The rating of a jet engine is the thrust performance that is guaranteed by the manufacturer for a new engine under specific operating conditions such as, take off, maximum continuous, climb, cruise.

Some non Prat and Whitney (P&W) engines are rated to a constant compressor speed (RPM). P&W rates there engines to a constant exhaust gas temperature (EGT). This is referred to as the flat rating concept. To get your head around this concept you must understand the following principle.

The temperature and density of the ambient air vary inversely.
Lower temperature = > Higher Density
Higher Temperature = >Lower Density

The amount of airflow (lbs/sec) through the engine is a function of compressor speed and air density. It is greater when the compressor speed and density are high.

The compressor speed is a function of the energy available to the compressors turbine. That energy comes from the combustion or air and fuel, so the turbine turns faster when the fuel flow rate is greater. The compressor speed is also a function of the airflow through the compressor. Higher rates of air flow reduce the speed of the compressor.

The compressors rotational speed and the amount of airflow through the compressor are independent, they affect each other though.

The turbine inlet temperature is proportional to the energy available to turn the turbine. The exhaust temperature is proportional to the turbine inlet temperature. So a higher EGT corresponds to a larger amount of energy to the turbine so it can turn the compressor faster.

When EGT is held constant, or lowered the result is a prolonged hot section life and at the same time provides the thrust to meet the certification requirements.

Clear as mud, OK.