Francis Pitard

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Sampling Theory and Methods:Reasons for Courses

Prepared and Presented by Francis F. Pitard

Francis Pitard Sampling Consultants, LLC

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.

Your decisions are only as good asyour samples!


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Responsibility of aMining Company

If stakeholders cannot see the value of correct

sampling, it is the companys responsibility toshow 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 reliabledatabase 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 copy right 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 learnto better understand variability:

Small-scale variability,

which can be called the IrrelevantVariability:

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.


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

The four solutions to minimize acatastrophic

inflation ofV[0] are:

Optimizing Sampling Protocols,

Implementing Sampling Protocols

using correct sampling systems,

Preserving samples integrity,

Minimizing the Analytical Error.


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Optimization ofSampling 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 ImplementationOf Sampling Protocols

The nightmare of sampling

Three major sources ofsampling 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 mustnot be selective.)

Increment Weighting Error IWE

(Sampling systems must be reasonably proportional.)


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Preserving the Integrityof Samples

Another major source ofsampling 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?) takingplace at each of the following points, and give solutions.

You have 10 minutes.

Current Sub-drill

Former Sub-drill

Ideal

sample

Actual

sample

A

B

C

D

F

G

Segregation

E

Francis Pitard's drawingprotected by copyright law, 2004


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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 ateach of the following points, and give solutions. You have 10minutes.

1

2

3

4

5

6

7

9

10

11

8


protected by copyright law, 2004


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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 10minutes.

Falling stream

1

2 3

4 57

9

6

8

10

11

Francis Pitard's drawingprotected 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 10minutes.

1

2

3

4

5

6

7




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Why is it that a training courseis so essential?

Because all the possible problems created by eachpoint addressed in the 4 exercises, that should be

solved within minutes, usually are the object ofunnecessary

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 devastatingmoney losses for the unaware company.

Lets give a few stunning examples.


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Case #1:A bad protocol followed by

incorrect implementation

Large Copper mine

in northern Chile:

US $ 134 000 000 loss differencebetween a bad sampling and sub-

sampling protocol and a better one, for

blast-holes, over a 10-yearperiod.

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-yearperiod

P. Carrasco: WCSB1, Denmark 2003


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Summary:Who are the enemies?

Remember this sign:

n

n

FSEn

S2

n

GSEn

S2

2

INES

]0[V2

1HES

n

AES

2

n

IEEn

S2

n

IDEn

S2

nIWEnS

2

n

IPEn

S2




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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 youroperations, the following problems take place:

Endless meetings to solve puzzles, argue, andfinger pointing,

Correcting factors are applied until data fitnormality,

Geologists and Geostatisticians cannot dotheir work,

Miners and metallurgists are at war,

Companys 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 companysfiscal 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 indifferent 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 criticallyimportant tasks, leading to a reliable

feasibility study, become weak.


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During Mining

Selection of ore grade control drilling pattern, and

drilling density

Selection of a Kriging technique

Selection of a realistic, economic cutoffgrade

Selection of a pit design

Selection of an acceptance level forconciliation

differences between ore grade control and the

geological model


recovery of natural resources,become weak.


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During Processing

Believable metallurgical accounting needs tomonitor 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 beidentified and either eliminated or minimized.

Reliable control charts must be updated at manyplaces.

Over-correction of the process must beprevented.


recovery of natural resources,become weak.


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During Trade with Customers

Customers like a fair price, but hate bad surpriseson product quality.

Penalty application is a common way of doingbusiness:What costs me must cost you!

You cannot control the quality of a productafter the fact, but you should implement themany things that lead to a good product, from thegeological model, to the mine, and to the plant.


quality of products, become weak.


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A long list of benefitsand opportunities:

How can good sampling practicesgive access to all this?

Good Sampling Practices, just like Good

Laboratory Practices, is the heart of themanagement decision process.

Decisions are not made by looking at a depositor 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 adeposit or a process?

Your decisions are only as good as yoursamples.


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Opportunities:The Facts

Compulsory

action on causes

of problems

Analyze existing

data and find

structural

problems

If cause eliminated:

standardizeIf cause not

eliminated:

re-analyze

Short Courses,

Workshops,

and Training

Lost opportunities with

emphasis on effects of

problems

Continuous improvement of

Mining Process

with emphasis on causes of

problemsFrancis Pitard's drawing



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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 amining companyImplementation of company'sguidelines

Selection and offeringof short courses,workshops, and training

Guidelines of bestpracticesSelection of world experts

Identification of StructuralProblems

and Continuous Improvementof Mining Process

Compulsory

actions Accountability

Communication with topmanagement at a

company's operations

Communication withQA/QC and Laboratory

Managers

Francis Pitard

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