Dwarf spheroidal galaxies are excellent systems to probe the nature of fermionic dark matter due to their high observed dark matter phase-space density. In this work, we review, revise and improve upon previous phase-space considerations to obtain lower bounds on the mass of fermionic dark matter particles. The refinement in the results compared to previous works is realised particularly due to a significantly improved Jeans analysis of the galaxies. We discuss two methods to obtain phase-space bounds on the dark matter mass, one model-independent bound based on Paulis principle, and the other derived from an application of Liouvilles theorem. As benchmark examples for the latter case, we derive constraints for thermally decoupled particles and (non-)resonantly produced sterile neutrinos. Using the Pauli principle, we report a model-independent lower bound of $m geq 0.18,mathrm{keV}$ at 68% CL and $m geq 0.13,mathrm{keV}$ at 95% CL. For relativistically decoupled thermal relics, this bound is strengthened to $m geq 0.59,mathrm{keV}$ at 68% CL and $m geq 0.41,mathrm{keV}$ at 95% CL, whilst for non-resonantly produced sterile neutrinos the constraint is $m geq 2.80,mathrm{keV}$ at 68% CL and $m geq 1.74,mathrm{keV}$ at 95% CL. Finally, the phase-space bounds on resonantly produced sterile neutrinos are compared with complementary limits from X-ray, Lyman-$alpha$ and Big Bang Nucleosynthesis observations.
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