  We consider interacting many particle systems with quenched disorder having
strong Griffiths singularities, which are characterized by the dynamical
exponent, z, such as random quantum systems and exclusion processes. In several
d=1 and d=2 dimensional problems we have calculated the inverse time-scales,
t^{-1}, in finite samples of linear size, L, either exactly or numerically. In
all cases, having a discrete symmetry, the distribution function, P(t^{-1},L),
is found to depend on the variable, u=t^{-1}L^{z/d}, and to be universal given
by the limit distribution of extremes of independent and identically
distributed random numbers. This finding is explained in the framework of a
strong disorder renormalization group approach when, after fast degrees of
freedom are decimated out the system is transformed into a set of
non-interacting localized excitations. The Frechet distribution of P(t^{-1},L)
is expected to hold for all random systems having a strong disorder fixed
point, in which the Griffiths singularities are dominated by disorder
fluctuations.
