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We present an analytical model for measuring the dispersion of integrated waveguides, leveraging the Michelson interferometry effects observed in devices with chirped Bragg gratings. Building on our previous experimental work, we derived a theoretical framework that simulates the group delay and subsequent dispersion values from the reflected spectrum of a device under test (DUT) which is a linearly chirped Bragg grating fabricated on a silicon-on-insulator (SOI) platform. This model incorporates the principles of interference fringes generated by reflections within the waveguide, enabling a precise calculation of group delay (τ) in the DUT as a function of frequency. Our model predicts the dispersion by determining the spacing between the peaks (Δf) from the local period of the interferometric fringes, with τ being inversely proportional to Δf. Simulations were conducted on a DUT that is designed to produce a dispersion of -45.9 ps2. The model yielded a dispersion of -45.6 ± 0.67 ps2, demonstrating close alignment with both the theoretical design and our experimental results, which recorded a dispersion of -45.5 ± 11.2 ps2 from 7 different DUTs that were measured.