8.19 A sensor is used to monitor the performance of a nuclear reactor. The senso

Question

8.19 A sensor is used to monitor the performance of a nuclear reactor. The sensor accu ely reflects the state of the reactor with a probability of .97. But with a probability of.02, it gives a false alarm (by reporting excessive radiation even though the reac tor is performing normally), and with a probability of.01, it misses excessive radia- tion (by failing to report excessive radiation even though the reactor is performing abnormally). (a) What is the probability that a sensor will give an incorrect report, that is, either a false alarm or a miss? (b) To reduce costly shutdowns caused by false alarms, management introduces a sec- ond completely independent sensor, and the reactor is shut down only when both sensors report excessive radiation. (According to this perspective, solitary reports of excessive radiation should be viewed as false alarms and ignored, since both sen- sors provide accurate information much of the time.) What is the new probability that the reactor will be shut down because of simultaneous false alarms by both the first and second sensors? 1 l Beina more concerned about failures to detect excessive radiation, someone who lives near the nuclear reactor proposes an entirely diferent strategy: Shut down the reactor whenever either sensor reports excessive radiation of view, even a solitary report of excessive radiation should trigger a failure to detect excessive radiation is potentially catastrophic adopted, what is the new probability that excessive radiation will be neously by both the first and second sensors? (A ccording to this point a shutdown, since catastrophic.) If this policy were

Explanation / Answer

QUestion 8.19

here i am solving part(c) only.

Here Pr(acurately) = 0.97

Pr(False alarm) = 0.02 ; Pr(Missed excessive radiation) = 0.01

Here shut down the reactor whenever either sensor reports excessive radiation.

So,
Pr(Both of the sensors missed excessive radiation) = Pr(Sensor A missed radiation) * Pr(Sensor B also missed radiation) = 0.01 * 0.01 = 0.001

Related Questions

Navigate

• Browse (All)
• Browse 8
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.