# Duplicate measures

> RPD = 2× HARD; tolerances widen up the chain

Source: https://geodb.io/guide/topic/qaqc_duplicate_measures/ · Category: QAQC
Two precision statistics dominate duplicate QC, and **mixing them up
silently doubles or halves every threshold**:

- **HARD** = |x₁−x₂| / (x₁+x₂) × 100
- **RPD** = |x₁−x₂| / mean × 100 — **exactly 2× HARD**

A "10% pulp criterion" means opposite things depending on which statistic
is meant. Always label which one a chart or threshold uses.

## The tolerance ladder

Precision degrades up the sampling chain, so tolerance widens with it:

| Duplicate type | Typical tolerance (RPD) | What it monitors |
|---|---|---|
| Field / twin | **30%** | sampling + prep + analysis + geology |
| Coarse / prep | **20%** | prep + analysis + geology |
| Pulp / lab | **10%** | analysis only |

## The better form: population rules

Per-pair pass/fail on nuggety mineralisation generates meaningless
failures. The population form ranks pairs by HARD and asks what fraction
beat the line: **pulp 90% under 10%, coarse 80% under 10%, field 70%
under 10%** — the "90/80/70" ranked-HARD rule. Aggregate variants ("no
more than 10% of pairs outside tolerance") serve the same purpose.

For precision as a function of grade, the **Thompson–Howarth** method
(pairs sorted by concentration, grouped in 11s, median-based regression)
is the standard chart — use robust regression, never ordinary least
squares.

## In geoDB

geoDB judges duplicate pairs on **RPD**, with warnings out to 1.5× the pass
threshold:

| Duplicate type | geoDB pass threshold |
|---|---|
| Field / twin | **20%** |
| Coarse / prep | **20%** |
| Pulp / lab | **10%** |

Our **field** threshold is tighter than the industry's 30% — deliberate,
and a change we'd measure before making.

A project can set a **per-element override** (e.g. Au = 15%). An override
tightens any tier, and may loosen only the **field** tier: field tolerance
is your deposit's variability, while the coarse and pulp tolerances are the
lab's precision, which a per-element preference shouldn't relax.

Pairs near the detection limit are judged on absolute difference instead —
see *Duplicates near DL*. Each row on the certificate page says which test
produced its verdict.

The duplicate charts plot RPD; ranked-HARD and Thompson–Howarth plots
aren't built into the pages yet — ask Petra when you need one.