A Door-Exit Witness for Night Wandering: Detecting the Departure, Pricing the Minutes

A camera-free, wearable-free door-exit witness design for night wandering by a person with dementia living alone: door contact and threshold pressure mats, a sequence rule with detection delay T, a computed false-alarm rate per month (cat and doorstep cases modelled explicitly), a response chain and square-law search area, and a cold-exposure clock at -2 C. At T=10 minutes the model gives 1.30 false alarms per month, search beginning 17.5 minutes after departure over 2.81 km2, 24.5 minutes before the stated exposure limit, with overall detection of 58.8% of wandering departures under the stated assumptions. SIMULATED, NOT MEASURED.