Question

If a part on a production line is present in an inspection area, a sensor detects...

If a part on a production line is present in an inspection area, a sensor detects it with probability 0.99. If a part is not present, the sensor generates a false alarm with probability 0.02. Assume that the probability of a part being present is 0.1.

a) What is the probability of seeing a false alarm?

b) What is the probability of having a missed detection?

Math   Statistics-And-Probability   
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Answer #1

Contingency table for the data given :

True Part on production
No part present Part present
P(D)=0.9 P(D)=0.1
0.9 0.1
Test positive Test negative Test positive Test negative
2.00% 98.00% 99.00% 1.00%
False Positive True Negative True positive False negative
0.018 0.882 0.099 0.001

Sensitivty = 0.99 = 99%

Specificity = 0.98 = 98%

(a) P(false alarm) = 0.018 (i.e. sensor generates a false alarm)

(b) P(missed detection) = 0.001 (i.e. false negative- part present but not detected)

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