A production line has three machines A,B,and C, with reliabilities of .99, .96,

Question

A production line has three machines A,B,and C, with reliabilities of .99, .96, and .93, respectively. The machines are arranged so that if one machine 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 will be used with reliabilities equal to the original three. the answer to which plan will provide the higher reliability is plan 2 =.9934 Please explain the answer.

Explanation / Answer

Reliability of line = 0.99*0.96*0.93 = 0.8839 Plan 1 Reliability of backup line = 0.8839 Reliability of system = 0.8839+(1-0.8839)*0.8839 = 0.9865 Plan 2 Reliability of system = (0.99+(1-0.99)* 0.99)*(0.96+(1-0.96)* 0.96)*(0.93+(1-0.93)* 0.93) =0.9934 So plan 2 is better

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