Vigilance Decrement: A Signal-Detection Radar Watch

Watch Controls

Event rate 15 / min

Signal salience 0.65

Time acceleration 20×

Watch State

Elapsed (sim.)

00:00

Events seen

Sensitivity d′

—

Criterion c

—

Hit rate (last 20)

—

False-alarm rate

—

Watch not started.

How it works

This models the vigilance decrement: the well-documented drop in an observer's ability to detect rare signals over a sustained-attention task (Mackworth's radar/clock studies; Parasuraman & Davies). It is built directly on signal detection theory (SDT).

Each event: internal response x
  target present  → x = d'(t) + N(0,1)
  target absent    → x = N(0,1)
Respond "yes"       → x > c(t)

Hit           = target present & "yes"
Miss          = target present & "no"
False alarm   = target absent  & "yes"
Correct rej.  = target absent  & "no"

Sensitivity d'(t) decays exponentially with simulated time on watch, and the response criterion c(t) drifts upward (more conservative) — the classic pattern reported when event rate is high:

d'(t) = d0 · exp(−t / τ)
c(t)  = c0 + κ · t
d0, τ  scale with Signal salience
τ, κ   scale inversely with Event rate

Event rate — how often a radar blip (target or distractor) appears; higher rates accelerate the decrement, matching the classic finding that high-event-rate vigils fatigue faster than low-event-rate ones.
Signal salience — how discriminable a true target is from noise; higher salience raises baseline d′ and slows its decay.
Time acceleration — compresses a multi-minute watch into a short session so the decrement is visible without waiting in real time.

Watch the radar sweep: green rings are hits, dim red are misses, amber are false alarms, gray dots are correct rejections. As the shift wears on, green rings thin out and red/gray dots dominate even though nothing about the targets themselves has changed — only the observer's state has.

Hit Miss False alarm Correct rejection

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