A Probability-Based Reliability Model for Evaluating Ro-Ro Ferry Sailing-Speed Compliance on an Indonesian Short-Sea Route Using AIS Data
DOI:
https://doi.org/10.35870/ijsecs.v6i2.7589Keywords:
Automatic Identification System (AIS), Service-Speed Reliability, Probability Distribution, Weibull Distribution, Monte Carlo Simulation, Ro-Ro FerryAbstract
Automatic Identification System (AIS) data provide continuous operational records that can be transformed into computational indicators for evaluating maritime service performance. This study aims to develop an AIS-based probabilistic model for assessing Ro-Ro ferry service-speed reliability through sailing-speed compliance. Speed over Ground (SOG) observations were used to determine whether vessels operated within a predefined reliable speed range during sailing. The reliable speed range was defined as 7–9 knots based on the performance indicator required by the local transportation authority responsible for route licensing, while sailing observations were identified using a 3–15 knot SOG filter. From 32,358 raw AIS messages collected between 1 January and 31 March 2026, 11,166 sailing observations were retained. Observation-based reliability was 35.63%, while duration-based reliability was 36.63%, indicating that 324.76 of 886.64 estimated sailing hours were spent within the reliable speed range. Vessel-level analysis showed substantial variation, with two vessels recording duration-based reliability above 50% and two others below 10%. The Weibull distribution provided the best parametric fit, with an Akaike Information Criterion (AIC) of 44,051.48, the lowest among the fitted candidate distributions. The cumulative distribution function indicated a 35.88% probability of operating within the 7–9 knot range. Monte Carlo bootstrap resampling with 10,000 iterations produced 95% confidence intervals of 34.75–36.53% and 35.38–37.88% for observation-based and duration-based reliability, respectively. These findings indicate that AIS data can support a reproducible screening approach for evaluating aggregate and vessel-level ferry service-speed reliability.
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Amuta, E. O., Wara, S. T., Agbetuyi, A. F., & Sawyerr, B. A. (2022). Weibull distribution-based analysis for reliability assessment of an isolated power micro-grid system. Materials Today: Proceedings, 65, 2215–2220. https://doi.org/10.1016/j.matpr.2022.06.244
Arekar, K., Jain, R., & Kumar, S. (2021). Bayesian estimation of system reliability models using Monte-Carlo technique of simulation. Journal of Statistical Theory and Applications, 20(1), 149–163. https://doi.org/10.2991/jsta.d.210201.001
Betz, W., Papaioannou, I., & Straub, D. (2022). Bayesian post-processing of Monte Carlo simulation in reliability analysis. Reliability Engineering & System Safety, 227, Article 108731. https://doi.org/10.1016/j.ress.2022.108731
Capobianco, S., Millefiori, L. M., Forti, N., Braca, P., & Willett, P. (2021). Deep learning methods for vessel trajectory prediction based on recurrent neural networks. IEEE Transactions on Aerospace and Electronic Systems, 57(6), 4329–4346. https://doi.org/10.1109/TAES.2021.3096873
Clavijo-Blanco, J. A., González-Cagigal, M. A., & Rosendo-Macías, J. A. (2024). Statistical characterization of reliability indices in medium voltage networks using a Monte Carlo-based method. Electric Power Systems Research, 234, Article 110585. https://doi.org/10.1016/j.epsr.2024.110585
Deriba, A. Z., & Yang, D. Y. (2025). Performance-based risk assessment for large-scale transportation networks using the transitional Markov chain Monte Carlo method. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 11(1), Article 04024090. https://doi.org/10.1061/AJRUA6.RUENG-1402
Gómez, Y. M., Gallardo, D. I., Marchant, C., Sánchez, L., & Bourguignon, M. (2024). An in-depth review of the Weibull model with a focus on various parameterizations. Mathematics, 12(1), Article 56. https://doi.org/10.3390/math12010056
Labeau, P. E., & Zio, E. (2002). Procedures of Monte Carlo transport simulation for applications in system engineering. Reliability Engineering & System Safety, 77(3), 217–228. https://doi.org/10.1016/S0951-8320(02)00055-8
Li, H., Jiao, H., & Yang, Z. (2023a). AIS data-driven ship trajectory prediction modelling and analysis based on machine learning and deep learning methods. Transportation Research Part E: Logistics and Transportation Review, 175, Article 103152. https://doi.org/10.1016/j.tre.2023.103152
Li, H., Jiao, H., & Yang, Z. (2023b). Ship trajectory prediction based on machine learning and deep learning: A systematic review and methods analysis. Engineering Applications of Artificial Intelligence, 126, Article 107062. https://doi.org/10.1016/j.engappai.2023.107062
Li, Z., Fu, H., & Guo, J. (2025). Reliability assessment of a series system with Weibull-distributed components based on zero-failure data. Applied Sciences, 15(5), Article 2869. https://doi.org/10.3390/app15052869
Liang, M., Su, J., Liu, R. W., & Lam, J. S. L. (2024). AISClean: AIS data-driven vessel trajectory reconstruction under uncertain conditions. Ocean Engineering, 306, Article 117987. https://doi.org/10.1016/j.oceaneng.2024.117987
Martinčič, T., Štepec, D., Costa, J. P., Čagran, K., & Chaldeakis, A. (2020). Vessel and port efficiency metrics through validated AIS data. In Global Oceans 2020: Singapore–U.S. Gulf Coast (pp. 1–6). IEEE. https://doi.org/10.1109/IEEECONF38699.2020.9389112
Nguyen, D., Simonin, M., Hajduch, G., Vadaine, R., Tedeschi, C., & Fablet, R. (2020). Detection of abnormal vessel behaviours from AIS data using GeoTrackNet: From the laboratory to the ocean. In 2020 21st IEEE International Conference on Mobile Data Management (MDM) (pp. 264–268). IEEE. https://doi.org/10.1109/MDM48529.2020.00061
Nie, Y., Li, J., Liu, G., & Zhou, P. (2023). Cascading failure-based reliability assessment for post-seismic performance of highway bridge network. Reliability Engineering & System Safety, 238, Article 109457. https://doi.org/10.1016/j.ress.2023.109457
Oszczypała, M., Ziółkowski, J., & Małachowski, J. (2023). Modelling the operation process of light utility vehicles in transport systems using Monte Carlo simulation and semi-Markov approach. Energies, 16(5), Article 2210. https://doi.org/10.3390/en16052210
Pokorádi, L. (2024). Monte-Carlo simulation of reliability of system with complex interconnections. Vehicles, 6(4), 1801–1811. https://doi.org/10.3390/vehicles6040087
Singh, S. K., & Heymann, F. (2020). Machine learning-assisted anomaly detection in maritime navigation using AIS data. In 2020 IEEE/ION Position, Location and Navigation Symposium (PLANS) (pp. 832–838). IEEE. https://doi.org/10.1109/PLANS46316.2020.9109806
Vukša, S., Vidan, P., Bukljaš, M., & Pavić, S. (2022). Research on ship collision probability model based on Monte Carlo simulation and Bi-LSTM. Journal of Marine Science and Engineering, 10(8), Article 1124. https://doi.org/10.3390/jmse10081124
Wang, N., & Yuen, K. F. (2022). Resilience assessment of waterway transportation systems: Combining system performance and recovery cost. Reliability Engineering & System Safety, 226, Article 108673. https://doi.org/10.1016/j.ress.2022.108673
Wolsing, K., Roepert, L., Bauer, J., & Wehrle, K. (2022). Anomaly detection in maritime AIS tracks: A review of recent approaches. Journal of Marine Science and Engineering, 10(1), Article 112. https://doi.org/10.3390/jmse10010112
Xin, X., Liu, K., Yang, Z., Zhang, J., & Wu, X. (2021). A probabilistic risk approach for the collision detection of multi-ships under spatiotemporal movement uncertainty. Reliability Engineering & System Safety, 215, Article 107772. https://doi.org/10.1016/j.ress.2021.107772
Yan, Z., Xiao, Y., Cheng, L., He, R., Ruan, X., Zhou, X., Li, M., & Bin, R. (2020). Exploring AIS data for intelligent maritime routes extraction. Applied Ocean Research, 101, Article 102271. https://doi.org/10.1016/j.apor.2020.102271
Yang, C.-H., Wu, C.-H., Shao, J.-C., Wang, Y.-C., & Hsieh, C.-M. (2022). AIS-based intelligent vessel trajectory prediction using Bi-LSTM. IEEE Access, 10, 24302–24315. https://doi.org/10.1109/ACCESS.2022.3154812
Yang, D., Wu, L., Wang, S., Jia, H., & Li, K. X. (2019). How big data enriches maritime research: A critical review of automatic identification system (AIS) data applications. Transport Reviews, 39(6), 755–773. https://doi.org/10.1080/01441647.2019.1649315
Yang, Y., Liu, Y., Li, G., Zhang, Z., & Liu, Y. (2024). Harnessing the power of machine learning for AIS data-driven maritime research: A comprehensive review. Transportation Research Part E: Logistics and Transportation Review, 183, Article 103426. https://doi.org/10.1016/j.tre.2024.103426
Zang, Z., Xu, X., Qu, K., Chen, R., & Chen, A. (2022). Travel time reliability in transportation networks: A review of methodological developments. Transportation Research Part C: Emerging Technologies, 143, Article 103866. https://doi.org/10.1016/j.trc.2022.103866
Zohoori, S., Jafari Kang, M., Hamidi, M., & Maihami, R. (2023). An AIS-based approach for measuring waterway resiliency: A case study of Houston ship channel. Maritime Policy & Management, 50(6), 797–817. https://doi.org/10.1080/03088839.2022.2047813
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Copyright (c) 2026 Hardiyanto Hardiyanto, Andri Nofiar. Am, Teguh Widodo, Supria Supria, Depandi Enda, Zulyani Zulyani

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