# Pre-Warning for the Remaining Time to Alarm Based on Variation Rates and Mixture Entropies

## TL;DR

This paper introduces a pre-warning system for industrial processes that predicts the remaining time before an alarm triggers, using variation rates and entropy measures to improve safety.

## Contribution

The novel contribution is a pre-warning method that combines variation rates and mixture entropy to estimate remaining alarm time and optimize thresholds using Bayesian estimation.

## Key findings

- The proposed method effectively estimates remaining time to alarm using variation rates and mixture entropy.
- Bayesian estimation helps determine optimal pre-warning thresholds by analyzing confidence intervals.
- Numerical and industrial examples demonstrate the method's effectiveness and advantages over existing approaches.

## Abstract

Alarm systems play crucial roles in industrial process safety. To support tackling the accident that is about to occur after an alarm, a pre-warning method is proposed for a special class of industrial process variables to alert operators about the remaining time to alarm. The main idea of the proposed method is to estimate the remaining time to alarm based on variation rates and mixture entropies of qualitative trends in univariate variables. If the remaining time to alarm is no longer than the pre-warning threshold and its mixture entropy is small enough then a warning is generated to alert the operators. One challenge for the proposed method is how to determine an optimal pre-warning threshold by considering the uncertainties induced by the sample distribution of the remaining time to alarm, subject to the constraint of the required false warning rate. This challenge is addressed by utilizing Bayesian estimation theory to estimate the confidence intervals for all candidates of the pre-warning threshold, and the optimal one is selected as the one whose upper bound of the confidence interval is nearest to the required false warning rate. Another challenge is how to measure the possibility of the current trend segment increasing to the alarm threshold, and this challenge is overcome by adopting the mixture entropy as a possibility measurement. Numerical and industrial examples illustrate the effectiveness of the proposed method and the advantages of the proposed method over the existing methods.