It is impossible to design a test that can detect something without the possibility of a false alarm (false positive). The only way to guarantee no false alarms is to never detect anything. When you design a test, you select the highest false alarm rate you can live with and then calculate the true positive rate based on the signal to noise ratio (SNR) and the type of test.
The relationship between the probability of false alarm and the probability of detection is shown by a receiver operator characteristic (ROC) curve (receiver, as in a radar receiver). ROC curves are used in radar, sonar, and many other applications. Below is a great example of a ROC curve.
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