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.

中文翻译：

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用于提高火灾报警系统可靠性的分层 k-out-of-n 优化模型


火灾报警系统对于降低与过程工业火灾相关的风险和损害至关重要。这些系统在很大程度上依赖于火灾探测传感器的性能来提供早期检测和警告，从而促进及时疏散和采取干预措施。为了提高传感器系统的可靠性，通常需要使用冗余分配技术，例如 k-out-of-n 配置。在 k-out-of-n 配置中，来自所有传感器的信号都定向到选民，选民会比较它们，并在至少匹配 k 个信号后传输最终信号。然而，由于不同的故障模式对系统的影响不同，因此出现了挑战。当只有一个选民时，通过单层 k-out-of-n 配置集成传感器无法充分突出传感器系统中冗余的潜在优势。本文通过引入分层 k-out-of-n 系统来解决传统配置的局限性，其中传感器可以跨多个层集成。在 k-out-of-n 分层系统中，传感器被组织成不同的组，每个组都有自己的 k-out-of-n 子系统。随后，这些传感器组的输出可以通过层次结构更高层中各自的选民与其他组集成。最终，在顶层，前几层的所有选民都必须连接到顶层选民才能传输最终信号。此外，还开发了一个优化模型，以最大限度地降低系统成本，同时最大限度地提高可靠性，同时考虑传感器的最佳选择和系统配置。 所提出的优化模型考虑了具有两种竞争故障模式的多传感器系统，并结合了系统中传感器故障模式的概率。分层 k-out-of-n 系统提供了一个机会，通过在指定组中比较传感器来验证传感器，从而识别故障位置并相应地规划适当的措施。将所提出的优化模型应用于仓库中的火灾探测系统案例，以证明其相对于传统模型的优势。