Permutation Entropy and Ordinal Patterns as a Resilience Indicator

Resilience quantification in production systems is essential for making informed decisions. This paper introduces a novel resilience indicator derived from time-series data of system availability. The proposed approach involves symbolic time-series analysis where the availability data is discretized into symbolic sequences. Each symbol in the sequence represents a range of availability values. Using these symbolic sequences, we apply permutation entropy based on ordinal patterns to assess system complexity and resiliency. The methodology is exemplified through a case study involving two production systems with different availability profiles. The symbolic sequences are generated based on predefined thresholds and labeled as “High,” “Medium,” and “Low” availability. Unique ordinal patterns are identified, and their frequencies are calculated to derive the permutation entropy for each system. Special emphasis is placed on dramatic performance declines and spikes, with these events weighted differently in the entropy calculations. Our results indicate that the proposed resilience indicator is computationally efficient and robust to noise and variability, making it ideal for realtime analysis of large datasets. Comparative entropy values provide insights into the relative resilience of the systems under study. The system with lower entropy demonstrated greater regularity and, by extension, higher resilience. This innovative approach promises a new avenue for quantifying resilience in complex systems. Future work will focus on empirical validation in various applications and continuous refinement of the underlying algorithm.