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.

中文翻译：

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优化多变量警报系统：使用线性规划技术的关节误报率和关节漏报率的研究


在现代复杂的工业系统中，多个过程变量相互交互。警报系统在确保这些系统安全方面的作用至关重要。因此，对多变量警报系统性能的评估越来越重要。随着系统维度和变量数量的增加，使用传统方法（如概率密度函数估计）为多变量警报系统设计最佳参数变得越来越复杂。在本文中，提出了一种近似方法来计算两个指数，即联合误报率 （JFAR） 和联合漏报率 （JMAR），用于评估多变量警报系统的性能。这些指数是使用多元马尔可夫链方法计算的。马尔可夫链是通过解决最优线性规划 （LP） 问题构建的。随后，根据多元马尔可夫链的稳态估计定义联合指数。为了验证在 JFAR 和 JMAR 上获得的理论结果，并演示所提出的性能评估和警报系统设计程序，提供了数值示例和工业案例研究。