An advanced exergetic analysis converts the most important limitations of the conventional analysis into strengths. An advanced analysis provides options to estimate (a) the real potential for improving the components (splitting the exergy destruction into unavoidable and avoidable parts); and (b) the mutual interdependencies among the exergy destructions within the components of a system (splitting the exergy destruction into endogenous and exogenous parts). Distinctions between avoidable and unavoidable exergy destruction on one side and endogenous and exogenous exergy destruction on the other side (with a further splitting of the exogenous exergy destruction) allow engineers to focus on the thermodynamic inefficiencies that can be avoided by simultaneously considering the interactions among system components. The avoidable endogenous and the avoidable exogenous exergy destructions provide the best guidance for improving the thermodynamic performance of energy conversion systems. The drawbacks associated with the advanced exergetic analysis are the need for simulating some non-standard cycles (e.g., so-called hybrid cycles), the large number of required simulations and the associated engineering time. Within this Maple-aided analysis, the potential for improving the thermodynamic efficiency of components and the overall vapor-compression refrigeration system as well as the interactions among components and their effect on the exergy destruction within each component can be estimated.