Sorry if this is a trivial question.
Let $ \mathfrak{X} $ be a model category such that all objects of $ \mathfrak{X} $ are fibrant. Then we have a total derived functor of the product $ \mathfrak{X}\times\mathfrak{X}\to\mathfrak{X} $, because, in this case, by the Ken Brown's Lemma, the product functor preserves weak equivalences.
However, I wonder if there are conditions which assure that the product reflects weak equivalences.
Thank you in advance