TITLE:
Modeling the Random Failure of the B3 Jaw Crusher Using the Euler-Maruyama Method: Determination of the Critical Intervention Threshold at KTC
AUTHORS:
Lumpungu Mabeya Deguy, Meni Babakidi Narcisse
KEYWORDS:
Random Failure, Optimization, Critical Intervention Threshold, Euler-Maruyama Method, Predictive Maintenance, Monte Carlo Simulation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.11,
November
11,
2026
ABSTRACT: The progressive functional degradation of the B3 jaw crusher, a critical asset in the mineral processing circuit of the Kamoto Concentrator (KTC, Kamoto Copper Company), causes random shutdowns that threaten production continuity. This study proposes a stochastic model to determine when the crusher should be serviced. Functional performance is described by an Itô-type stochastic differential equation with a degradation drift proportional to the current state and additive Brownian noise, solved with the Euler-Maruyama method and coupled with Monte Carlo simulation. The degradation rate is calibrated so that the expected time to functional failure matches the mean time between failures observed over one year of operation (11 major failures), and the condition of the crusher is checked at weekly inspections. The intervention threshold is optimized by minimizing the long-run average direct maintenance cost per operating day. The optimal threshold is C* = 0.40, giving a mean cycle of 17.7 operating days, a preventive share of 95% and an average direct cost of 312 USD per operating day, against 609 USD for the observed run-to-failure practice—a direct saving of about 80,000 USD per year. The optimum is stable with respect to the time step and moderately sensitive to volatility, degradation rate and inspection interval; with monthly inspections, most interventions become corrective, which explains the current situation. The approach provides a basis for condition-based maintenance of the crusher within a sensor-fed Computerized Maintenance Management System (CMMS).