  We report the detection and analysis of the red giant branch luminosity
function bump in a sample of isolated dwarf galaxies in the Local Group. We
have designed a new analysis approach comparing the observed color-magnitude
diagrams with theoretical best-fit color-magnitude diagrams derived from
precise estimates of the star formation histories of each galaxy. This analysis
is based on studying the difference between the V-magnitude of the RGB bump and
the horizontal branch at the level of the RR Lyrae instability strip
(Delta_vhbb) and we discuss here a technique for reliably measuring this
quantity in complex stellar systems. By using this approach, we find that the
difference between the observed and predicted values of Delta_vhbb is +0.13 +/-
0.14 mag. This is smaller, by about a factor of two, than the well-known
discrepancy between theory and observation at low metallicity commonly derived
for Galactic globular clusters. This result is confirmed by a comparison
between the adopted theoretical framework and empirical estimates of the
Delta_vhbb parameter for both a large database of Galactic globular clusters
and for four other dSph galaxies for which this estimate is available in the
literature. We also investigate the strength of the red giant branch bump
feature (R_bump), and find very good agreement between the observed and
theoretically predicted R_bump values. This agreement supports the reliability
of the evolutionary lifetimes predicted by theoretical models of the evolution
of low-mass stars.
