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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 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. Which plan will provide the higher reliability?

b. Explain why the two reliabilities are not the same.

c. What other factors might enter into the decision of which plan to adopt?

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Answer: plan B is better

Explanation:

Machines _____reliability

__A__________ 0.99

__B__________ 0.96

__C__________ 0.93

Backup machines A, B, C also have similar probabilities :

PLAN 1:

P(success) = 0.99 * 0.96 * 0.93 = 0.8839

P(line fails) = 1 - 0.8839 = 0.1161

P(backup) = 0.99 * 0.96 * 0.93 = 0.8839

P(success) + [p(line fails) * p(backup)]

0.8839 + (0.1161 * 0.8839)

0.8839 + 0.10262079

= 0.9865

Plan B:

Backup is provided for each machine ;

P(success) + [p(line fails) * p(backup)] for each of machine A, B and C

Machine A:

0.99 + (1 - 0.99)*0.99 = 0.9999

Machine B:

0.96 + (1 - 0.96)*0.96 = 0.9984

Machine C:

0.93 + (1 - 0.93)*0.93 = 0.9951

A*B*C = 0.9999 * 0.9984 * 0.9951 = 0.9934

Plan B has greater probability of success.

2.) plan A provides a central or one single backup option should any of the machines fail. However, plan B provides separate backup options for each of machines A, B and C.

3.) choosing a plan may also depend on the cost of providing each backup plan.

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