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A general model of a complex technical system is considered. The system is built of multiple two-state components which can be either operable or failed. The functioning of a component is influenced in a specific way by the other components' states, thus the components are not mutually s-independent. Failures occur randomly, and are handled by several repair teams. If a repair team is available when a failure occurs, then the repair (or replacement) is started immediately; otherwise the component waits in the repair queue. It is assumed that each component's time to failure is exponentially distributed, and the failure intensity depends on the other components' states. No assumption is made about the components' repair time distributions. The model's complexity makes it impossible to analytically compute the parameters of the system's failure-repair process. For this reason, the sought parameters are evaluated using a combination of Monte Carlo simulation and statistical estimation. Finding the confidence interval is a non-trivial task. The first part of the paper is theoretical; the conditions under which the failure-repair process is recurrent are given, and the confidence intervals for the sought parameters are defined. The second part has an applicable character; a commodity transport network is considered as an exemplary system with inter-component dependencies, and the algorithm estimating its reliability parameters is presented with some illustrative examples.