This thesis presents the development of a system analysis model for a QEPAS (Quartz Enhanced Photo Acoustic Spectroscopy)-based trace gas detection system with pulsed-laser input and sample-mean test-statistic output. For this QEPAS-based system, the input laser signal is pulsed, and its beam is centered between the tines of a quartz tuning fork placed in a gas cell. If the trace gas is present, it absorbs the energy from the beam, resulting in the generation of an acoustic pressure wave P(r, t). This pressure wave strikes the fork tines causing them to vibrate at resonant frequency. These vibrations result in the flow of current within the tines, due to the piezoelectric effect. On obtaining the current flow signal waveform in the fork, and using statistical signal processing of multiple samples of this waveform, the trace gas can be detected and its concentration estimated. This analysis model will allow one to assess the performance of such a system for various parameter values that define a given system. The project involves the generation and assessment of solutions of differential equations for the pulsed-laser generated acoustic pressure wave, the resulting tuning-fork tines vibration, and the tuning fork generated current. This work is a different, but related, approach to that of N. Petra, et al., that considered a QEPAS-based system with a continuous-wave wavelength-sinusoidal-modulated laser signal [1].