The problem of fault detection in a turbojet engine is formulated as a binary programming problem by denning the output of the various units of the engine by an appropriate boolean equation. The objective function, which is required to be maximized, is a likelihood function, whereas the constraints describe the input-output relations of the units of the engine and prohibit non-causal illegal outputs. The results obtained by applying various test inputs and observing some of the outputs have been verified experimentally. A modified version of the method used is also proposed for fault diagnosis in large-scale systems.