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A complete thermodynamic analysis of the cogeneration system based on molten carbonate fuel cell (MCFC) as the primary actuator and the Lithium / Bromide single-effect absorption chiller as a refrigerant generator to produce combined electricity, heat, and cold (CCHP) is introduced, modeled by EES, and examined. Some part of the results showed that by increasing the fuel utilization factor, M factor and the output Hydrogen of the MCFC decreases. In this study, the primary drive produced 770.08 and 891.57 heat and power, respectively. Thermodynamic analysis of the first scenario for this presented study showed that the energy and the exergy efficiency of the CCHP hybrid system are 87.85% and 86.62%, respectively. Results of risk analysis and reliability that have been studied for the first time in cogeneration systems show that the average time of the first failure for the molten carbonate fuel cell, polymer fuel cell, and absorption chiller, if they work normally, are 19459.57, 14074.04 and 86104.07 working hours, respectively. The economic efficiency and payback period of the second scenario by taking the inflation rate into account were calculated 6.3 and 3.2, respectively.