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The developments of energy storage and substitution techniques have made it possible for customers to self-schedule their energy consumption behaviors, to better satisfy their demands in response to uncertain supply conditions. The interdependency of multiple energies, the chronological characteristics, and uncertainties in the self-scheduling context bring about additional complexities to secure the reliable energy requirements of multi-energy customers. As a necessary and challenging task, the operational reliability of multi-energy customers is tackled in this paper. Considering that the consumed energies eventually come down to the energy-related services, the self-scheduling of multi-energy customers is implemented from the perspective of specific energy-related services rather than energy carriers. Firstly, an optimal self-scheduling model for multi-energy customers is developed with the consideration of chronological service curtailment, service shifting and possible failures during service shifting. In the optimal self-scheduling model, the costs of service curtailment and shifting are formulated based on the proposed evaluation method. The time-sequential Monte Carlo simulation approach is applied to model the chronological volatilities of multi-energy demands over the entire study period, embedded with a scenario reduction technique to reduce the computational efforts. Taking full account of the possible scenarios, the quantitative reliability indices of the multi-energy customers can be obtained. The results in test cases demonstrate that the expected energy not supplied of the multi-energy customer drops significantly by 56.32% with the self-scheduling strategy. It can be also concluded that, the self-scheduling and its inherent uncertainties do have significant impacts on the operational reliability of the multi-energy customer.