A hierarchical k-out-of-n optimization model for enhancing reliability of fire alarm systems

Abstract

Fire alarm systems are crucial for mitigating the risks and damages associated with fires in process industries. These systems heavily depend on the performance of fire detection sensors to provide early detection and warnings, facilitating prompt evacuation and intervention measures. In order to improve the reliability of sensor systems typically requires the use of redundancy allocation techniques, such as a k-out-of-n configuration. In k-out-of-n configuration, the signals from all sensors are directed to a voter, which compares them and transmits a final signal once at least k signals are matched. However, challenges arise due to diverse failure modes with distinct impacts on the system. Integrating sensors through a single-layer k-out-of-n configuration, when there is only one voter, fails to fully highlight the potential advantages of redundancy in sensor systems. This paper addresses the limitations of the conventional configurations by introducing a hierarchical k-out-of-n system in which sensors can be integrated across multiple layers. In the k-out-of-n hierarchical system, sensors are organized into distinct groups, each employing its own k-out-of-n sub-system. Subsequently, the outputs of these sensor groups can be integrated with other groups through their respective voters in higher layers of the hierarchy. Ultimately, at the top layer, all the voters from the preceding layers must be connected to a top voter to transmit a final signal. Furthermore, an optimization model is developed to minimize the system cost while maximizing reliability, considering the best selection of sensors and the system configuration. The proposed optimization model takes into account a multi-sensor system with two competing failure modes and incorporates the probability of sensors' failure modes in the system. The hierarchical k-out-of-n system provides an opportunity to validate sensors by comparing them within their designated groups, allowing for the identification of the location of a failure and the planning of appropriate actions accordingly. The proposed optimization model is applied to a case of a fire detection system in storage warehouse to demonstrate its advantages over the conventional model.