The thermodynamic performance of real irreversible cooling and refrigeration systems (chillers) can be summarized in simple rectangular temperature-entropy diagrams, in analogy to classic pedagogical examples for idealized reversible devices. The key to translating complex dissipative losses into this graphical framework is the process average temperature - a factor that can be calculated from nonintrusive experimental measurements, for converting entropy production into lost work. An uncomplicated thermodynamic model is used to transform the governing chiller performance equations into an easily-interpreted graph. Examples based upon actual data from commercial work-driven (reciprocating) and heat-driven (absorption) chillers are presented, and are used to highlight the predominance of internal dissipation in determining chiller efficiency. With the thermodynamic diagram representation, the relative roles of each irreversibility source, as well as the reversible and endoreversible limits, become transparent.