A method is provided for monitoring operation of an engine (14). During this method, a database is provided for a parameter of the engine (14). The database includes a plurality of values for the parameter determined over a period of time. Confidence bands are established using a probability density function on the database. An action is performed in response to a comparison of a first updated value for the parameter to the confidence bands. The engine (14) may be configured as a gas turbine engine (14) or another type of heat engine.