Sampling in mining: TOS-based consulting, audits & QA/QC

Sampling in mining is the process of collecting representative portions of material -ore, rock, slurry or processed product- to determine grade, mineralogy, and other characteristics. It forms the foundation of every critical decision from exploration through production. Sampling data drives resource estimation, mine planning, grade control, metallurgical accounting, and process optimization.

The challenge is that we cannot measure entire ore bodies or process streams. All decisions -resource estimation, mine planning, grade control, process optimization, metallurgical accounting- rely on samples. If those samples are not representative, every decision downstream carries unquantified error.

The Theory of Sampling (TOS) is the scientific framework for collecting representative samples from heterogeneous materials such as ores, concentrates, slurries, and process streams. Developed by Pierre Gy, TOS classifies all sampling errors into seven categories and provides the principles needed to control or eliminate each.

A core finding: the overall measurement error (OE) equals the Total Sampling Error (TE) plus the Analytical Error (AE). In most mining operations, TE dominates AE making sampling system design the primary lever for improving data quality (Brochot, TOS forum, 2015, DOI: 10.1255/tosf.73).

TOS is embedded in AMIRA P754 code for metallurgical accounting and is the methodological basis for sampling audits required by NI 43-101 and JORC.

By applying TOS, CASPEO helps mining companies design sampling systems that deliver reliable, defensible, and decision‑ready data, from exploration to final product shipment.

Pierre Gy’s Theory of Sampling identifies seven types of sampling errors:

• Fundamental Sampling Error (FSE) from material heterogeneity of constitution, controlled through adequate sample mass
• Grouping and Segregation Error (GSE) when particles are not taken individually and separate by size or density during sampling
• Delimitation Error (DE) from incorrect sampling geometry where equipment doesn’t assure equiprobability
• Extraction Error (EE) when particles near the sample boundary are incorrectly included or excluded
• Integration Error (IE) from material heterogeneity of distribution when time-based composite sampling misses process variations
• Preparation Errors (PE) from contamination, losses, or alterations during sample handling
• Analytical Error (AE) from laboratory measurement uncerainty

In mineral processing, FSE, GSE, and IE typically dominate. Delimitation errors from worn or poorly designed cross-stream samplers can introduce severe, systematic bias.

▶️ This article could interest you

Brochot, S. (2015). The overall measurement error – TOS and uncertainty budget in metal accounting. TOS forum, 2015(5), 83-86. https://doi.org/10.1255/tosf.73

▶️ This article could interest you

Brochot, S. & Mounié, F. (2015). Placer gold sampling — the overall measurement error using gravity concentration on particle size ranges during sample treatment. TOS forum, 2015(5), 43-50. https://doi.org/10.1255/tosf.65

Fundamental Sampling Error (FSE) is the irreducible random error arising from the natural variability in how valuable minerals are distributed within individual ore particles, the heterogeneity of constitution. It contributes approximately 50% of total sampling variance in most mining operations.

FSE cannot be eliminated, only minimized. Pierre Gy’s formula calculates the required sample mass to achieve a target FSE for a given ore and particle size. Collecting a 2 kg sample when the target precision requires 10 kg guarantees unreliable results regardless of laboratory quality.

The financial impact of sampling errors is systematic and quantifiable.

Published case studies document losses from hundreds of thousands to tens of millions of dollars per year from biases that were undetected without a proper audit.

• Hidden production losses
  Case of a copper smelter with hidden bias in slag sampling
  Manual sampling every 2 hours missed systematic matte entrainment in slags.
  Bias: 0.29 percentage points Cu (0.66% detected vs 0.95% actual).
  Annual loss: USD 9.54 million (350 days × 1,000 t/day × 0.29% Cu × USD 9,400/t)
  Secondary effect: the imbalance accumulated as phantom copper in Work-In-Progress inventories reaching physically impossible figures and triggering accounting adjustments that impacted the company’s stock market valuation.

• Commercial disadvantage in metal trading
  Case of copper concentrate trading where measurement uncertainty shifts commercial power
  Delivery: 17,000 t,
  Provisional Cu grade (seller): 26.000%
  Smelter grade (buyer): 25.825%
  Difference: 0.175 percentage points
  Value at stake on one lot: approximately USD 280,000With a TOS-correct sampling system: annual benefit for the smelter up to USD 1 million per year

These cases share a common pattern: the financial loss was ongoing, undetected, and correctable. In each case, the cost of the sampling improvement was recovered within months. The loss before correction had accumulated for years.

▶️ Cases studies extracted from this article

Brochot, S. (2021). Metal accounting: a direct link between sampling and financial management. Spectroscopy Europe, vol. 33, no. 7.

Poor sampling introduces two types of error into grade estimaton:

• bias (systematic deviation)
• excess variance (random scatter)

Sampling bias of just 0.1% absolute grade might seem small but translates to millions in misclassified ore or incorrect resource statements for large deposits. Grade control bias sends ore to waste dumps or dilutes mill feed with barren rock, both destroying economic value.

High sampling variance widens confidence intervals on grade estimates, forcing wider drill-hole spacing or higher cut-off grades.

Reconciliation discrepancies between mine and mill grades typically trace back to sampling problems rather than actual material losses. But without a proper sampling audit, the root cause remains unidentified.

▶️ This article could interest you

Brochot, S. (2021). Metal accounting: a direct link between sampling and financial management. Spectroscopy Europe, vol. 33, no. 7.

Best practices for sampling in the mining industries include:

• Calculating correct sample mass to control fundamental sampling error using Pierre Gy’s formula based on material heterogeneity and target precision
• Using correct sampling equipment geometry (delimitation) that extracts representative portions following the Principle of Equiprobability and Centre of Gravity
• Positioning sampling points to capture true material variability while minimizing bias
• Minimizing preparation errors through proper comminution, correct splitting, and contamination prevention protocols
• Implementing robust QA/QC monitoring with certified reference materials (standards), blank samples, and duplicates at statistically justified insertion rates
• Following Theory of Sampling principles throughout the sampling chain from collection through analysis
• Maintaining and calibrating equipment regularly to prevent drift
• Training personnel in correct sampling techniques
• Documenting all protocols to ensure consistency and regulatory compliance with NI 43-101, JORC Code, and AMIRA guidelines

Three reporting codes govern sampling requirements for publicly listed mining companies:

• NI 43-101: Canadian standard for disclosure of mineral projects; requires qualified person sign-off on sampling procedures
• JORC Code: Australian/international standard for public reporting of exploration results, mineral resources, and ore reserves
• AMIRA P754: best-practice standard for metallurgical accounting; defines 10 principles including representative sampling and uncertainty quantification

All three require that sampling protocols be designed, documented, and audited against recognized technical standards, primarily Pierre Gy’s Theory of Sampling.

ECHANT is CASPEO’s software for sampling protocol design and sample mass calculation in mineral processing operations. It implements Pierre Gy’s TOS formulas to calculate the Fundamental Sampling Error (FSE) for a given ore and particle size, and determines the minimum sample mass required to achieve a specified precision target.

CASPEO uses ECHANT within consulting engagements to produce defensible, calculated sample mass specifications replacing rules of thumb with quantified, ore-specific protocol design. It is an everyday tool that mining engineers, geologists, and metallurgists can use confidently to design better sampling programs and maintain data quality.

▶️ Test ECHANT sampling software for free here