Question

In: Operations Management

A production line has three machines A, B, and C, with reliabilities of .90, .95, and...

A production line has three machines A, B, and C, with reliabilities of .90, .95, 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.

a. Compute overall system reliability under Plan 1. (Round your intermediate calculations 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.)

Reliability

Expert Solution

Let reliability for A = Ra = 0.90

Rb = 0.95

Rc = 0.91

If machines are arranged so that if one breaks down, the others must shut down; this means that the machines are in series.

Hence, Overall Reliability of the line Rs = Ra * Rb * Rc = 0.90 * 0.95 * 0.91 = 0.7781

Plan 1:

Back-up is added in parallel. Overall system reliability under Plan 1 = Rp1= 1 - (1 - Rs) * (1 - Rs) = 1 - (1-0.7781)*(1-0.7781) = 0.9508

Plan 2:

Reliability of A with back-up = Rpa = 1 - (1 - Ra) * (1 - Ra) = 1 - (1 - 0.90) * (1 - 0.90) = 0.9900

Reliability of B with back-up = Rpb = 1 - (1 - Rb) * (1 - Rb) = 1 - (1 - 0.95) * (1 - 0.95) = 0.9975‬

Reliability of C with back-up = Rpc = 1 - (1 - Rc) * (1 - Rc) = 1 - (1 - 0.91) * (1 - 0.91) = 0.9919‬

Overall system reliability under Plan 2 = Rp2= Rpa * Rpb * Rpc = 0.9900 * 0.9975 * 0.9919 = 0.9795

a. Overall system reliability under Plan 1 = 0.9508

b. Overall system reliability under Plan 2 = 0.9795

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keosha answered 3 months ago

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