a production line has three machines My Account l Cheggcom

My Account l Chegg.com × Secure https://newconnect.mheducation.com/flow/connecthtml Reliability Help Save & Exit Submit A production line has three machines A, B, and C, with reliabilities of 90, 95. and .98, respectively. 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. Plan 1 involves adding an identical backup line, and plan 2 involves providing a backup for each machine. In either case, three machines (A, B. and C) would be used with reliabilities equal to the original three a. Compute overall system reliability under Plan 1. (Round your intermediate colculations and final answer to 4 decimal places.) Reliability ] b. Compute overall system reliability under Plan 2. (Round your intermediate calculations and final answer to 4 decimal places.) Rellability c. Which plan will provide the higher reliability? Plan2

Solution

Answer 1:- Overall system reliability under plan 1:-

Prob (line works)=0.90*0.95*0.98 = 0.8379

Overall system reliability=Prob (line works)+ Prob (line fails)*Prob(backup works)

Overall system reliability=0.8379+[(1-0.8379)*0.83790)]=0.9737

So answer is :- 0.9737

Answer 2:- Overall system reliability under plan 2:-

For machine 1:- 0.90+[(1-0.90)*0.90] =0.99

For machine 2:- 0.95+[(1-0.95)*0.95] =0.9975

For machine 3:- 0.98+[(1-0.98)*0.98] =0.9996

Overall reliability = 0.99*0.9975*0.9996 =0.9871

Answer 3:- The higher reliability is of Plan 2 as overall reliability of plan 2 is 0.9871 while plan 1 is 0.9737