Question

It is known that the system operational temperature under the normal good condition follows the normal distribution N(30, 4). The engineer wants to develop a monitoring system to monitor whether the mean of operational temperature is changed based on a sample average of 9 temperature measurements at every hour.

(1) if alpha=5%, can you suggest the rejection thresholds? (i.e., when the sample average of 9 temperature measurements falls in your suggested rejection range, your decision is that the system is not operated under the normal condition).

(2) if another engineer has already made the rejection range with L=28 and U=32 (i.e., if the sample average is less than L=28 or larger than U=32, the normal condition is rejected), can you help judge what is the false alarm rate of this decision rule?

Answer 1