This paper focuses on the development of a methodology to monitor the health of an engine by detecting any failures in the fuel injectors or in-cylinder pressure sensors using an accelerometer that is non-intrusively mounted on the engine block. A multi-cylinder engine with each cylinder having its own pressure sensor and injector is considered. First, a model relating the combustion component of the measured acceleration signal to the combustion component of in-cylinder pressure is proposed. Then, gains of the model are tuned to reduce the cycle-to-cycle estimation error by analyzing cycle-to-cycle variations with respect to the combustion pressure peak and engine vibration peak. Using the developed model, cylinder combustion pressures are estimated from engine vibration signals with small cycle-to-cycle estimation errors. Subsequently, a health monitoring system that can detect faults in pressure sensors, fuel injectors, and the accelerometers is proposed based on residues obtained from the difference between estimated combustion pressure and measured pressure signals. The source of the failed component can be identified uniquely by analyzing the pattern of residues. The proposed combustion pressure estimation algorithms are validated by extensive evaluation with experimental data obtained by operating a four-cylinder compression-ignition direct-injection engine with a range of experimental data. Finally, the developed health monitoring system is evaluated with various failure scenarios involving faults in the in-cylinder pressure sensor, fuel injector, and accelerometer.