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We use Madan-Yor's argument to construct associated submartingales to a classof two-parameter processes that are ordered by the increasing convex dominance.This class includes processes which have MTP$_2$ integrated survival functions.We prove that the integrated survival function of an integrable two-parameterprocess is MTP$_2$ if and only if it is TP$_2$ in each pair of arguments whenthe remaining argument is fixed. This result can not be deduced from knownresults since there are several two-parameter processes whose integratedsurvival functions do not have interval support. The MTP$_2$ property ofcertain MRL processes is useful to exhibit numerous other processes having thesame property.

Mean residual life processes and associated submartingales