The Alert Budget Explorer

Every exception report spends a hidden budget: the false alarms your team wades through to find the real problems. Set your team's false-alarm budget below and watch two detectors spend it very differently on the same 730 days of demand.

14.1×
The textbook ±3σ band promises one false alarm every 370 days (a 0.27% rate). On this real demand series it delivered a 3.80% false-alarm rate. That is 14.1 times more noise than the math on the slide promised, and it still caught only 1 of the 3 real events.

Spending the budget — both detectors at α = 1.00%

730 days of demand — markers show where each detector raised an alarm

The calibration gap — what you asked for vs. what you got

The dashed diagonal is perfect honesty: delivered = requested. The calibrated detector hugs it. The naive detector sits far above it, delivering several times the false-alarm rate you budgeted for.

What this means for your team

Source & reproducibility. Simulation: 730 days, one SKU, seed 42. Detector A (“naive”) is a static Gaussian band centred on the training mean μ = 227.0 with σ = 23.3; an alarm fires when demand leaves the ±kσ band, where k is chosen to match the requested α. Detector B (“calibrated”) uses an adaptive residual model (timemachines Laplace PIT) whose z-scores are recalibrated online. False-alarm rates are measured over the 500 evaluation days (71.4 weeks) after a 120-day warm-up, counting only days outside the three known event windows. All figures match the accompanying R/Python analysis for the post “Your Exception Report Is Lying to You.”