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In this article we differentiate and characterize the standard two-processserial models and the standard two process parallel models by investigating thebehavior of (conditional) distributions of the total completion times andsurvivals of intercompletion times without assuming any particular forms forthe distributions of processing times. We address our argument throughmathematical proofs and computational methods. It is found that for thestandard two-process serial models, positive dependence between the totalcompletion times does not hold if no specific distributional forms are imposedto the processing times. By contrast, for the standard two-process parallelmodels the total completion times are independent. According to differentnature of process dependence, one can distinguish a standard two process serialmodel from a standard two-process parallel model. We also find that in standardtwo-process parallel models the monotonicity of survival function of theintercompletion time of stage 2 conditional on the completion of stage 1depends on the monotonicity of the hazard function of processing time. We alsofind that the survival of intercompletion time(s) from stage 1 to stage 2 isincreasing when the ratio of hazard function meets certain criterion. Then theempirical finding that the intercompletion time is grown with the growth of thenumber of recalled words can be accounted by standard parallel models. We alsofind that if the cumulative hazard function is concave or linear, the survivalfrom stage 1 to stage 2 is increasing.

A Theoretical Study of Process Dependence for Standard Two-Process Serial Models and Standard Two-Process Parallel Models