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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
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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
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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
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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
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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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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 cutoffgrade
Selection of a pit design
Selection of an acceptance level forconciliation
differences between ore grade control and the
geological model
With a large V[0] these criticallyimportant tasks, leading to a reliable
recovery of natural resources,become weak.
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Large-scale Variability:What are the main components?
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.
With a large V[0] these criticallyimportant tasks, leading to a reliable
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 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.
With a large V[0] these criticallyimportant tasks, leading to a reliable
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
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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