  Most of the stochastic orders for comparing random variables, considered in
the literature, are afflicted with two main drawbacks: (i) lack of connex
property and (ii) lack of consideration of any dependence structure between the
random variables. Both these drawbacks can be overcome at the cost of
transitivity with the stochastic precedence order, which may seem to be a good
choice in particular when only two random variables are under consideration, a
situation where the question of transitivity does not arise. In this paper, we
show that even under such favorable conditions, stochastic precedence order may
direct to misleading conclusion in certain situations and develop variations of
the order to address the phenomenon.
