  We construct super Hamiltonian integrable systems within the theory of
Supersymmetric Poisson vertex algebras (SUSY PVAs). We provide a powerful tool
for the understanding of SUSY PVAs called the super master formula. We attach
some Lie superalgebraic data to a generalized SUSY W-algebra and show that it
is equipped with two compatible SUSY PVA brackets. We reformulate these
brackets in terms of odd differential operators and obtain super bi-Hamiltonian
hierarchies after performing a supersymmetric analog of the Drinfeld-Sokolov
reduction on these operators. As an example, an integrable system is
constructed from $\mathfrak{g}=\mathfrak{osp}(2|2)$.
