A use of Bayes' theorem for insight of false alarm rates

Using Bayes' theorem, the false alarm rate is shown to be a function of the reliability of the monitored functional system, the reliability of the built-in-test (BIT) system, and the coverage by the BIT of the monitored functional system. Partial differentiation of the false alarm rate formula reveals that the false alarm rate varies inversely with BIT reliability, inversely with BIT coverage, and directly with the monitored functional system reliability. Improving a functional system's reliability increases the false alarm rate, even though there is no change in the frequency of false alarm events. Therefore a false alarm rate requirement may deter functional circuit design improvement. This paper advocates categorizing the sources of false alarm events in a system since false alarms rates can sometimes be relatively high due to the complexity of an adequate BIT.