
0.0615 | 0.4899 | 13.5516 | 13.5516 | 34.8572 | 34.8572 | 26.8132 | ||
0.7527 | 0.4900 | 4.5719 | 4.5719 | 3.5519 | 9.1437 | 8.3125 | ||
0.2965 | 0.3834 | 3.0077 | 3.0077 | 15.1962 | 15.1962 | 12.6635 | ||
0.5105 | 0.9385 | 3.1409 | 3.1409 | 8.4039 | 8.4039 | 7.6400 | ||
0.6856 | 0.5850 | 2.9814 | 2.9814 | 4.7180 | 5.9628 | 5.4207 | ||
0.4703 | 0.3585 | 1.0969 | 1.0969 | 9.4300 | 9.4300 | 8.5727 | ||
0.2133 | 0.5669 | 5.7169 | 5.7169 | 19.3123 | 19.3123 | 16.0936 | ||
0.3922 | 0.4735 | 1.7283 | 1.7283 | 11.7003 | 11.7003 | 10.6366 | ||
0.2094 | 0.1301 | 7.4647 | 7.4647 | 19.5464 | 19.5464 | 16.2886 | ||
0.2469 | 0.6212 | 4.5674 | 4.5674 | 17.4842 | 17.4842 | 14.5702 | ||
0.0228 | 0.7752 | 9.0816 | 9.0816 | 47.2479 | 47.2479 | 33.7485 | ||
0.9017 | 0.4853 | 11.9454 | 11.9454 | 1.2934 | 23.8908 | 21.7189 | ||
0.3221 | 0.5344 | 2.7466 | 2.7466 | 14.1630 | 14.1630 | 12.8755 | ||
0.5064 | 0.7939 | 2.2733 | 2.2733 | 8.5042 | 8.5042 | 7.7311 | ||
0.1334 | 0.5945 | 8.8652 | 8.8652 | 25.1810 | 25.1810 | 20.9842 | ||
0.4110 | 0.3157 | 1.2370 | 1.2370 | 11.1140 | 11.1140 | 10.1036 | ||
0.9022 | 0.7035 | 8.8934 | 8.8934 | 1.2865 | 17.7868 | 16.1698 | ||
0.1862 | 0.0126 | 14.2268 | 14.2268 | 21.0136 | 28.4535 | 23.7113 | ||
0.5649 | 0.2327 | 0.9347 | 0.9347 | 7.1388 | 7.1388 | 6.4898 | ||
0.4055 | 0.9727 | 3.6881 | 3.6881 | 11.2834 | 11.2834 | 10.2576 | ||
0.5242 | 0.9697 | 3.5071 | 3.5071 | 8.0733 | 8.0733 | 7.3394 | ||
0.1633 | 0.6548 | 7.2196 | 7.2196 | 22.6509 | 22.6509 | 18.8757 | ||
0.8697 | 0.1220 | 18.2051 | 18.2051 | 1.7446 | 36.4102 | 33.1001 | ||
0.8912 | 0.0852 | 25.0496 | 25.0496 | 1.4397 | 50.0991 | 45.5447 | ||
0.0834 | 0.3225 | 16.4835 | 16.4835 | 31.0455 | 32.9670 | 25.3593 | ||
0.2861 | 0.6407 | 3.6247 | 3.6247 | 15.6427 | 15.6427 | 13.0356 | ||
0.6898 | 0.3077 | 2.5425 | 2.5425 | 4.6417 | 5.0849 | 4.6227 | ||
0.9836 | 0.7764 | 9.0945 | 9.0945 | 0.2072 | 18.1889 | 16.5354 | ||
0.0173 | 0.4983 | 14.4876 | 14.4876 | 50.6776 | 50.6776 | 36.1983 | ||
0.6285 | 0.9038 | 3.2837 | 3.2837 | 5.8060 | 6.5674 | 5.9704 | ||
0.2317 | 0.6209 | 5.0132 | 5.0132 | 18.2795 | 18.2795 | 15.2329 | ||
0.9389 | 0.7883 | 8.4949 | 8.4949 | 0.7882 | 16.9898 | 15.4453 | ||
0.2793 | 0.4567 | 3.5632 | 3.5632 | 15.9424 | 15.9424 | 13.2854 | ||
0.2106 | 0.9851 | 4.6759 | 4.6759 | 19.4717 | 19.4717 | 16.2264 | ||
0.5595 | 0.2373 | 0.9239 | 0.9239 | 7.2597 | 7.2597 | 6.5997 | ||
0.1054 | 0.2780 | 15.8254 | 15.8254 | 28.1195 | 31.6507 | 26.3756 | ||
0.8577 | 0.2122 | 13.4989 | 13.4989 | 1.9188 | 26.9978 | 24.5434 | ||
0.3912 | 0.3648 | 1.4900 | 1.4900 | 11.7308 | 11.73083 | 10.66440 |