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A production line has 2 machines A, B, and C, with reliabilities of .97, .87, and .88...

Question:

A production line has 2 machines A, B, and C, with reliabilities of .97, .87, and .88 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.

B. Compute overall system reliability under Plan 2.

C. Which plan will provide the higher reliability?

Reliability:

Reliability is the probability that a machine, a component, a process, or a product functions properly during a specific time period. The reliability of a system can be improved by adding redundancy, either in the form of backups or parallel paths to the system.

Answer and Explanation:

Answer to Question A:

Probability that the original production line works properly = {eq}0.97 \times 0.87 \times 0.88 = 0.742632 {/eq}

Probability...

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Probability of Simple, Compound and Complementary Events

from Math 102: College Mathematics

Chapter 13 / Lesson 5
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