Given any two univariate survival functions, not necessarily from the same class of the corresponding probability distributions. We present a new method for construction such bivariate survival functions that the two, given in advance, univariates become either the marginal or baseline distributions for it.

The constructed joint survival functions are given in two equivalent product forms which are universal.  Each bivariate model can be expressed in either form, one when using baseline distributions, and the other when the marginals are initially given. The simple and nice relationship between the two forms is expressed as the proven theorem. Both representations are always analytical representations of the same bivariate model, and each model possesses both the representations, which in some cases are analytically identical.

The representations yield a powerful tool for construction of new stochastic models with numerous applications such as reliability, biomedical problems and econometric. 

The universality of both the representations suggests to be an alternative to the copula methodology.