An engine production line has 3 milling machines with reliabilities of 0.98, 0.96, and 0.93, respectively. The production line was designed in a way that if one of the machines is malfunctions, the line will shut down. To increase the line's reliability, En. Abu who is the maintenance engineer has considered two designs options. Option 1 is to add an identical backup line and Option 2 is to provide a backup for each machine. The reliability of machine 1 is similar, while machines 2 and 3 are 0.97 and 0.92, respectively. Choose the best plan that will provide higher reliability. Next, explain the reason of two reliabilities is not the same. [CO2/PO2/C3] (5 marks) Z .00 .01 .06 .07 .08 .09 0.0 0.1 0.2 0.4 0.5 0,6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 .00000 .03983 .07926 .11791 .15542 .19146 22575 25804 .28814 31594 .34134 36433 .38493 40320 41924 43319 44520 45543 46407 47128 47725 48214 48610 48928 49180 .49379 49534 49653 49744 49813 49865 49903 .00399 .04380 .08317 12172 .15910 .19497 22907 26115 .29103 31859 .34375 36650 .38686 40490 42073 43448 44630 45637 46485 47193 47778 48257 48645 48956 49202 .49396 49547 49664 49752 49819 49869 49906 .00798 .04776 .08706 .12552 .16276 .19847 .23237 .26424 .29389 .32121 34614 .36864 38877 40658 .42220 43574 44738 45728 .46562 .47257 47831 48300 48679 48983 49224 .49413 .49560 49674 49760 49825 49874 49910 .03 .01197 .05172 .09095 12930 .16640 .20194 .23565 .26730 .29673 32381 .34850 37076 .39065 40824 .42364 .43699 44845 45818 .46638 .47320 47882 48341 .48713 49010 49245 .49430 .49573 49683 49767 49831 .49878 .49913 Appendix 1 .04 .05 .01595 .01994 .05567 .05962 .09483 .09871 .13307 .13683 .17003 .17364 20540 .20884 23891 .24215 .27035 .27337 .29955 .30234 .32639 .32894 .35083 .35314 .37286 .37493 .39251 .39435 40988 41149 .42507 42647 .43822 .43943 44950 45053 .45907 45994 .46712 .46784 47381 .47441 47932 47982 48382 48422 .48745 48778 49036 .49061 49266 49286 .49446 49461 -49585 .49598 49693 49702 49774 49781 .49836 49841 .49882 .49886 49916 49918 .02392 .06356 .10257 .14058 .17724 .21226 .24537 .27637 30511 .33147 .35543 37698 .39617 41309 .42786 .44062 45154 46080 .46856 .47500 48030 .48461 48809 .49086 49305 .49477 49609 49711 49788 49846 49889 .49921 .02790 .06749 .10642 .14431 .18082 21566 24857 27935 30785 .33398 .35769 37900 39796 41466 .42922 44179 45254 46164 46926 47558 48077 48500 .48840 49111 49324 .49492 .49621 49720 49795 49851 49893 49924 03188 .07142 .11026 14803 .18439 21904 25175 28230 31057 33646 35993 38100 39973 41621 43056 44295 45352 46246 46995 47615 48124 48537 48870 49134 49343 .49506 49632 49728 49801 49856 49897 49926 .03586 .07535 .11409 .15173 .18793 .22240 25490 .28524 31327 33891 .36214 .38298 40147 41174 .43189 44408 45449 46327 .47062 47670 48169 48574 48899 49158 49361 .49520 .49643 49736 49807 49861 49900 49929 An engine production line has 3 milling machines with reliabilities of 0.98, 0.96, and 0.93, respectively. The production line was designed in a way that if one of the machines is malfunctions, the line will shut down. To increase the line's reliability, En. Abu who is the maintenance engineer has considered two designs options. Option 1 is to add an identical backup line and Option 2 is to provide a backup for each machine. The reliability of machine 1 is similar, while machines 2 and 3 are 0.97 and 0.92, respectively. Choose the best plan that will provide higher reliability. Next, explain the reason of two reliabilities is not the same. [CO2/PO2/C3] (5 marks) Z .00 .01 .06 .07 .08 .09 0.0 0.1 0.2 0.4 0.5 0,6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 .00000 .03983 .07926 .11791 .15542 .19146 22575 25804 .28814 31594 .34134 36433 .38493 40320 41924 43319 44520 45543 46407 47128 47725 48214 48610 48928 49180 .49379 49534 49653 49744 49813 49865 49903 .00399 .04380 .08317 12172 .15910 .19497 22907 26115 .29103 31859 .34375 36650 .38686 40490 42073 43448 44630 45637 46485 47193 47778 48257 48645 48956 49202 .49396 49547 49664 49752 49819 49869 49906 .00798 .04776 .08706 .12552 .16276 .19847 .23237 .26424 .29389 .32121 34614 .36864 38877 40658 .42220 43574 44738 45728 .46562 .47257 47831 48300 48679 48983 49224 .49413 .49560 49674 49760 49825 49874 49910 .03 .01197 .05172 .09095 12930 .16640 .20194 .23565 .26730 .29673 32381 .34850 37076 .39065 40824 .42364 .43699 44845 45818 .46638 .47320 47882 48341 .48713 49010 49245 .49430 .49573 49683 49767 49831 .49878 .49913 Appendix 1 .04 .05 .01595 .01994 .05567 .05962 .09483 .09871 .13307 .13683 .17003 .17364 20540 .20884 23891 .24215 .27035 .27337 .29955 .30234 .32639 .32894 .35083 .35314 .37286 .37493 .39251 .39435 40988 41149 .42507 42647 .43822 .43943 44950 45053 .45907 45994 .46712 .46784 47381 .47441 47932 47982 48382 48422 .48745 48778 49036 .49061 49266 49286 .49446 49461 -49585 .49598 49693 49702 49774 49781 .49836 49841 .49882 .49886 49916 49918 .02392 .06356 .10257 .14058 .17724 .21226 .24537 .27637 30511 .33147 .35543 37698 .39617 41309 .42786 .44062 45154 46080 .46856 .47500 48030 .48461 48809 .49086 49305 .49477 49609 49711 49788 49846 49889 .49921 .02790 .06749 .10642 .14431 .18082 21566 24857 27935 30785 .33398 .35769 37900 39796 41466 .42922 44179 45254 46164 46926 47558 48077 48500 .48840 49111 49324 .49492 .49621 49720 49795 49851 49893 49924 03188 .07142 .11026 14803 .18439 21904 25175 28230 31057 33646 35993 38100 39973 41621 43056 44295 45352 46246 46995 47615 48124 48537 48870 49134 49343 .49506 49632 49728 49801 49856 49897 49926 .03586 .07535 .11409 .15173 .18793 .22240 25490 .28524 31327 33891 .36214 .38298 40147 41174 .43189 44408 45449 46327 .47062 47670 48169 48574 48899 49158 49361 .49520 .49643 49736 49807 49861 49900 49929