Per-session outlier detection — the diagnostic counterpart to cost-burn's aggregate-trend signal.
| Question | Skill |
|---|---|
| "Is the AGGREGATE rate accelerating?" | cost-burn |
| "Which SPECIFIC sessions are anomalous outliers?" | cost-anomaly ← this |
| "Could we have spent less in aggregate?" | cost-counterfactual |
| "When will we hit budget?" | cost-projection |
Algorithm
Implementation: scripts/anomaly.mjs.
- Read all
session-*records fromcost-trackingnamespace. - Filter to
--sincewindow (default: all-time). - Compute
median(total_cost_usd)andMAD = median(|x - median|). - Per-session modified z-score (Iglewicz-Hoaglin 1993):
z = 0.6745 * (x - median) / MAD - Flag sessions with
|z| > --threshold(default 3.5).
Why MAD and not mean + sigma?
| Approach | What breaks |
|---|---|
mean + sigma | A single $50 session inflates BOTH mean and sigma so badly that subsequent outliers hide inside the new "normal" band. Catastrophic on small samples. |
median + MAD | Both estimators ignore up to 50% of the data — the outliers themselves can't shift them. Robust on n=10. The canonical cutoff |z| > 3.5 is from Iglewicz-Hoaglin (1993). |
Smoke transcript (5 baseline sessions $0.08-$0.12 + 1 outlier $5.00)
| Sessions considered | 5 |
| Threshold (|modified z|) | 3.5 |
| Median spend | $0.100000 |
| MAD | $0.010000 |
| Min / Max | $0.080000 / $5.000000 |
| **Outliers found** | **1** |
## Outlier sessions
| Session | Spend | Deviation | Modified z | Direction |
| outlier- | $5.000000 | +$4.900000 | 330.505 | high |
Exit codes
$ cost anomaly --alert-on-outliers 1
⚠ ALERT: found 1 outlier session(s) (|modified z| > 3.5); threshold was ≥1
exit 1
$ cost anomaly --alert-on-outliers 5
✓ found 1 outlier session(s); under threshold ≥5 — OK
exit 0
CI integration
# Fail the build if any session this week is a >3.5σ outlier
cost anomaly --since 7d --alert-on-outliers 1 || investigate-bad-session
Most useful when paired with cost-burn:
cost burn --alert-on-acceleration-pct 50 || page-oncall # rate-of-change alert
cost anomaly --alert-on-outliers 1 || investigate # point-anomaly alert
Together they cover "is the average shifting?" AND "is there a single rogue session?" — both can fire independently.
Edge cases
- n < 3: emit "Insufficient data" message, exit 0. MAD on 1-2 samples is meaningless.
- MAD = 0: ≥50% of sessions share the exact same spend, so z-scores collapse. Emit explainer instead of dividing by zero. Common cause: dry-run sessions all at $0.
- Low-direction outliers: usually crashed or dropped sessions, not over-spending. The output table explicitly labels direction so operators interpret correctly.
- Very small MAD: even tiny absolute deviations produce huge z-scores. The $5 outlier with MAD=$0.01 yields z=330 — that's correct, not a bug.
Direction column
| Direction | Likely cause | Action |
|---|---|---|
high | Long session, stuck in expensive tier, or runaway loop | cost report + cost conversation to investigate |
low | Crash, dropped session, or unfinished work | Verify the session completed normally |