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We present an exact analytic expression for the Hong-Ou-Mandel manifold (HOMM) for any number of identical microring resonators (MRRs) in a linear chain. The HOMM is the higher-dimensional manifold of solutions for which the HOM effect is obtained; for the types of MRR systems investigated in this work, it is a one-dimensional curve. We investigate the extreme stability of this HOMM, showing that the HOM effect in linear arrays of MRRs is highly robust. We further use this expression to derive three figures of merit for the HOMM of linear chains of MRRs: the minimum MRR coupling value τ_{c}, the curvature of the one-dimensional HOMM ξ[over ¯]_{N}, and the 5% tolerance in the probability for complete destructive interference to occur on the HOMM δτ_{N}. We promote these metrics to characterize the pros and cons of various linear chains of MRRs and inform design and fabrication.