Detector Sensitivity and Nuisance Alarm Rate Are One Setting, Not Two
Every detector reduces a noisy signal — light obscured in a chamber, a temperature rise, a ratio of infrared bands, a change in a camera image — to a yes by comparing it against a threshold. Move that threshold down and the device catches smaller and earlier fires, and in the same movement it starts calling steam, cooking aerosol, dust, welding arcs, vehicle exhaust and sun glinting off a windscreen. Move it up and both numbers fall together. You are not setting sensitivity and nuisance rate separately; you are choosing one point on a curve that trades detection probability against false alarm rate, and the threshold only slides you along it. What moves the whole curve to a better place is a better sensor, a second sensing mode that the nuisance source does not trigger, or an algorithm that uses persistence and shape rather than a single sample. The confusion resolved is the request for more sensitivity without more false alarms: that is a request for a different detector, not a different setting. After this Concept you can tell a threshold adjustment apart from a genuine improvement in a detection system.
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Every detector reduces a noisy signal — light obscured in a chamber, a temperature rise, a ratio of infrared bands, a change in a camera image — to a yes by comparing it against a threshold. Move that threshold down and the device catches smaller and earlier fires, and in the same movement it starts calling steam, cooking aerosol, dust, welding arcs, vehicle exhaust and sun glinting off a windscreen. Move it up and both numbers fall together. You are not setting sensitivity and nuisance rate separately; you are choosing one point on a curve that trades detection probability against false alarm rate, and the threshold only slides you along it. What moves the whole curve to a better place is a better sensor, a second sensing mode that the nuisance source does not trigger, or an algorithm that uses persistence and shape rather than a single sample. The confusion resolved is the request for more sensitivity without more false alarms: that is a request for a different detector, not a different setting. After this Concept you can tell a threshold adjustment apart from a genuine improvement in a detection system.
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