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Critical parts of the definitions of standard serial and standard parallelmodes refer to stochastic independence. Standard serial models are defined bystochastic independence and identical distributions of their processing times.Processing times in the serial models are identical to the intercompletion timestatistics. Similarly, standard parallel models assume stochasticallyindependent and identical processing times. Their processing times areequivalent to the statistic known as total completion times. Little is knownabout what standard serial models can predict for the total completion time orwhat standard parallel models can predict for the intercompletion times. Herewe demonstrate that standard serial models possess a tendency to predict apositive dependence for the total completion times with that always being truein the case of a single processing order. However, with mixtures of processingorders, standard serial models may predict negative dependence of the totalcompletion times. Comparably, standard parallel models typically predictneither independence of the intercompletion times nor identical distributions.In fact, standard parallel models predict increasing intercompletion times asthe individual channels continue to finish. Nevertheless, dramaticallyincreasing hazard functions of the channels can defeat that tendency. And,standard parallel models can predict intercompletion time independence but onlywhen individual channel distributions are exponential. Finally, we use theseand ancillary mathematical results to conclude that standard serial andstandard parallel models can never perfectly mimic one another. Therefore, ourfindings set the stage for explicit model testing between these classes.

A Theoretical Study of Process Dependence for Critical Statistics in Standard Serial Models and Standard Parallel Models