I know this is probably way easier than I\'m making it, but I\'m confused at how
ID: 3206511 • Letter: I
Question
I know this is probably way easier than I'm making it, but I'm confused at how I am supposed to be calculating these.
3. A production line has three machines A, B, andC with reliabilities of .99, .96, and -93, respective The machines are arranged so that if one breaks down, the others must shut down. Engineers are weighing two alternative designs for increasing the line's reliability. Backup components may be installed according to the two plans described below. The backup machines will have slightly lower reliabilities than the originals taking into account switching to the backups. Plan 1 involves adding an identical backup line 94 93 96 Plan 2 involves providing independent backups for each machine. 97 91 96 93 99 a. Which plan will provide the higher reliability? Support your answer by calculating the system reliability for each plan. b. What other factors might enter into the decision of which plan to adopt?Explanation / Answer
a) first plan:
reliabilty of upper row =0.97*0.94*0.91=0.8297
reliability of lower row=0.99*0.96*0.93=0.8839
hence reliabilty of system for work=1-P(both upper and lower row will not work)=1-(1-0.8297)*(1-0.8839)
=0.9802
second plan:
relaibilty of first parallel unit=1-P(both component will not work)=1-(1-0.97)(1-0.99)=0.9997
relaibilty of second parallel unit=1-(1-0.94)*(1-0.96)=0.9976
reliability of third unit =1-(1-0.91)*(1-0.93)=0.9937
hence reliability of overall system=0.9997*0.9976*0.9937=0.9910
from above comparison plan 2 looks better.
b) as switching will take time for plan b; hence its relaibilty will get affected by time taken to replace the defected unit.