A production line has three machines A, B, and C, with reliabilities of .97, .90

Question

A production line has three machines A, B, and C, with reliabilities of .97, .90, and .91, 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.

Compute overall system reliability under Plan 1. (Round your intermediate calculations and final answer to 4 decimal places.)

Compute overall system reliability under Plan 2. (Round your intermediate calculations and final answer to 4 decimal places.)

A production line has three machines A, B, and C, with reliabilities of .97, .90, and .91, 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.

Explanation / Answer

a) Reliability =1-both lines will fail=1-(1-0.97*0.90*0.91)*(1-0.97*0.90*0.91) =0.9577

b)reliabilty=at least one of A will work*at least one of B will work*at least one of C will work

=(1-(1-0.97)*(1-0.97))*(1-(1-0.90)*(1-0.90))*(1-(1-0.91)*(1-0.91))=0.9811

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