A 7.2-Second System Inside a 15-Minute Budget

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

A 7.2-Second System Inside a 15-Minute Budget

A fall detector is designed backward from a 15-minute clinical response window: subtract 8 minutes for the ambulance, and the entire IoT contribution — fall confirmation plus the notification chain — is just 7.2 seconds, leaving a 6.9-minute caregiver window. Yet across 500 patients the same system fires about 502 alerts a day, of which only 2 are real falls. If the IoT link is that small a slice of the budget while false alarms swamp the real ones, where does the engineering leverage actually lie?

Companion to the chapter Elderly Care and Fall Detection — every number here comes from that chapter.

Ada: Two of this chapter’s numbers drive design decisions: the caregiver window carved out of the 15-minute clinical budget, and the daily alert volume behind the alert-fatigue warning. Let me rebuild both from the stated inputs.

  • Clinical budget: 15 x 60 = 900 s; after an 8-minute EMS commitment, 900 - 480 = 420 s remain.
  • System latency: 5.1 + 2.1 = 7.2 s of detection plus notification.
  • Caregiver window: 420 - 7.2 = 412.8 s, i.e. 412.8 / 60 = 6.88 min, the stated 6.9 minutes.
  • Alert volume for 500 patients at 95% sensitivity and 95% specificity: true positives 0.95 x 2 = 1.9, false positives 0.05 x 10,000 = 500, total 501.9, about 502 alerts/day.
  • Alert reliability: 1.9 / 501.9 = 0.38% of alerts are real falls.
  • (One caution: the worked example’s “43% safety margin” does not follow from these inputs – the caregiver-window basis gives 412.8 / 900 = 45.9%, and the designed 5-minute cascade leaves 15 - (5 + 8 + 0.12) = 1.9 minutes of slack, so the honest figures are ~46% or ~1.9 min, not 43%.)

The core figures reconcile. The design meaning is a study in scale: the entire IoT contribution – 7.2 seconds – is trivial against the roughly 13 minutes owned by humans and EMS, while 500 daily false alarms swamp fewer than 2 real falls, so the engineering leverage lives in the escalation ladder and in pushing specificity past 99% with sensor fusion, not in shaving milliseconds off inference.

Every number above is taken from the chapter’s own material and re-derived step by step.