The primary cooling unit in a nuclear power plant has a reliability of 0.95. There is alsoa back-up cooling unit to substitute for the primary unit when it fails. The reliability ofthe back-up unit is 0.85. The cooling system of the plant is considered reliable if eitherone of the systems is working. Assuming that the two systems are independent, thereliability of the cooling system of the power plant is:单项选择题
A
a. 0.95
B
b. 0.8075
C
c. 0.9925
D
d. 0.85

Question

The primary cooling unit in a nuclear power plant has a reliability of 0.95. There is alsoa back-up cooling unit to substitute for the primary unit when it fails. The reliability ofthe back-up unit is 0.85. The cooling system of the plant is considered reliable if eitherone of the systems is working. Assuming that the two systems are independent, thereliability of the cooling system of the power plant is:单项选择题

A

a. 0.95

B

b. 0.8075

C

c. 0.9925

D

d. 0.85

BlackTom AI · Accepted Answer

For systems arranged in parallel (system works if at least one component works), the system reliability R_system = 1 − P(all components fail). With independence, P(all fail) = product of individual failure probabilities.

1) Relevant concepts
- Reliability of a component Ri is the probability it functions.
- Failure probability = 1 − Ri.
- For independent components in parallel (either unit working suffices), system reliability = 1 − P(both fail) = 1 − [(1 − R1)(1 − R2)].

2) Step-by-step reasoning
- Primary unit reliability R1 = 0.95, so its failure probability = 1 − 0.95 = 0.05.
- Backup unit reliability R2 = 0.85, so its failure probability = 1 − 0.85 = 0.15.
- Independence allows multiplication: P(both fail) = 0.05 × 0.15.

3) Intermediate calculations
- Compute product: 0.05 × 0.15 = 0.0075.
- System reliability: R_system = 1 − 0.0075 = 0.9925.

4) Why this is correct
Because the cooling system is considered reliable if either the primary or the backup works, we treat the two units as parallel elements. The only way the overall system fails is if both units fail simultaneously. Using failure probabilities and independence gives the exact probability of joint failure (0.0075); subtracting from 1 yields the probability at least one works (0.9925).

5) Why the other options are incorrect
- a. 0.95: ignores the backup; this is just the primary’s reliability, not the combined system.
- b. 0.8075: equals 0.95 × 0.85, the reliability if both needed to work (series configuration), not applicable here.
- d. 0.85: equals the backup’s reliability alone and ignores the primary.

6) Conclusion
The correct combined reliability is 0.9925, which matches option c.

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