1987
DOI: 10.1177/001872088702900603
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A Two-Term Exponential Functional Description of the Time Course of Sustained Attention

Abstract: A consensus of critical reviews of single-process theories of vigilance or sustained attention has supported the view that the vigilance decrement must be the result of two or more coacting or interacting processes or systems. One theoretical position, as well as the ubiquity of exponential functions in characterizing the time course of biological processes, led to the hypothesis that the time course of sustained attention could be best modeled by the function A[e-T1-time 11(1 + eT2*time)]. An experimental t… Show more

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Cited by 30 publications
(29 citation statements)
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“…First, we extracted the linear slope of the reciprocal of reaction times (RRT). Additionally, we measured two parameters based on a least-squares fit to a two-component exponential function [39], which has been found to account for more of the variance in TOT than a simple linear fit. The equation used was:where A is a multiplicative constant and t is time from test onset.…”
Section: Methodsmentioning
confidence: 99%
“…First, we extracted the linear slope of the reciprocal of reaction times (RRT). Additionally, we measured two parameters based on a least-squares fit to a two-component exponential function [39], which has been found to account for more of the variance in TOT than a simple linear fit. The equation used was:where A is a multiplicative constant and t is time from test onset.…”
Section: Methodsmentioning
confidence: 99%
“…Since increasing time on task is presumably correlated with changes in several variables (e.g., facets of arousal, fatigue, task engagement, or effort investment), the functional interpretation of time-related changes in brain activity might benefit from a moderation analysis approach, which examines how within-subject associations between brain and performance or subjective state are moderated by time on task, including non-linear relationships (cf. Giambra & Quilter, 1987). …”
Section: Limitations and Future Directionsmentioning
confidence: 99%
“…At the beginning of task execution, FP(t) is 1 and declines as time on task elapses, which causes production utilities to decrease. This equation reflects mathematical characterizations of the vigilance decrement, which has fit exponential functions to vigilance data (Giambra & Quilter, 1987). The probability of microlapses is influenced by the utility values of the productions and the utility threshold.…”
Section: Fatigue Mechanismsmentioning
confidence: 99%