Optimizing multivariate alarm systems: A study on joint false alarm rate, and joint missed alarm rate using linear programming technique

In modern complex industrial systems, multiple process variables interact with one another. The role of alarm systems in ensuring the safety of these systems is of utmost importance. Consequently, there is an increasing value placed on the assessment of the performance of multivariate alarm systems. As the dimensions of the system and the number of variables grow, designing optimal parameters for the multivariate alarm system using traditional approaches such as probability density function estimation becomes increasingly convoluted. In this paper, an approximate method is proposed for calculating two indices known as the Joint False Alarm Rate (JFAR) and Joint Missed Alarm Rate (JMAR), which are used to evaluate the performance of multivariate alarm systems. These indices are computed using the multivariate Markov chain method. The Markov chain is constructed by solving an optimal Linear Programming (LP) problem. Subsequently, joint indices are defined based on steady state estimations of a multivariate Markov chain. To validate the theoretical results obtained on the JFAR and JMAR and to demonstrate the proposed performance assessment and alarm system design procedures, numerical example and an industrial case study are provided.