3.3.Modelling Sources of Variability Adequate representation of the sources of variability is the element that distinguishes a robust simulation model from a mere animation of a flow diagram. The main sources of variability in an underground mining operation are the following: Hang-ups and oversized material. Hang-ups and the generation of oversized material are disturbances that reduce the availability of drawpoints and generate secondary breaking and hang-up clearing activities that consume productive time of loading equipment. Their frequency depends on the cumulative extraction height at each point and the rock mass characteristics of the sector and must be modelled using distributions calibrated from historical records by geotechnical domain. Unscheduled equipment failures. Both mobile equipment and MHS equipment are subject to unscheduled failures that take them out of service for variable periods. Their modelling requires time-between-failure and repair time distributions fitted to historical maintenance data, differentiating between failure types according to their cause and typical duration. Planned operational interferences. Shift changes, meal breaks, fuel loading, safety inspections, equipment cleaning, and scheduled maintenance are planned events that, collectively, represent a significant fraction of shift time. Their omission from the model produces systematically optimistic capacity estimates that do not reflect operational reality. Variability in operating parameters. Loading times, travel speeds, and equipment maneuvering times are not fixed values, but distributions influenced by operator experience, infrastructure condition, and working point conditions. Their representation through statistical distributions rather than average values allows the model to correctly reproduce the variability observed in real records. 3.4.Calibration Process and Number of Replications Model calibration follows an iterative process: the model is built with parameters derived from available data, an initial number of replications is run, results are compared with historical records using formal statistical tests, and parameters are adjusted until statistical equivalence is achieved. The standard calibration and validation approach, described by Banks et al. (2005) and elaborated by Law (2015), uses formal statistical tests to compare model output distributions with historical distributions. The Student's t-test evaluates the equivalence of means; Anderson-Darling or Kolmogorov-Smirnov tests evaluate distributional similarity. A model that passes these tests on the calibration period data, and then correctly reproduces an independent validation period, provides a solid foundation for future scenario projections. The number of replications required to obtain statistically robust results is determined empirically, monitoring the convergence of the cumulative mean and variance
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