Francis Pitard

Sampling Theory and Methods: Reasons for Courses Prepared and Presented by Francis F. Pitard Francis Pitard Sampling Consultants, LLC

Your decisions are only as good as your samples! Communicating the importance of Correct Sampling

 to management,

 to the board,

 to shareholders,  to geologists and drillers,  to miners and metallurgists,  to analytical chemists,  to statisticians,  to sales people, to get cash flow, more profit, and added share value. 1

Responsibility of a Mining Company

If stakeholders cannot see the value of correct sampling, it is the company’s responsibility to show them through…  Education of management to get resources,  Training of key personnel to get results,  Education of geologists, miners, metallurgists to monitor and verify the quality of data, So statisticians can perform reliable, believable risk assessments.

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Acquisition of a reliable database as a company asset

A correct, balanced strategy is needed: The three-legged Table Company $ benefits, added stakeholder value, and market perception

Emphasis on causes of problems by proactive management

A strong commitment to good sampling and good laboratory practices

Capability to understand variability and to perform reliable statistical studies

Francis Pitard's drawing protected by copyright law, 2004

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However, implementing correct sampling is easier said than done.

Exactly like safety issues, it must…  be internally standardized through:  correctness,

 internal guidelines,  sustained training,  enforcement auditing.  be monitored for its added value through:  improved metal recovery,  improved conciliation,  added stakeholder value.

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Course attendees must learn to better understand variability:

 Small-scale variability, which can be called the Irrelevant Variability: It is a nuisance.  Large-scale variability, which can be called the Relevant Variability: It is the one we must measure to know our processes better. 5

Small-scale Variability: The term V[0] in a variogram

The four solutions to minimize a catastrophic inflation of V[0] are:  Optimizing Sampling Protocols,  Implementing Sampling Protocols using correct sampling systems,  Preserving samples integrity,  Minimizing the Analytical Error.

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Optimization of Sampling protocols

Three critically important issues:  In situ Nugget Effect INE (e.g., Selection of diameter/length of a core sample)

 Fundamental Error FSE (e.g., sample and sub-samples mass)

 Grouping & Segregation Error GSE (e.g., Homogenization and number of increments)

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The Practical Implementation Of Sampling Protocols The nightmare of sampling

Three major sources of sampling bias:  Increment Delimitation Error IDE (Every part of the lot to be sampled must have exactly the

same chance of becoming part of the sample.)

 Increment Extraction Error IEE (The sample recovery error: The sampling system must not be selective.)

 Increment Weighting Error IWE (Sampling systems must be reasonably proportional.)

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Preserving the Integrity of Samples

Another major source of sampling bias:  Increment Preparation Errors IPE (Errors taking place between sampling stages)

 Contamination  Losses

 Alteration  Human errors, ignorance  Fraud

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Practical exercise 1: Sampling of Blast-holes Name the possible error (IDE, IEE, IWE, or IPE?) taking place at each of the following points, and give solutions. You have 10 minutes.

F

E D

Segregation

G

Ideal sample Actual sample

A

Former Sub-drill

C

Current Sub-drill

B

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Practical Exercise 2: Primary Sampler for the Feed of a Plant Name the possible error (IDE, IEE, IWE, or IPE?) taking place at each of the following points, and give solutions. You have 10 minutes. 1

11

3 6 7

5

4

2

9 10

8

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Practical Exercise 3: The Rotating Vezin Sampler A very common sampler in the mining industry

Name the possible error (IDE, IEE, IWE, or IPE?) taking place at each of the following points, and give solutions. You have 10 minutes.

2

6

3

9 Falling stream

4

5 7

10

11

8 1

Francis Pitard's drawing protected by copyright law, 2004

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Practical Exercise 4: The Cross-belt Sampler A very popular, dangerous sampling system Name the possible error (IDE, IEE, IWE, or IPE?) taking place at each of the following points, and give solutions. You have 10 minutes.

7 6

4

1 2 3

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Why is it that a training course is so essential?

Because all the possible problems created by each point addressed in the 4 exercises, that should be solved within minutes, usually are the object of unnecessary…  doubts and arguments,  time-consuming meetings,  endless arguments with manufacturers and engineering firms,  very expensive bias tests followed by doubtful statistics,

furthermore,… because each point can lead to devastating money losses for the unaware company. Let’s give a few stunning examples. 14

Case #1: A bad protocol followed by incorrect implementation

Large Copper mine in northern Chile:

US $ 134 000 000 loss difference between a bad sampling and subsampling protocol and a better one, for blast-holes, over a 10-year period.

P. Carrasco: WCSB1, Denmark 2003

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Case #2: An incorrect sampling system for the tailings of a floatation plant

Example of a large Copper mine in Chile:

US $2 000 000 000 loss through tailings over a 20-year period

P. Carrasco: WCSB1, Denmark 2003

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Summary: Who are the enemies?

2 S IDE n 2 S IWE n

n

S

2 FSEn

S

n

n

2 GSEn

n

S

2 HE1

2 S AE n

V [0]

n

2 S INE Francis Pitard's drawing protected by copyright law, 2004

2 S IPE n

2 S IEE n

n

n

Remember this sign:

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Large-scale Variability: The variability you need to see to optimize your operations

When the small-scale variability overwhelms the large-scale variability relevant to optimize your operations, the following problems take place:  Endless meetings to solve puzzles, argue, and finger pointing,  Correcting factors are applied until data fit normality,  Geologists and Geostatisticians cannot do their work,  Miners and metallurgists are at war,  Company’s performance deteriorates,  Management is not happy,  Market share value goes down.

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Large-scale Variability: Why and where is it important?

 To find new natural resources  To quantify natural resources  To show reasonable continuity of natural resources  To understand conciliation problems during mining

 To optimize processes at mines and plants  To raise the quality of products  To secure fair money return from products  To diminish penalties  To curtail fraud  To minimize environmental liability  To lift the market perception of the company’s fiscal health  To improve profitability trends

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Large-scale Variability: What are the main components? During Exploration

 It is important to measure the anisotropy of a geological unit.  Grade trends may be different North-South than East-West or than along a vertical axis.  Variogram ranges need to be defined in different directions.  Density of drilling needs to be optimized in different directions.  Ore continuity and zone of influence need to be defined in different directions.  A reliable geological model must be created.

With a large V[0] these critically important tasks, leading to a reliable feasibility study, become weak. 20

Large-scale Variability: What are the main components? During Mining

 Selection of ore grade control drilling pattern, and drilling density  Selection of a Kriging technique  Selection of a realistic, economic cutoff grade  Selection of a pit design  Selection of an acceptance level for conciliation differences between ore grade control and the geological model

With a large V[0] these critically important tasks, leading to a reliable recovery of natural resources, become weak. 21

Large-scale Variability: What are the main components? During Processing

 Believable metallurgical accounting needs to monitor performance.  Control of key process parameters need to be implemeted.  Process trends need to be tamed in due time.  Process cycles, always very costly, need to be identified and either eliminated or minimized.  Reliable control charts must be updated at many places.

With a large V[0] these critically

 Over-correction of the process must be important tasks, leading to a reliable prevented.

recovery of natural resources, become weak.

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Large-scale Variability: What are the main components? During Trade with Customers

Customers like a fair price, but hate bad surprises on product quality. Penalty application is a common way of doing business: “What costs me must cost you!”  You cannot control the quality of a product after the fact, but you should implement the many things that lead to a good product, from the geological model, to the mine, and to the plant.

With a large V[0] these critically important tasks, leading to a reliable quality of products, become weak.

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A long list of benefits and opportunities: How can good sampling practices give access to all this?

 Good Sampling Practices, just like Good Laboratory Practices, is the heart of the management decision process.  Decisions are not made by looking at a deposit or at a process.

 Decisions are made by looking at samples representing a deposit or a process, by proxy.

By Proxy!…  Do the samples have authority to represent a deposit or a process?  Your decisions are only as good as your samples.

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Opportunities: The Facts

If cause eliminated:

standardize If cause not eliminated:

re-analyze

Compulsory action on causes of problems

Short Courses, Workshops, and Training

Analyze existing data and find structural problems

Lost opportunities with emphasis on effects of problems

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Continuous improvement of Mining Process with emphasis on causes of problems

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Opportunities: The Road Map

Director of Standards of Mining Process: The Synergy Necessary for Mining Process Efficiency

Selection of Standards useful to a mining company Implementation of company's guidelines

Selection and offering of short courses, workshops, and training

Guidelines of best practices Selection of world experts

Identification of Structural Problems and Continuous Improvement of Mining Process

Compulsory actions

Communication with QA/QC and Laboratory Managers

Accountability

Communication with top management at a company's operations Francis Pitard's drawing protected by copyright law, 2004

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