21. Nuclear power plants have redundant components in important systems to reduc

Question

21. Nuclear power plants have redundant components in important systems to reduce the chance of catastrophic failure. Assume that a plant has two gauges to measure the level of coolant in the reactor core and that each gauge has probability 0.01 of failing. Assume that one potential cause of gauge failure is that the electric ca- bles leading from the core to the control room where the gauges are located may burn up in a fire. Someone wishes to estimate the probability that both gauges fail, and makes the following calculation: P (both gauges fail) = P (first gauge fails) P (second gauge fails) = (0.01)(0.01) = 0.0001 What assumption is being made in this calculation? Explain why this assumption is probably not justi- fied in the present case. a. b. c. Is the probability of 0.0001 likely to be too high or too low? Explain.

Explanation / Answer

a) An assumption of independence of failure in the two gauges is being made here.

b) This assumption is not justified because failing of gauges due to electrical cables buring is not independent. If cables burn, both gauges may fail at the same time.

c) Probability of 0.0001 is too low in this case. Actual probability can be thought to be closer to 0.01 if correlation is 1 between the two gauges.

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