  Critical parts of the definitions of standard serial and standard parallel
modes refer to stochastic independence. Standard serial models are defined by
stochastic independence and identical distributions of their processing times.
Processing times in the serial models are identical to the intercompletion time
statistics. Similarly, standard parallel models assume stochastically
independent and identical processing times. Their processing times are
equivalent to the statistic known as total completion times. Little is known
about what standard serial models can predict for the total completion time or
what standard parallel models can predict for the intercompletion times. Here
we demonstrate that standard serial models possess a tendency to predict a
positive dependence for the total completion times with that always being true
in the case of a single processing order. However, with mixtures of processing
orders, standard serial models may predict negative dependence of the total
completion times. Comparably, standard parallel models typically predict
neither independence of the intercompletion times nor identical distributions.
In fact, standard parallel models predict increasing intercompletion times as
the individual channels continue to finish. Nevertheless, dramatically
increasing hazard functions of the channels can defeat that tendency. And,
standard parallel models can predict intercompletion time independence but only
when individual channel distributions are exponential. Finally, we use these
and ancillary mathematical results to conclude that standard serial and
standard parallel models can never perfectly mimic one another. Therefore, our
findings set the stage for explicit model testing between these classes.
