We show how to use Jantzen's sum formula for Weyl modules to prove semisimplicity criteria for endomorphism algebras of Uq-tilting modules (for any field 핂 and any parameter q∈핂−{0,−1}). As an application, we recover the semisimplicity criteria for the Hecke algebras of types A and B, the walled Brauer algebras and the Brauer algebras from our more general approach.