  In this article we differentiate and characterize the standard two-process
serial models and the standard two process parallel models by investigating the
behavior of (conditional) distributions of the total completion times and
survivals of intercompletion times without assuming any particular forms for
the distributions of processing times. We address our argument through
mathematical proofs and computational methods. It is found that for the
standard two-process serial models, positive dependence between the total
completion times does not hold if no specific distributional forms are imposed
to the processing times. By contrast, for the standard two-process parallel
models the total completion times are independent. According to different
nature of process dependence, one can distinguish a standard two process serial
model from a standard two-process parallel model. We also find that in standard
two-process parallel models the monotonicity of survival function of the
intercompletion time of stage 2 conditional on the completion of stage 1
depends on the monotonicity of the hazard function of processing time. We also
find that the survival of intercompletion time(s) from stage 1 to stage 2 is
increasing when the ratio of hazard function meets certain criterion. Then the
empirical finding that the intercompletion time is grown with the growth of the
number of recalled words can be accounted by standard parallel models. We also
find that if the cumulative hazard function is concave or linear, the survival
from stage 1 to stage 2 is increasing.
