# SIST ISO 3084:2000

(Main)## Iron ores -- Experimental methods for evaluation of quality variation

## Iron ores -- Experimental methods for evaluation of quality variation

This International Standard specifies experimental methods for the evaluation of quality variation of iron ores for each type of iron ore being traded and for each handling plant.

Two distinct approaches are specified. The first is to analyse interleaved samples composed of a number of paired increments taken and combined alternately following stratified sampling or systematic sampling as specified in ISO 3082. The second is to collect and analyse individual increments and then to analyse the data using variographic methods.

Using interleaved samples involves less work, but use of variograms provides a better estimate of quality variation and hence a better estimate of the sampling variance. The variogram method is usually used to fine tune a sampling operation.

NOTE The experimental methods may be applied approximately to time basis sampling when the flowrate is almost uniform.

## Minerais de fer -- Méthodes expérimentales pour l'évaluation de la variation de qualité

## Železove rude - Eksperimentalne metode za vrednotenje spremembe kakovosti

### General Information

### Relations

### Standards Content (Sample)

INTERNATIONAL ISO

STANDARD 3084

Third edition

1998-12-15

Iron ores — Experimental methods for

evaluation of quality variation

Minerais de fer — Méthodes expérimentales pour l’évaluation de la

variation de qualité

A

Reference number

ISO 3084:1998(E)

---------------------- Page: 1 ----------------------

ISO 3084:1998(E)

Contents

1 Scope .1

2 Normative references .1

3 Definitions .1

4 General conditions .2

5 Evaluation of quality variation using interleaved sampling .2

6 Estimation of quality variation from the variogram.8

7 Classification of quality variation .10

Annex A (informative) Examples for calculations of standard deviation .12

© ISO 1998

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic

or mechanical, including photocopying and microfilm, without permission in writing from the publisher.

International Organization for Standardization

Case postale 56 • CH-1211 Genève 20 • Switzerland

Internet iso@iso.ch

Printed in Switzerland

ii

---------------------- Page: 2 ----------------------

© ISO

ISO 3084:1998(E)

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO

member bodies). The work of preparing International Standards is normally carried out through ISO technical

committees. Each member body interested in a subject for which a technical committee has been established has

the right to be represented on that committee. International organizations, governmental and non-governmental, in

liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical

Commission (IEC) on all matters of electrotechnical standardization.

Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.

Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.

International Standard ISO 3084 was prepared by Technical Committee ISO/TC 102, Iron ores, subcommittee

SC 1, Sampling.

This third edition cancels and replaces the second edition (ISO 3084:1986) which has been technically revised.

Annex A of this International Standard is for information only.

iii

---------------------- Page: 3 ----------------------

©

INTERNATIONAL STANDARD ISO ISO 3084:1998(E)

Iron ores — Experimental methods for evaluation of quality

variation

1 Scope

This International Standard specifies experimental methods for the evaluation of quality variation of iron ores for each

type of iron ore being traded and for each handling plant.

Two distinct approaches are specified. The first is to analyse interleaved samples composed of a number of paired

increments taken and combined alternately following stratified sampling or systematic sampling as specified in

ISO 3082. The second is to collect and analyse individual increments and then to analyse the data using

variographic methods.

Using interleaved samples involves less work, but use of variograms provides a better estimate of quality variation

and hence a better estimate of the sampling variance. The variogram method is usually used to fine tune a sampling

operation.

NOTE The experimental methods may be applied approximately to time basis sampling when the flowrate is almost uniform.

2 Normative references

The following standards contain provisions which, through reference in this text, constitute provisions of this

International Standard. At the time of publication, the editions indicated were valid. All standards are subject to

revision, and parties to agreements based on this International Standard are encouraged to investigate the possibility

of applying the most recent editions of the standards indicated below. Members of IEC and ISO maintain registers of

currently valid International Standards.

1)

ISO 3082:— , Iron ores — Sampling and sample preparation procedures.

ISO 3085:1996, Iron ores — Experimental methods for checking the precision of sampling.

ISO 11323:1996, Iron ores — Vocabulary.

3 Definitions

For the purposes of this International Standard, the definitions given in ISO 11323 and the following apply.

3.1 interleaved samples

samples constituted by placing consecutive primary increments alternately into two sample containers

1)

To be published. (Revision of ISO 3081:1986, ISO 3082:1987 and ISO 3083:1986)

1

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©

ISO

ISO 3084:1998(E)

4 General conditions

4.1 Quality variation

The quality variation or degree of heterogeneity of iron ore shall be determined in terms of the standard deviation.

The standard deviation of a quality characteristic between increments taken from within strata, denoted by σ , shall

w

be determined either by estimating the variance between interleaved samples or by measuring individual increments

and determining the slope and intercept of a linear fit to a variogram corrected by subtraction of sample preparation

and measurement variances. In both cases, where corrections for sample preparation and measurement variances

are made (see 5.6.2, note 2, and 6.1), it is essential that the sample preparation and measurement variances be

determined at the same time as the experiments to determine quality variation are carried out.

4.2 Quality characteristics

The quality characteristic chosen for determining the quality variation is generally the total iron content, but silica

content, alumina content, moisture content, size distribution and other quality characteristics may also be chosen.

When separate samples are taken for the determination of chemical composition, moisture content, size distribution,

etc., the quality variation for the individual characteristics shall be adopted. When the sample is used for the

determination of more than one quality characteristic, the largest classification category for quality variation among

these characteristics shall be adopted.

4.3 Sampling, sample preparation and measurement

Sampling and sample preparation shall be carried out in accordance with ISO 3082. Measurement of samples shall

be carried out in accordance with the relevant International Standards for chemical analysis, moisture content and

size analysis of iron ores.

The sampling for evaluation of quality variation may be conducted in conjunction with routine sampling for

determination of the quality of the lot. In other words, the samples collected from the lot may be used for both

purposes.

5 Evaluation of quality variation using interleaved sampling

5.1 General

The procedures for evaluating the standard deviation within strata, s , applicable to both stratified and systematic

w

sampling, are described in 5.2 to 5.7.

5.2 Type of investigation

5.2.1 Type 1

When lots are frequently delivered, the quality variation may be determined from a large number of lots of almost

equal mass as follows:

a) treat each lot separately;

b) make up a pair of interleaved samples for each lot as shown in figure 1a) and example 1.

2

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©

ISO

ISO 3084:1998(E)

5.2.2 Type 2

When large lots are infrequently delivered, the quality variation may be determined from a single lot as follows:

a) split the lot into at least 10 parts of almost equal mass;

b) make up a pair of interleaved samples for each part by combining the increments taken from each part as

shown in figure 1b) and example 2.

5.2.3 Type 3

When small lots are frequently delivered, the quality variation may be determined from several lots of almost equal

mass as follows:

a) split all the lots involved into at least 10 parts of almost equal mass;

b) make up a pair of interleaved samples for each part by combining the increments taken from each part as

shown in figure 1c) and example 3.

5.2.4 Type 4

When sampling a wagon-borne lot and when increments are taken from all wagons comprising the lot, the sampling

scheme may be regarded as stratified sampling. When lots are frequently delivered, the procedure for determining

quality variation is as follows:

a) treat each lot separately;

b) make up a pair of interleaved samples for each lot as shown in figure 1d).

5.3 Number of increments and constitution of interleaved samples

5.3.1 Number of increments

The number of increments to be taken from one or several lots may be the same as that selected for routine

sampling. However, when the routine sampling is based on the classification category of "small" quality variation and

the number of increments is considered to be insufficient to obtain a reliable standard deviation, then the number of

increments shall be increased (see ISO 3082).

5.3.1.1 Type 1 investigation

For type 1 investigations, the number of increments, n , to be taken from each lot shall be in accordance with

1

ISO 3082, and a pair of interleaved samples shall be constituted for each lot [see figure 1a)].

5.3.1.2 Type 2 investigation

For type 2 investigations, the number of increments, n , shall be determined from ISO 3082, and at least 10 pairs of

1

interleaved samples shall be constituted [see figure 1b)].

5.3.1.3 Type 3 investigation

For type 3 investigations, the number of increments, n , to be taken from each lot shall be in accordance with

1

ISO 3082. Each lot shall be divided into a number of strata, and increments from each stratum shall be combined

into a pair of interleaved samples [see figure 1c)].

5.3.1.4 Type 4 investigation

For type 4 investigations, the number of increments, n , being collected from each lot shall be determined from table

1

3 of ISO 3082, and the number of increments, n , to be taken from each wagon shall be in accordance with

w

3

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©

ISO

ISO 3084:1998(E)

ISO 3082. If the number is odd, it shall be increased by one to make it even. A pair of interleaved samples shall be

constituted for each lot [see figure 1d)].

5.3.2 Constitution of interleaved samples

The interleaved samples shall be made up according to the following procedure:

allocate a serial number to the increments from each lot or part-lot in order of sampling;

constitute pairs of interleaved samples from consecutive odd-numbered increments (denoted by interleaved

sample A ) and consecutive even-numbered increments (denoted by interleaved sample B ) for each lot or part-

i i

lot (see figure 2);

for each investigation, prepare n sets of paired interleaved samples.

Each interleaved sample shall be made up of two or more increments.

5.4 Preparation of test samples and measurement

Separate test samples shall be prepared from the interleaved samples, A and B .

i i

Chemical analysis, moisture determination, size determination or physical testing shall be carried out on the test

samples as required.

4

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©

ISO

ISO 3084:1998(E)

a) Type 1 investigation — n lots: one lot = one part

Key: The rectangular box indicates one lot; each division of the box made by broken lines indicates one part; a pair of circles

indicates a pair of interleaved samples. This also applies to a) and c).

b) Type 2 investigation — One lot (example for 10 parts)

c) Type 3 investigation — Several lots (example for three lots and 12 parts)

Key: Each box indicates a wagon; points in the box indicate increments; circles indicate interleaved samples.

d) Type 4 investigation — Stratified sampling of wagon-borne lots.

5

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©

ISO

ISO 3084:1998(E)

Figure 1 — Schematic diagram for one investigation

NOTE This diagram is an example for a single lot of 5 000 t to 15 000 t of ore of "large" quality variation. In accordance with

ISO 3082, the required minimum number of increments is 100, and 10 pairs of interleaved samples A and B (i = 1, 2, ., 10),

i i

each comprising five increments, are prepared.

Figure 2 — Example of schematic diagram for constitution of pairs of interleaved samples (type 2)

5.5 Number of investigations

Because the standard deviation, s , of a quality characteristic within strata cannot be estimated very precisely from a

w

small number of investigations, the following minimum number of investigations is recommended:

a) for type 2 and 3 investigations, at least five separate investigations;

b) for type 1 and 4 investigations, at least 10 separate investigations.

5.6 Calculation of standard deviation within strata

5.6.1 Data sheet

The experimental data generated by chemical analysis, moisture determination, size determination or physical

testing of individual test samples shall be recorded on a suitable form (see examples 1 to 3).

5.6.2 Calculation

The estimated standard deviation within strata shall be calculated from equation (4).

The range, R , of paired measurements is given by equation (1):

i

RA=−B (1)

ii i

6

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©

ISO

ISO 3084:1998(E)

where

A is the measured quality characteristic (such as % Fe) of the test sample prepared from interleaved sample

i

A ;

i

B is the measured quality characteristic of the test sample prepared from interleaved sample B , which is from

i i

the same part-lot as interleaved sample A ;

i

i is a subscript designating each part-lot.

The mean, R , of ranges R is given by equation (2):

i

1

R R

= (2)

∑ i

n

4

where n is the number of ranges, R , which is the same as the number of part-lots in the investigation.

4

i

The mean, x , of paired measurements for each part is given by equation (3):

i

1

xA=+()B (3)

ii i

2

The estimated standard deviation within strata, $s , is given by equation (4):

w

R

n (4)$σ =

w 5

d

2

where

n is the number of increments comprising each interleaved sample A or B ;

5

i i

is the factor to estimate standard deviation from the range; for paired data 1/ = 0,886 2.

d d

2 2

NOTES

1 For type 3 investigations, the mean value of the quality characteristic for the j-th lot, x , may be obtained from equation (5).

j

1

x= x (5)

jj∑i

n

6

where

x is the mean of paired measurements for each part in lot j;

ji

n is the number of parts in the lot.

6

2 The estimated standard deviation within strata, $s , obtained from equation (4) is a measure of the combined standard

w

deviation of sampling, sample preparation and measurement. While the standard deviation within strata is overestimated, this

value may be used for the classification in clause 7 (see 5.7).

When it is desired to obtain an unbiased estimate of the standard deviation within strata, and when the estimated standard

deviation of sample preparation, denoted by $s , and the estimated standard deviation of measurement, denoted by $s , are

P M

known, the estimated standard deviation within strata should be calculated using equation (6):

R

222

$$$σσ=−n () −σ (6)

w 5 PM

d

2

7

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©

ISO

ISO 3084:1998(E)

3 If the number of increments is determined according to 5.3.1 and those increments are taken, the variation among the

numbers of increments comprising the various interleaved samples will be small. If the variation is 10 % or less, equations (4)

and (6) can be applied approximately by using the mean value of n .

5

5.7 Expression of results

5.7.1 Type 2 and 3 investigations

For type 2 and 3 investigations, the estimated mean value of standard deviation within strata, $s , for a particular

w

iron ore and handling plant evaluated from a series of investigations shall be reported as the square root of the mean

2

of all measured values of $s , i.e.:

w

1

2

σσ$$= (7)

ww∑

n

7

where n is the number of individual values of $s .

w

7

5.7.2 Type 1 and 4 investigations

For type 1 and 4 investigations, the value of $s obtained from equation (4) or equation (6) shall be reported as the

w

estimated standard deviation within strata for the particular iron ore and handling plant.

6 Estimation of quality variation from the variogram

6.1 General variogram method

Using this method, a large number (say 20 to 40) of successive increments, n, are extracted, prepared and

measured in duplicate. The variogram, which examines the differences between increments at various intervals

(called lags) apart, can then be calculated. The value of the variogram, V (t), corresponding to a lag of k increments

E

is given by equation (8):

N

k

2

xx−

[]

ik+ i

∑

i=1

Vt()= (8)

E

2N

k

where

t is kDt, where Dt is the sampling interval in units of time or mass, depending on w

**...**

SLOVENSKI STANDARD

SIST ISO 3084:2000

01-junij-2000

Železove rude - Eksperimentalne metode za vrednotenje spremembe kakovosti

Iron ores -- Experimental methods for evaluation of quality variation

Minerais de fer -- Méthodes expérimentales pour l'évaluation de la variation de qualité

Ta slovenski standard je istoveten z: ISO 3084:1998

ICS:

73.060.10 Železove rude Iron ores

SIST ISO 3084:2000 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------

SIST ISO 3084:2000

---------------------- Page: 2 ----------------------

SIST ISO 3084:2000

INTERNATIONAL ISO

STANDARD 3084

Third edition

1998-12-15

Iron ores — Experimental methods for

evaluation of quality variation

Minerais de fer — Méthodes expérimentales pour l’évaluation de la

variation de qualité

A

Reference number

ISO 3084:1998(E)

---------------------- Page: 3 ----------------------

SIST ISO 3084:2000

ISO 3084:1998(E)

Contents

1 Scope .1

2 Normative references .1

3 Definitions .1

4 General conditions .2

5 Evaluation of quality variation using interleaved sampling .2

6 Estimation of quality variation from the variogram.8

7 Classification of quality variation .10

Annex A (informative) Examples for calculations of standard deviation .12

© ISO 1998

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic

or mechanical, including photocopying and microfilm, without permission in writing from the publisher.

International Organization for Standardization

Case postale 56 • CH-1211 Genève 20 • Switzerland

Internet iso@iso.ch

Printed in Switzerland

ii

---------------------- Page: 4 ----------------------

SIST ISO 3084:2000

© ISO

ISO 3084:1998(E)

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO

member bodies). The work of preparing International Standards is normally carried out through ISO technical

committees. Each member body interested in a subject for which a technical committee has been established has

the right to be represented on that committee. International organizations, governmental and non-governmental, in

liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical

Commission (IEC) on all matters of electrotechnical standardization.

Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.

Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.

International Standard ISO 3084 was prepared by Technical Committee ISO/TC 102, Iron ores, subcommittee

SC 1, Sampling.

This third edition cancels and replaces the second edition (ISO 3084:1986) which has been technically revised.

Annex A of this International Standard is for information only.

iii

---------------------- Page: 5 ----------------------

SIST ISO 3084:2000

---------------------- Page: 6 ----------------------

SIST ISO 3084:2000

©

INTERNATIONAL STANDARD ISO ISO 3084:1998(E)

Iron ores — Experimental methods for evaluation of quality

variation

1 Scope

This International Standard specifies experimental methods for the evaluation of quality variation of iron ores for each

type of iron ore being traded and for each handling plant.

Two distinct approaches are specified. The first is to analyse interleaved samples composed of a number of paired

increments taken and combined alternately following stratified sampling or systematic sampling as specified in

ISO 3082. The second is to collect and analyse individual increments and then to analyse the data using

variographic methods.

Using interleaved samples involves less work, but use of variograms provides a better estimate of quality variation

and hence a better estimate of the sampling variance. The variogram method is usually used to fine tune a sampling

operation.

NOTE The experimental methods may be applied approximately to time basis sampling when the flowrate is almost uniform.

2 Normative references

The following standards contain provisions which, through reference in this text, constitute provisions of this

International Standard. At the time of publication, the editions indicated were valid. All standards are subject to

revision, and parties to agreements based on this International Standard are encouraged to investigate the possibility

of applying the most recent editions of the standards indicated below. Members of IEC and ISO maintain registers of

currently valid International Standards.

1)

ISO 3082:— , Iron ores — Sampling and sample preparation procedures.

ISO 3085:1996, Iron ores — Experimental methods for checking the precision of sampling.

ISO 11323:1996, Iron ores — Vocabulary.

3 Definitions

For the purposes of this International Standard, the definitions given in ISO 11323 and the following apply.

3.1 interleaved samples

samples constituted by placing consecutive primary increments alternately into two sample containers

1)

To be published. (Revision of ISO 3081:1986, ISO 3082:1987 and ISO 3083:1986)

1

---------------------- Page: 7 ----------------------

SIST ISO 3084:2000

©

ISO

ISO 3084:1998(E)

4 General conditions

4.1 Quality variation

The quality variation or degree of heterogeneity of iron ore shall be determined in terms of the standard deviation.

The standard deviation of a quality characteristic between increments taken from within strata, denoted by σ , shall

w

be determined either by estimating the variance between interleaved samples or by measuring individual increments

and determining the slope and intercept of a linear fit to a variogram corrected by subtraction of sample preparation

and measurement variances. In both cases, where corrections for sample preparation and measurement variances

are made (see 5.6.2, note 2, and 6.1), it is essential that the sample preparation and measurement variances be

determined at the same time as the experiments to determine quality variation are carried out.

4.2 Quality characteristics

The quality characteristic chosen for determining the quality variation is generally the total iron content, but silica

content, alumina content, moisture content, size distribution and other quality characteristics may also be chosen.

When separate samples are taken for the determination of chemical composition, moisture content, size distribution,

etc., the quality variation for the individual characteristics shall be adopted. When the sample is used for the

determination of more than one quality characteristic, the largest classification category for quality variation among

these characteristics shall be adopted.

4.3 Sampling, sample preparation and measurement

Sampling and sample preparation shall be carried out in accordance with ISO 3082. Measurement of samples shall

be carried out in accordance with the relevant International Standards for chemical analysis, moisture content and

size analysis of iron ores.

The sampling for evaluation of quality variation may be conducted in conjunction with routine sampling for

determination of the quality of the lot. In other words, the samples collected from the lot may be used for both

purposes.

5 Evaluation of quality variation using interleaved sampling

5.1 General

The procedures for evaluating the standard deviation within strata, s , applicable to both stratified and systematic

w

sampling, are described in 5.2 to 5.7.

5.2 Type of investigation

5.2.1 Type 1

When lots are frequently delivered, the quality variation may be determined from a large number of lots of almost

equal mass as follows:

a) treat each lot separately;

b) make up a pair of interleaved samples for each lot as shown in figure 1a) and example 1.

2

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SIST ISO 3084:2000

©

ISO

ISO 3084:1998(E)

5.2.2 Type 2

When large lots are infrequently delivered, the quality variation may be determined from a single lot as follows:

a) split the lot into at least 10 parts of almost equal mass;

b) make up a pair of interleaved samples for each part by combining the increments taken from each part as

shown in figure 1b) and example 2.

5.2.3 Type 3

When small lots are frequently delivered, the quality variation may be determined from several lots of almost equal

mass as follows:

a) split all the lots involved into at least 10 parts of almost equal mass;

b) make up a pair of interleaved samples for each part by combining the increments taken from each part as

shown in figure 1c) and example 3.

5.2.4 Type 4

When sampling a wagon-borne lot and when increments are taken from all wagons comprising the lot, the sampling

scheme may be regarded as stratified sampling. When lots are frequently delivered, the procedure for determining

quality variation is as follows:

a) treat each lot separately;

b) make up a pair of interleaved samples for each lot as shown in figure 1d).

5.3 Number of increments and constitution of interleaved samples

5.3.1 Number of increments

The number of increments to be taken from one or several lots may be the same as that selected for routine

sampling. However, when the routine sampling is based on the classification category of "small" quality variation and

the number of increments is considered to be insufficient to obtain a reliable standard deviation, then the number of

increments shall be increased (see ISO 3082).

5.3.1.1 Type 1 investigation

For type 1 investigations, the number of increments, n , to be taken from each lot shall be in accordance with

1

ISO 3082, and a pair of interleaved samples shall be constituted for each lot [see figure 1a)].

5.3.1.2 Type 2 investigation

For type 2 investigations, the number of increments, n , shall be determined from ISO 3082, and at least 10 pairs of

1

interleaved samples shall be constituted [see figure 1b)].

5.3.1.3 Type 3 investigation

For type 3 investigations, the number of increments, n , to be taken from each lot shall be in accordance with

1

ISO 3082. Each lot shall be divided into a number of strata, and increments from each stratum shall be combined

into a pair of interleaved samples [see figure 1c)].

5.3.1.4 Type 4 investigation

For type 4 investigations, the number of increments, n , being collected from each lot shall be determined from table

1

3 of ISO 3082, and the number of increments, n , to be taken from each wagon shall be in accordance with

w

3

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SIST ISO 3084:2000

©

ISO

ISO 3084:1998(E)

ISO 3082. If the number is odd, it shall be increased by one to make it even. A pair of interleaved samples shall be

constituted for each lot [see figure 1d)].

5.3.2 Constitution of interleaved samples

The interleaved samples shall be made up according to the following procedure:

allocate a serial number to the increments from each lot or part-lot in order of sampling;

constitute pairs of interleaved samples from consecutive odd-numbered increments (denoted by interleaved

sample A ) and consecutive even-numbered increments (denoted by interleaved sample B ) for each lot or part-

i i

lot (see figure 2);

for each investigation, prepare n sets of paired interleaved samples.

Each interleaved sample shall be made up of two or more increments.

5.4 Preparation of test samples and measurement

Separate test samples shall be prepared from the interleaved samples, A and B .

i i

Chemical analysis, moisture determination, size determination or physical testing shall be carried out on the test

samples as required.

4

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SIST ISO 3084:2000

©

ISO

ISO 3084:1998(E)

a) Type 1 investigation — n lots: one lot = one part

Key: The rectangular box indicates one lot; each division of the box made by broken lines indicates one part; a pair of circles

indicates a pair of interleaved samples. This also applies to a) and c).

b) Type 2 investigation — One lot (example for 10 parts)

c) Type 3 investigation — Several lots (example for three lots and 12 parts)

Key: Each box indicates a wagon; points in the box indicate increments; circles indicate interleaved samples.

d) Type 4 investigation — Stratified sampling of wagon-borne lots.

5

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SIST ISO 3084:2000

©

ISO

ISO 3084:1998(E)

Figure 1 — Schematic diagram for one investigation

NOTE This diagram is an example for a single lot of 5 000 t to 15 000 t of ore of "large" quality variation. In accordance with

ISO 3082, the required minimum number of increments is 100, and 10 pairs of interleaved samples A and B (i = 1, 2, ., 10),

i i

each comprising five increments, are prepared.

Figure 2 — Example of schematic diagram for constitution of pairs of interleaved samples (type 2)

5.5 Number of investigations

Because the standard deviation, s , of a quality characteristic within strata cannot be estimated very precisely from a

w

small number of investigations, the following minimum number of investigations is recommended:

a) for type 2 and 3 investigations, at least five separate investigations;

b) for type 1 and 4 investigations, at least 10 separate investigations.

5.6 Calculation of standard deviation within strata

5.6.1 Data sheet

The experimental data generated by chemical analysis, moisture determination, size determination or physical

testing of individual test samples shall be recorded on a suitable form (see examples 1 to 3).

5.6.2 Calculation

The estimated standard deviation within strata shall be calculated from equation (4).

The range, R , of paired measurements is given by equation (1):

i

RA=−B (1)

ii i

6

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SIST ISO 3084:2000

©

ISO

ISO 3084:1998(E)

where

A is the measured quality characteristic (such as % Fe) of the test sample prepared from interleaved sample

i

A ;

i

B is the measured quality characteristic of the test sample prepared from interleaved sample B , which is from

i i

the same part-lot as interleaved sample A ;

i

i is a subscript designating each part-lot.

The mean, R , of ranges R is given by equation (2):

i

1

R R

= (2)

∑ i

n

4

where n is the number of ranges, R , which is the same as the number of part-lots in the investigation.

4

i

The mean, x , of paired measurements for each part is given by equation (3):

i

1

xA=+()B (3)

ii i

2

The estimated standard deviation within strata, $s , is given by equation (4):

w

R

n (4)$σ =

w 5

d

2

where

n is the number of increments comprising each interleaved sample A or B ;

5

i i

is the factor to estimate standard deviation from the range; for paired data 1/ = 0,886 2.

d d

2 2

NOTES

1 For type 3 investigations, the mean value of the quality characteristic for the j-th lot, x , may be obtained from equation (5).

j

1

x= x (5)

jj∑i

n

6

where

x is the mean of paired measurements for each part in lot j;

ji

n is the number of parts in the lot.

6

2 The estimated standard deviation within strata, $s , obtained from equation (4) is a measure of the combined standard

w

deviation of sampling, sample preparation and measurement. While the standard deviation within strata is overestimated, this

value may be used for the classification in clause 7 (see 5.7).

When it is desired to obtain an unbiased estimate of the standard deviation within strata, and when the estimated standard

deviation of sample preparation, denoted by $s , and the estimated standard deviation of measurement, denoted by $s , are

P M

known, the estimated standard deviation within strata should be calculated using equation (6):

R

222

$$$σσ=−n () −σ (6)

w 5 PM

d

2

7

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SIST ISO 3084:2000

©

ISO

ISO 3084:1998(E)

3 If the number of increments is determined according to 5.3.1 and those increments are taken, the variation among the

numbers of increments comprising the various interleaved samples will be small. If the variation is 10 % or less, equations (4)

and (6) can be applied approximately by using the mean value of n .

5

5.7 Expression of results

5.7.1 Type 2 and 3 investigations

For type 2 and 3 investigations, the estimated mean value of standard deviation within strata, $s , for a particular

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iron ore and handling plant evaluated from a series of investigations shall be reported as the square root of the mean

2

of all measured values of $s , i.e.:

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1

2

σσ$$= (7)

ww∑

n

7

where n is the number of individual values of $s .

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7

5.7.2 Type 1 and 4 investigations

For type 1 and 4 investigations, the value of $s obtained from equation (4) or equation (6) shall be reported as the

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estimated standard deviation within strata for the particular iron ore and handling plant.

6 Estimation of quality variation from the variogram

6.1 General variogram method

Using this

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