PDF-Based Technique for Univariate Alarm Systems and Its Application to Mixture Distributions

Abstract

Alarm systems play a significant role in ensuring safety and preventing incidents in industrial plants. Since a mixture distribution can model every unknown distribution function, this paper proposes a novel probability distribution function (PDF)-based method to design a univariate alarm system for variables with a mixture distribution. In this method, the alarm system has four operating modes (No alarm, Alarm, Ready to raise alarm, and Ready to clear alarm). The status of the alarm signal in each mode and transitions between these modes are determined based on the probability density values and the design parameters of the alarm system. For the proposed method, three performance indices, namely, false alarm rate (FAR), missed alarm rate (MAR), and mean time to alarm (MTTA), are computed, and the Monte Carlo approach verifies the results. The effectiveness of the proposed method is investigated through a case study (DAMADICS benchmark). Finally, the method’s performance is compared with that of the reset method for an alarm variable with unmixed PDF through a simulation example. The comparison results show that the proposed method provided more acceptable performance (especially in FAR and MAR indices) than the primary delay timer (reset method) for alarm variables with an unmixed distribution.