A typical redundant signals experiment assesses response time (RT) performance when either of two (or more) presented signals is sufficient to make a correct response against response time to respond to either of the signals alone. In some studies perception of both signals takes place faster than either alone and even faster than what a parallel system with independent, unlimited capacity channels can predict. This behavior is referred to as super capacity (Townsend & Nozawa, 1995). In fact, J. Miller’s earlier 1982 data was interpreted as exhibiting performance that was so super capacity that it violated an upper bound on performance through a statistic known in mathematics as the Poisson Inequality, and now referred to in the literature as the race model inequality (RMI). The most popular type of explanatory model for these patterns assumes that information (treated as an activation random variable in each channel) from two parallel channels is summed into a subsequent single channel where the sum is compared with a criterion activation. Such a process is dubbed coactivation and several specific such models were shown to be able to account for RMI violations. Townsend and Nozawa (1995) later demonstrated that any arbitrary counter model (i.e., with arbitrary stochastic processes for the concurrent counters) perforce predicted violation of the RMI. Further, using the systems factorial technology statistical function named the survivor interaction contrast (SIC), which will be described below, they proved that standard Poisson counter models predict a specific distinctive function for coactive processing. However, they were able to derive the SIC signatures for other architectures (e.g., parallel and serial models) which were entirely general rather than being confined to Poisson counters. Subsequently, Houpt and Townsend (2011) generalized the SIC prediction for coactive models to the popular Ratcliff–Wiener drift–diffusion process. Our satisfied goal in the current work was to further extend the classes of coactive systems associated with this same SIC shape to the popular Linear Ballistic Accumulator (e.g., Brown & Heathcote, 2008), the entire class of Inhomogeneous Poisson Processes, and a novel system we call the bare bones stochastic process. In addition, we adduce a set of sufficient conditions that any monotone distribution should meet to predict for their convolution to obey the canonical SIC form.

The SIC functions on response times form a critical role in the experimental identification of mental (cognitive, perceptual, action, etc.) architectures combined with the pertinent decisional stopping rule as well as workload capacity (Townsend & Nozawa, 1995).1

Recall that the survivor function of a response time is the complement of the cumulative distribution function (i.e., S(t;ai,bj)=1−F(t;ai,bj) where F is the cumulative distribution function of time, ai indicates factor a at level i∈ low (l) or high (h), and the high level (h) selectively speeds up processing time of, say, subsystem A relative to the low level (l) (Dzhafarov, 2003, Schweickert, 1978, Townsend and Liu, 2022, Townsend and Schweickert, 1989). The simplest version of the SIC functions consist of a double difference of survivor functions across a factorial combination of 2 experimental factors at 2 levels (2 × 2). Thus, the SIC, an interaction contrast of survivor functions at the different factor levels, is given by, SIC(t)=S(t;l,l)−S(t;l,h)−S(t;h,l)−S(t;h,h).

For the classic results on identifying mental architectures to hold, selective influence of the factors on their respective subsystems must operate at least at the echelon of distribution ordering (Townsend, 1990a, Townsend and Liu, 2022). When selective influence holds, these continuous functions of times represent highly distinctive signatures of the various architectures plus stopping rule. The original predictions for the classical serial and parallel systems, along with the most popular stopping rules, are entirely distribution free. That is, the predictions are true for any stochastic processes obeying the definition of these architectures plus stopping rule. This paper will not go into detail regarding serial and parallel systems. The reader interested in more detail on those is referred to tutorials such as Algom et al. (2015), Townsend et al. (2018), Schweickert et al. (2012) or compendia containing theory and applications such as Little et al. (2017).

The case for coactive systems is more multifaceted and even thorny. To begin with, parallel and serial processing can be defined in a descriptive fashion, placing definitions on joint distributions of processing times. In contrast, coactive models are characterized through distributions on state spaces from the ground up. We here focus on investigating broader classes of coactive systems than have been covered heretofore.