Authors : Lumpungu Mabeya Deguy; Lumanji Mbunga Luc; Meni Babakidi Narcisse

Volume/Issue : Volume 11 - 2026, Issue 9 - September

Google Scholar : https://tinyurl.com/amjcjjtb

DOI : https://doi.org/10.38124/ijisrt/26sep1403

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.

Abstract : Unplanned stoppages of the B3 jaw crusher, the entry point of the comminution line at the Kamoto Concentrator (KTC) of Kamoto Copper Company, interrupt ore supply to the downstream mills and generate costly production losses. This paper treats the timing of maintenance on this ageing machine as a decision under uncertainty. A normalised performance indicator P(t) is described by the Itô equation dP(t) = −μP(t)dt + σdW(t), integrated with the Euler–Maruyama scheme and explored through Monte Carlo sampling. The preventive trigger level C is selected by minimising a renewaltype cost rate that weighs planned against unplanned interventions. The full probability law of the critical time is then characterised, including its skewness and kurtosis. The cost-optimal trigger is C* ≈ 0.42, giving a mean cycle of about 52 days, a cost rate of 5,800 USD/day and a 70 % share of preventive interventions. The critical time is right-skewed (skewness 1.23) and leptokurtic (kurtosis β₂ = 5.65, excess 2.65), whereas the Brownian increments and the performance level at fixed dates remain mesokurtic (β₂ ≈ 3.0). The probability of reaching C* is 0.15 at day 30, 0.61 at day 52 and 0.84 at day 70, and a Weibull law (β = 2.48) fits the critical time well. Field validation over seven months gives MAE = 7.71 % and RMSE = 8.32 %. A Random Forest regressor trained on vibration, temperature, current, throughput and operating hours reaches R² = 0.81 on a chronological test set. Both approaches are complementary and can be coupled within a sensor-fed CMMS.

Keywords : Jaw Crusher; Stochastic Differential Equation; Euler–Maruyama Scheme; First-Passage Time; Failure Probability; Kurtosis; Monte Carlo; Random Forest; Condition-Based Maintenance.

References :

1. AFNOR. (1988). X60-500: Terminologie relative à la fiabilité, la maintenabilité et la disponibilité. Association Française de Normalisation.
2. AFNOR. (2018). NF EN 13306: Maintenance – Terminologie de la maintenance. Association Française de Normalisation.
3. Barlow, R. E., & Hunter, L. C. (1960). Optimum preventive maintenance policies. Operations Research, 8(1), 90–100. https://doi.org/10.1287/opre.8.1.90
4. Birolini, A. (2023). Reliability engineering: Theory and practice. Springer.
5. Bousdekis, A., & Kokkinis, D. (2024). Data-driven decision-making methods for Industry 4.0 maintenance applications. Electronics, 13(1), 1–25.
6. Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32. https://doi.org/10.1023/A:1010933404324
7. Chhikara, R. S., & Folks, J. L. (1989). The inverse Gaussian distribution: Theory, methodology, and applications. Marcel Dekker.
8. DeCarlo, L. T. (1997). On the meaning and use of kurtosis. Psychological Methods, 2(3), 292–307. https://doi.org/10.1037/1082-989X.2.3.292
9. Dyer, D., & Stewart, R. M. (1978). Detection of rolling element bearing damage by statistical vibration analysis. Journal of Mechanical Design, 100(2), 229–235. https://doi.org/10.1115/1.3453905
10. Elsayed, E. A. (2021). Reliability engineering (3rd ed.). Wiley.
11. Gharaei, R., & Salehi, M. (2024). A multi-method machine learning framework for simulating power dynamics in an iron ore cone crusher plant. Mineral Processing and Extractive Metallurgy Review. Advance online publication.
12. Giles, M. B. (2008). Multilevel Monte Carlo path simulation. Operations Research, 56(3), 607–617. https://doi.org/10.1287/opre.1070.0496
13. Glasserman, P. (2004). Monte Carlo methods in financial engineering. Springer.
14. Higham, D. J. (2001). An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Review, 43(3), 525–546. https://doi.org/10.1137/S0036144500378302
15. Hu, Y., Zhang, X., & Wang, L. (2025). A nonlinear Wiener process degradation model with damage resistance for reliability analysis. Annals of Operations Research, 169–192.
16. Jardine, A. K. S., Lin, D., & Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mechanical Systems and Signal Processing, 20(7), 1483–1510. https://doi.org/10.1016/j.ymssp.2005.09.012
17. Joanes, D. N., & Gill, C. A. (1998). Comparing measures of sample skewness and kurtosis. Journal of the Royal Statistical Society: Series D (The Statistician), 47(1), 183–189.
18. Kamoto Copper Company. (2025). Historique du concasseur B3, 03/10/2024–03/10/2025 [Données internes]. KCC.
19. Kloeden, P. E., & Platen, E. (1992). Numerical solution of stochastic differential equations. Springer.
20. Kumar, M., Sharma, R., & Patel, V. (2023). Probabilistic modeling of wear and fatigue degradation in mechanical systems. Journal of Mechanical Engineering Science, 2456–2469.
21. Li, X., & Anderson, T. L. (2016). Reliability modeling of multiple performance based on degradation processes. Advances in Mechanical Engineering, 8(11), 1–12.
22. Maruyama, G. (1955). Continuous Markov processes and stochastic equations. Rendiconti del Circolo Matematico di Palermo, 4(1), 48–90.
23. Mobley, R. K. (2002). An introduction to predictive maintenance (2nd ed.). Butterworth-Heinemann.
24. O'Connor, P. D. T., & Kleyner, A. (2012). Practical reliability engineering (5th ed.). Wiley.
25. Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., & Duchesnay, É. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12, 2825–2830.
26. Randall, R. B. (2011). Vibration-based condition monitoring: Industrial, aerospace and automotive applications. Wiley.
27. Saxena, A., Goebel, K., Simon, D., & Eklund, N. (2008). Damage propagation modeling for aircraft engine run-to-failure simulation. In 2008 International Conference on Prognostics and Health Management (pp. 1–9). IEEE.
28. Si, X.-S., Wang, W., Hu, C.-H., & Zhou, D.-H. (2011). Remaining useful life estimation – A review on the statistical data driven approaches. European Journal of Operational Research, 213(1), 1–14. https://doi.org/10.1016/j.ejor.2010.11.018
29. Silva, R., & Ferreira, J. (2024). Stochastic modeling and sensitivity analysis in preventive maintenance scheduling. Journal of Industrial Engineering and Management, 55–70.
30. Sudadiyo, S. (2025). Nonhomogeneous Poisson process model for estimating mean time between failures of the JE01-AP03 primary pump implemented on the RSG-GAS reactor. Nuclear Technology, 211, 645–660.
31. Tabatabaei, S. A. (2021). Effect of feed rate on comminution products by fractal geometry. Amirkabir Journal of Civil Engineering.
32. Trivedi, K. S., & Bobbio, A. (2017). Reliability and availability engineering: Modeling, analysis, and applications. Cambridge University Press.
33. Uhlenbeck, G. E., & Ornstein, L. S. (1930). On the theory of the Brownian motion. Physical Review, 36(5), 823–841. https://doi.org/10.1103/PhysRev.36.823
34. Villemeur, A. (1995). Sûreté de fonctionnement des systèmes industriels : Fiabilité, facteurs humains, informatisation. Eyrolles.
35. Wang, Q. (2025). Dynamic reliability modeling and analysis of gear wear based on Wiener process thresholds. Scientific Reports, 15, 1–14.
36. Westfall, P. H. (2014). Kurtosis as peakedness, 1905–2014. R.I.P. The American Statistician, 68(3), 191–195. https://doi.org/10.1080/00031305.2014.917055
37. Ye, Z.-S., & Xie, M. (2015). Stochastic modelling and analysis of degradation for highly reliable products. Applied Stochastic Models in Business and Industry, 31(1), 16–32. https://doi.org/10.1002/asmb.2063
38. Zhang, H. W., & Liu, S. (2025). Condition-based maintenance for multi-state systems with prognostic and deep reinforcement learning. Reliability Engineering & System Safety, 255.