Averaged alarm delay and systematic design for alarm systems

The performance of a univariate alarm system can be assessed in many cases by three indices, namely, the false alarm rate (FAR), missed alarm rate (MAR) and averaged alarm delay (AAD). By contrast to the FAR and MAR, the AAD seemingly has been received litter attention. This paper firstly studies the definition and computation of the AAD for the basic mechanism of alarm generation solely based on a trip point, and for the advanced mechanism of alarm generation by exploiting alarm on-delays and moving average filters. Secondly, a systematic design for alarm systems is proposed based on the three performance indices. The trade-offs among FAR, MAR and AAD are investigated. Numerical examples are provided to validate the obtained theoretical results on the AAD and to illustrate the proposed alarm system design procedure.