System-Level CBM/PBM Aggregation: A Unified Framework for Proactive and Reactive Metrics in Redundant Architectures
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Abstract
Assessing the in-service performance of Condition-Based Maintenance (CBM) and Predictive-Based Maintenance (PBM) solutions remains a challenge, as traditional reliability formulas often fail to capture the true nature of proactive operations. First, this paper formally proves that applying classic reactive formulas to CBM/PBM KPIs (Key Performance Indicators) leads to a quantifiable underestimation of the actual Mean Time Between Failures (MTBF). While previous work established aggregation laws for "in-series" equipment configurations, this study extends the mathematical framework to "in-parallel" architectures. Indeed, such specific aggregation laws are essential for evaluating the global performance of CBM/PBM solutions applied to fault-tolerant systems involving redundancy.
Subsequently, this paper introduces a unified theory based on two distinct frames of reference: the "Operational Timeline," using the Mean Time Between Proactive Removals (MTBPR) to measure logistical workload, and the "Effectiveness Timeline," using the Mean Lifetime Reduction (MLR) correction term to account for the residual life lost due to early removal. Following a review of the laws governing MTBF and the reliability function, we demonstrate the laws applicable to key CBM/PBM indicators, including Recall and Precision-based metrics.
Finally, this framework elevates equipment-level performance into system-wide strategic indicators. Ultimately, this enables a holistic evaluation of the global performance of a CBM/PBM solution at the system or aircraft level by balancing the Proactive Aggregated Recall (PAR) for detection coverage, and the Proactive Aggregated Precision (PAP) for detection confidence.
How to Cite
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PBM, CBM, System reliability, Aggregation laws, Redundant architecture, PHM KPI, Performance metrics
Fitzpatrick, M., & Paasch, R. K. (n.d.). Analytical method for the prediction of reliability and maintainability-based lifecycle labor costs.
Fu, S., & Avdelidis, N. P. (2023). Prognostic and health management of critical aircraft systems and components: An overview. PMC - PubMed Central.
Fu, S., Avdelidis, N. P., Plastropoulos, A., & Fan, I.-S. (2023). Fusion and comparison of prognostic models for remaining useful life of aircraft systems.
Goebel, K., & Rajamani, R. (2021). Policy, regulations and standards in prognostics and health management. International Journal of Prognostics and Health Management, 12(1).
Li, J., & Xu, H. (2012). Reliability analysis of aircraft equipment based on FMECA method.
Luna, J. J. (2021). Metrics, models, and scenarios for evaluating PHM effects on logistics support.
Maataoui, S., Bencheikh, G., Ezziani, M., & Bencheikh, G. (2024). Data-driven predictive analysis for cutting machine failures: A technical report on reliability optimization.
Meissner, R., Rahn, A., & Wicke, K. (2021). Developing prescriptive maintenance strategies in the aviation industry based on a discrete-event simulation framework for post-prognostics decision making.
Modarres, M. (2016). Reliability engineering and risk analysis: A practical guide (3rd ed.).
Romeu, J. L. (2006). Understanding series and parallel systems reliability.
SAE International. (2020). Integrated vehicle health management: The technology.
SAE International. (2023). JA6268: Design and run-time information exchange for health-ready components (1st ed. 2018).
Saxena, A., Celaya, J., Balaban, E., Goebel, K., Saha, B., Saha, S., & Schwabacher, M. (2008). Metrics for evaluating performance of prognostic techniques. In International Conference on Prognostics and Health Management.
Saxena, A., Celaya, J., Saha, B., Saha, S., & Goebel, K. (2010). Metrics for offline evaluation of prognostic performance. International Journal of Prognostics and Health Management.
Sen Gupta, J., Trinquier, C., Medjaher, K., & Zerhouni, N. (2015). Continuous validation of the PHM function in aircraft industry. In First International Conference on Reliability Systems Engineering (ICRSE) (pp. 1–7). doi: https://doi.org/10.1109/ICRSE.2015.7366505
Teubert, C., Jarvis, K., Corbetta, M., Kulkarni, C., & Daigle, M. (2022). ProgPy Python prognostic packages v1.4. Retrieved from https://nasa.github.io/progpy
Teubert, C., Pohya, A. A., & Gorospe, G. (2023). An analysis of barriers preventing the widespread adoption of predictive and prescriptive maintenance in aviation.
Torres, C. E. (2024). Challenges in implementing condition-based maintenance. Power-MI Blog.
Wagner, C., & Hellingrath, B. (2020). Supporting the implementation of predictive maintenance: A process reference model. In International Conference on Industrial Engineering and Operations Management.
Wei, P., Lu, Z., & Tian, L. (2013). Addition laws of failure probability and their applications in reliability analysis of structural system with multiple failure modes.
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