Standard Guide to the Evaluation of Measurements Made by Online Coal Analyzers

SIGNIFICANCE AND USE
5.1 Online analyzers are used to provide quality data on lots of coal. The resulting quality data are used as a production tool or for some contractual application. This guide provides the means of evaluating the analyzer system and the data produced.  
5.2 Become familiar with the document's terminology and layout. The section on test design and data collection will provide the means by which all the analysis data will be gathered. The test should be carefully designed to ensure the user’s requirements are met.  
5.3 The procedures defined in this guide can be used to estimate the accuracy and precision of an online analyzer: (1) to conduct acceptance testing following installation and (2) to monitor the accuracy and precision (a) during routine use (quality control), (b) when significant changes are made to the analyzer, and (c) when a significant change in the coal being analyzed occurs (for example, a different seam at a mine, or a new coal source at a power plant). These procedures can also be used for calibration purposes.
SCOPE
1.1 This guide provides techniques to be used for the evaluation of the measurement performance of online coal analyzers.  
1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

Status
Published
Publication Date
31-Jan-2020
Technical Committee
D05 - Coal and Coke
Drafting Committee
D05.23 - Sampling

Relations

Effective Date
01-Mar-2024
Effective Date
01-Dec-2019
Effective Date
15-Apr-2018
Effective Date
01-Mar-2018
Effective Date
01-Nov-2017
Effective Date
15-Oct-2017
Effective Date
15-Sep-2016
Effective Date
15-Sep-2016
Effective Date
15-Jun-2016
Effective Date
01-Jun-2016
Effective Date
01-Jun-2016
Effective Date
01-Mar-2016
Effective Date
01-Sep-2015
Effective Date
15-May-2015
Effective Date
01-Feb-2015

Overview

ASTM D6543-20e1: Standard Guide to the Evaluation of Measurements Made by Online Coal Analyzers provides a comprehensive framework for assessing the measurement performance of online coal analyzers. Developed by ASTM International, this standard supports both producers and users in obtaining reliable coal quality data used for production control, quality assurance, and meeting contractual obligations. The guidance covers test design, data collection, calibration, and ongoing accuracy and precision evaluations, ensuring that analyzer systems deliver dependable and actionable results.

Key Topics

  • Measurement Performance Evaluation: The standard outlines methods for objectively assessing the accuracy and precision of online coal analyzers.
  • Test Design and Data Collection: Emphasizes careful planning and execution of comparative tests, applying standardized sampling and analysis practices.
  • Calibration and Standardization: Provides procedures for calibrating online analyzers and verifying performance via benchmarks with reference materials.
  • Routine Quality Monitoring: Recommends regular checks and comparative evaluations to maintain ongoing measurement integrity.
  • Handling System Changes: Advises on conducting new evaluations after significant changes to equipment, calibration, processes, or coal sources.
  • Statistical Analysis: Details the use of graphical (trend plots, scatter plots) and statistical tools (RMSD, Grubbs estimators, Latent Variable Models) to interpret test results and detect bias or outliers.

Applications

  • Power Generation: Power plants depend on accurate online coal analyzer data to optimize fuel use, control emissions, and meet environmental regulations.
  • Coal Mines and Preparation Plants: Coal producers utilize analyzer systems for real-time quality monitoring, process control, and ensuring delivery meets buyer requirements.
  • Contractual Compliance: Analytical quality data form the basis for contractual agreements and settlements between coal suppliers and buyers.
  • Research and Development: Testing of new analyzer technologies or coal sources often requires validated comparative measurement practices outlined in this standard.
  • Quality Assurance Programs: Continuous monitoring as specified by the standard supports root-cause analysis and corrective measures in coal handling operations.

Related Standards

ASTM D6543-20e1 references and aligns with several other important standards to ensure comprehensive evaluation and comparability:

  • ASTM D121: Terminology of Coal and Coke, providing definitions used throughout coal analysis.
  • ASTM D2013: Practice for Preparing Coal Samples for Analysis.
  • ASTM D2234/D2234M: Practice for Collection of a Gross Sample of Coal.
  • ASTM D7430: Practice for Mechanical Sampling of Coal.
  • ASTM E178: Practice for Dealing With Outlying Observations.

Practical Value

Implementing ASTM D6543-20e1 offers several tangible benefits:

  • Enhanced Data Integrity: Standardized procedures boost trust in measurement results.
  • Operational Efficiency: Real-time, reliable analytics enable better process control and immediate corrective action.
  • Risk Mitigation: Early detection of analyzer drift or systematic errors minimizes the risk of non-compliance or financial loss.
  • Global Relevance: Developed under international standards principles, the guide supports harmonization and mutual acceptance of coal quality data across borders.

Keywords

online coal analyzer, coal quality measurement, ASTM D6543, measurement evaluation, calibration, accuracy, precision, coal sampling, comparative analysis, quality control, RMSD, Grubbs estimator, latent variable model, ASTM standards

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Frequently Asked Questions

ASTM D6543-20e1 is a guide published by ASTM International. Its full title is "Standard Guide to the Evaluation of Measurements Made by Online Coal Analyzers". This standard covers: SIGNIFICANCE AND USE 5.1 Online analyzers are used to provide quality data on lots of coal. The resulting quality data are used as a production tool or for some contractual application. This guide provides the means of evaluating the analyzer system and the data produced. 5.2 Become familiar with the document's terminology and layout. The section on test design and data collection will provide the means by which all the analysis data will be gathered. The test should be carefully designed to ensure the user’s requirements are met. 5.3 The procedures defined in this guide can be used to estimate the accuracy and precision of an online analyzer: (1) to conduct acceptance testing following installation and (2) to monitor the accuracy and precision (a) during routine use (quality control), (b) when significant changes are made to the analyzer, and (c) when a significant change in the coal being analyzed occurs (for example, a different seam at a mine, or a new coal source at a power plant). These procedures can also be used for calibration purposes. SCOPE 1.1 This guide provides techniques to be used for the evaluation of the measurement performance of online coal analyzers. 1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. 1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

SIGNIFICANCE AND USE 5.1 Online analyzers are used to provide quality data on lots of coal. The resulting quality data are used as a production tool or for some contractual application. This guide provides the means of evaluating the analyzer system and the data produced. 5.2 Become familiar with the document's terminology and layout. The section on test design and data collection will provide the means by which all the analysis data will be gathered. The test should be carefully designed to ensure the user’s requirements are met. 5.3 The procedures defined in this guide can be used to estimate the accuracy and precision of an online analyzer: (1) to conduct acceptance testing following installation and (2) to monitor the accuracy and precision (a) during routine use (quality control), (b) when significant changes are made to the analyzer, and (c) when a significant change in the coal being analyzed occurs (for example, a different seam at a mine, or a new coal source at a power plant). These procedures can also be used for calibration purposes. SCOPE 1.1 This guide provides techniques to be used for the evaluation of the measurement performance of online coal analyzers. 1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. 1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

ASTM D6543-20e1 is classified under the following ICS (International Classification for Standards) categories: 73.040 - Coals. The ICS classification helps identify the subject area and facilitates finding related standards.

ASTM D6543-20e1 has the following relationships with other standards: It is inter standard links to ASTM D121-15(2024), ASTM D2234/D2234M-19, ASTM D7430-18a, ASTM D7430-18, ASTM D7430-17, ASTM D2234/D2234M-17, ASTM D7430-16be1, ASTM D7430-16b, ASTM D7430-16a, ASTM D7430-16, ASTM E178-16, ASTM D2234/D2234M-16, ASTM D121-15, ASTM D7430-15a, ASTM D7430-15. Understanding these relationships helps ensure you are using the most current and applicable version of the standard.

ASTM D6543-20e1 is available in PDF format for immediate download after purchase. The document can be added to your cart and obtained through the secure checkout process. Digital delivery ensures instant access to the complete standard document.

Standards Content (Sample)


This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
´1
Designation: D6543 − 20
Standard Guide to
the Evaluation of Measurements Made by Online Coal
Analyzers
This standard is issued under the fixed designation D6543; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
ε NOTE—An editorial correction was made to 7.3.3.5 in November 2022.
1. Scope 3.2 Definitions of Terms Specific to This Standard:
3.2.1 analyzer system, n—a coal quality measurement sys-
1.1 This guide provides techniques to be used for the
tem which includes an online coal analyzer and which may
evaluation of the measurement performance of online coal
include one or more stages of a coal-sampling system.
analyzers.
3.2.2 calibration, n—mathematical modeling of analyzer
1.2 This standard does not purport to address all of the
and comparative coal sampling and analysis data.
safety concerns, if any, associated with its use. It is the
3.2.2.1 Discussion—Factors from the model are used in the
responsibility of the user of this standard to establish appro-
online analyzer control software.
priate safety, health, and environmental practices and deter-
3.2.3 full-stream analyzer, n—an analyzer system that inter-
mine the applicability of regulatory limitations prior to use.
rogates the coal on a process belt.
1.3 This international standard was developed in accor-
dance with internationally recognized principles on standard-
3.2.4 Grubbs estimator, n—an estimate of the measurement
ization established in the Decision on Principles for the
precision of an online analyzer (1-3).
Development of International Standards, Guides and Recom-
3.2.5 Latent Variable Model, n—a mathematical model that
mendations issued by the World Trade Organization Technical
can estimate each system’s precision, when the analyzer is
Barriers to Trade (TBT) Committee.
compared to two independent reference systems.
3.2.6 online analyzer, n—an analytical tool consisting of an
2. Referenced Documents
2 instrumentandsystems,whichtogetherprovidemeasurements,
2.1 ASTM Standards:
or estimates, or both, of coal quality parameters.
D121Terminology of Coal and Coke
3.2.7 outlier, n—an extreme value that statistical tests indi-
D2013Practice for Preparing Coal Samples for Analysis
cate to be far enough from other results in a population under
D2234/D2234MPractice for Collection of a Gross Sample
considerationtocausesuspicionthatthevalueisnotamember
of Coal
of the population.
D6518Practice for Bias Testing a Mechanical Coal Sam-
pling System (Withdrawn 2008)
3.2.8 reference material, n—material of stable composition
D7430Practice for Mechanical Sampling of Coal
that may be used to generate static analyzer measurements.
E178Practice for Dealing With Outlying Observations
3.2.9 reference system, n—a measurement system used to
measure the characteristics of a lot of coal that are also
3. Terminology
measured by an online analyzer, and against which the online
3.1 Definitions—For additional definitions of terms used in
analyzer measurements are compared.
this standard, refer to Terminology D121.
3.2.10 sample stream analyzer, n—an analyzer system that
is fed a save or reject stream from a sampling system.
This guide is under the jurisdiction of ASTM Committee D05 on Coal and
3.2.11 standardization, n—calibration of an instrument to a
Coke and is the direct responsibility of Subcommittee D05.23 on Sampling.
reference material using static stability measurements.
Current edition approved Feb. 1, 2020. Published February 2020. Originally
approved in 2000. Last previous edition approved in 2017 as D6543–17a. DOI:
3.2.12 static stability, n—an estimate of the measurement
10.1520/D6543-20E01.
precision of an instrument obtained on material that is not
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
moving.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
3 4
The last approved version of this historical standard is referenced on Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
www.astm.org. this standard.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
´1
D6543 − 20
3.2.12.1 Discussion—The estimate normally is expressed as all the performance measures that are gathered on a routine
the standard deviation and average of the measurements for a basis, including mean analysis value of reference material,
given period of time. RMSD, etc.
6.1.3 Whenever there is a major change to the operating
3.2.13 synchronization error, n—an error that occurs from
parameters, the configuration, the calibration, the processes, or
comparing measurements made by an online analyzer and a
the hardware associated with the analyzer or the reference
reference system that are not measuring exactly the same lot
system, the user may wish to perform comparative tests. In
because of temporal or spatial offsets, or both.
addition to comparative tests, standardization or static tests, or
both, as recommended by the online analyzer manufacturer,
4. Summary of Guide
may be helpful.
4.1 This guide describes how to measure performance of an
6.1.4 Changes in coal characteristics may also impact ana-
online analyzer using comparative measurements. The perfor-
lyzer performance. Particle size, source of coal, mining
mance evaluation consists of a paired comparison of analyses
techniques, and degree of preparation, which if changed from
from a reference method using ASTM sampling, sample
previous test periods and which are not in the analyzer
preparation, and analysis methods for several lots of coal with
calibration database, may affect analyzer precision and accu-
the analyses from the online analyzer for the same lots of coal.
racy.
The data resulting from the comparative test may be evaluated
6.1.5 Additional changes which could merit performance
using graphical and statistical techniques outlined below.
testing include a change in the material or width of the
4.2 Varioustechniquesarerecommendedbyonlineanalyzer
conveyor,orcoalflowrates(inthecaseoffull-flowanalyzers).
manufacturers for standardization or static testing. These
6.2 Static Stability Measurements for Baseline
techniques are useful for establishing a benchmark before
Assessment—A reference material may be used to provide a
conducting a comparative test. These techniques may also be
baseline assessment of static measurement precision. The
used as diagnostic tests in accordance with methods recom-
reference material may be used to compare current mean and
mended by online analyzer manufacturers and graphical and
standard deviation values with mean and standard deviation
statistical techniques included in this guide.
values previously collected in the same manner. The resulting
comparative data may help determine whether any apparent
5. Significance and Use
decline in analyzer dynamic performance may be attributed to
5.1 Onlineanalyzersareusedtoprovidequalitydataonlots
a change in the operating characteristics of the analyzer, in the
ofcoal.Theresultingqualitydataareusedasaproductiontool
absenceoftheinfluenceofsampling,preparation,andanalysis.
or for some contractual application. This guide provides the
6.2.1 The results of this evaluation can indicate whether
means of evaluating the analyzer system and the data pro-
analyzer precision has significantly degraded or whether a bias
duced.
may have occurred. If so, it may be possible to adjust the
5.2 Become familiar with the document’s terminology and
analyzer to restore initial performance. If the user wishes only
layout. The section on test design and data collection will
to measure current static stability, any available coal may be
provide the means by which all the analysis data will be
used in the analysis zone of the analyzer. Note, however, that
gathered. The test should be carefully designed to ensure the
the actual standard deviation in static stability tests might be
user’s requirements are met.
influenced by the composition or mass of the coal being
examined or analyzer factors, such as the strength of the
5.3 The procedures defined in this guide can be used to
radioactive sources used by the analyzer or condition of
estimate the accuracy and precision of an online analyzer: (1)
analyzer electronic components.
to conduct acceptance testing following installation and (2) to
6.2.2 It is essential that the length of the analysis period be
monitor the accuracy and precision (a) during routine use
defined (for example, 1min, 2min, or 5min) and be constant
(quality control), (b) when significant changes are made to the
inthestaticstabilitytest.Thestandarddeviationresultingfrom
analyzer, and (c) when a significant change in the coal being
the static stability test decreases as the length of the analysis
analyzed occurs (for example, a different seam at a mine, or a
period increases.
new coal source at a power plant). These procedures can also
be used for calibration purposes.
6.3 Comparison of Analyzer System to Reference System
Measurements:
6. Selection and Conduct of Performance Evaluations
6.3.1 Once an analyzer installation has been completed and
6.1 Introduction: calibration adjustments have been made, the analyzer owner
6.1.1 Several techniques can be used to evaluate the perfor- may require acceptance testing.Also, the analyzer owner may
mance of an online analyzer. These techniques provide data decide to relocate the analyzer. In these cases, comparison
that can be evaluated by using the graphical and statistical tests—that is, to compare the analyzer system results to
conventional sampling and analysis techniques—will provide
methods described in Section 7 of this guide.
6.1.2 At the time of installation, all of the graphical and the user calibration verification data or data that could be used
for recalibration of the analyzer, or both.
numericalmethodsoutlinedinthisguidemayproveuseful.On
a routine basis, conducting any of the instrument stability 6.3.2 Sinceperformanceevaluationsusuallyconsistof30or
checks and comparative evaluations that do not disrupt normal more comparisons, with each of these lasting from 30min to
operations may prove useful. Control charts may be applied to 3h, these comparisons may be conducted in a batch over
´1
D6543 − 20
several hours or days, or continuously throughout the opera-
tional life of the analyzer system.
6.3.3 If two independent conventional coal-sampling and
laboratory analysis measurements can be made from each of a
series of batches of coal interrogated by the analyzer, methods
developed by Grubbs (1-3) or the Latent Variable Model
(LVM) can be used to provide unbiased estimates of the
measurement precision of the analyzer and of the conventional
sampling and analysis systems.
6.3.4 Any two series of measurements are independent if
their measurement errors are uncorrelated. Correlation of
FIG. 1 Key to Schematics
measurement errors can be avoided and independence assured
by use of a true random selection of physical increments or
samples of material or by using different schemes and equip-
ment for collection, preparation, and laboratory analysis of the
samples, or both. A complete treatment of the subject of
independence of measurements and the various means of
assuring independence is beyond the scope of this guide.
6.4 Sampling Considerations:
6.4.1 SelectionofAppropriateSamplingandSamplePrepa-
rationMethods—Decisionsregardingsamplecollectionshould
be governed by Practices D2234/D2234M and D7430 as
appropriate. The method to be used for sample preparation
should be determined before the beginning of increment
collection. Sample preparation techniques should remain con-
sistent (see Practice D2013). Before installation of the
analyzer, consideration should be given to the ability to obtain
representative samples for comparison to analyzer measure-
ments and the regimen for sample handling and analysis. For
the use of mechanical sampling systems, inspection (see
Practice D7430, Part C) and bias testing (see Practice D7430,
Part D) are good methods for evaluation of the system’s
FIG. 2 Analyzer on Secondary Reject—Three-Stage Mechanical
suitability for the test.
Sampling
6.4.2 Selection of Reference Sample Point(s):
6.4.2.1 Comparative tests can be used to evaluate the
performance of either the analyzer itself or the “analyzer
system” (consisting of the analyzer and the sampling system
that feeds it). The comparative evaluations of the analyzer
system can be used to determine the ability of the analyzer
system to measure the characteristics of the main coal stream.
The selection of the reference system sample point(s) deter-
mineswhetherthecomparativetestswillassesstheanalyzeror
the analyzer system.
6.4.2.2 The most direct and practical two-instrument test,
when the analyzer is fed the secondary reject of a mechanical
sampling system, uses the final save to compare directly to the
analyzer. A manual or mechanical sample collected from the
analyzer discharge may provide an independent sample, which
may be used to assess the performance of the analyzer (see
Figs. 1-3).
6.4.2.3 There are instances when there is no save sample
(see Fig. 4) associated with the system feeding the analyzer. In
this case, it is possible to construct a test with several
comparisons by collecting separate samples from the analyzer
FIG. 3 Analyzer on Secondary Reject—Two-Stage Mechanical
feed and discharge.
Sampling
6.4.2.4 Insomeinstances,thedischargeoftheanalyzermay
be fed to further stages of mechanical sampling.Asingle stage
of sampling downstream of the analyzer is most common (see Fig. 5). In this case, the secondary save will provide a
´1
D6543 − 20
FIG. 6 Analyzer Distinct from Reference
third instrument. Practical considerations of increment collec-
tion at the secondary reject should be balanced with consider-
ations of sampling variances introduced by crushing and
tertiary sampling. For two instruments to be independent of
FIG. 4 Single-Stage Mechanical Sampling
eachother,oneorbothinstrumentsmustinterrogatethestream
of interest without changing the characteristics of the stream.
This may be true in some through-belt noncontacting configu-
rations. In the case of flow-through analyzers that require a
sample, the independence of systems is obtained in a case in
which the primary coal stream is sampled by one instrument
beforebeingsampledbyanotherinstrument(seeFig.6).Inthis
case, the two systems may be evaluated by comparing the
analyzervaluestothefinalsaveofthemechanicalsystem.The
analyzer itself may be evaluated by comparison to samples
collected at its discharge.
6.4.3 Synchronization—To evaluate the analyzer’s
performance, the lot of coal interrogated by the analyzer must
be the same lot of coal measured by the reference system.This
evaluationisusuallyaccomplishedbysamplingthecoalstream
after it passes the analyzer’s analysis zone except for sample
stream analyzers. Care should be taken to ensure that transport
times within the coal-handling system of interest, within
mechanical sampling systems used to provide comparative
measurements,andbetweensamplecollectionandtheanalyzer
be measured and accounted for in any comparisons. Compari-
FIG. 5 Analyzer on Primary Save—Two-Stage Mechanical Sam- sons in which intervening storage of the coal takes place
pling
between the analyzer and reference measurements should be
avoided.
convenient comparison sample. A test of such a system that 6.4.4 Length of Comparison Period—The length of time
requires more than one set of comparative data might incor- chosen for a comparison period should be commensurate with
porate a series of samples (stopped belt or full stream cut) the period of time—that is, the lot time—during which the
collected from the analyzer discharge or the secondary reject analyzer will normally produce a result of interest to the user.
stream, as well. In the relatively rare circumstances in which 6.4.5 Number of Comparisons—Although as few as 15
theanalyzerdischargefeedstwoadditionalstagesofsampling, comparisonsmaybeusefulinconventionalcontrolcharting,as
the tertiary save is recommended for two-instrument and bias many as 60 comparisons are recommended if one is to obtain
testing, and a stopped belt or full stream cut of the secondary usefulconfidencelimitsfortheLatentVariableModelestimate
or tertiary rejects of the analyzer discharge may be used as a of precision.
´1
D6543 − 20
FIG. 7 Trend Plot Showing the Analyzer and Reference System Measurements Versus the Lot Number on the Same Graph
7. Evaluation of Data aregiveninPracticeE178.InapplyingthemethodsofPractice
E178, the difference between the analyzer and reference value
7.1 Introduction—Once comparative data have been
is computed for each pair.
collected, it is recommended that the data be evaluated using
7.3.1.2 Each difference is then divided by the sample
both graphical and statistical, that is, numerical techniques.
standarddeviationofthedifferences,withtheabsolutevalueof
The sections that follow give recommendations for the con-
th
thequotientdesignatedasU forthei pair.Itisrecommended
struction and interpretation of various charts or graphs as well
i
as the techniques used to compute and interpret various here that any pair (i), whose U value is found using Table1 of
Practice E178 to exceed the table value for an appropriate
statistics.
upper significance level, that is, 99%, be treated as an outlier.
7.2 Stability Evaluations:
An investigation of the cause of the outlier should be
7.2.1 Graphical Techniques, see 7.3.2.
undertaken, and it may be appropriate to exclude the outlier
7.2.2 Numerical Methods and Their Interpretation—The
data from analyzer performance evaluation calculations.
twostatisticsmostrelevanttostaticstabilityevaluationsarethe
7.3.2 Graphical Methods—Regardless of the numerical
meanandstandarddeviationofthestaticanalyses.Tocalculate
method(s) used to assess instrument performance, any com-
the mean and standard deviation of the static analyses, the
parison between analyzer values and reference system values
individual analyzer static analysis data points (analysis by
should include graphical displays.At a minimum, a trend plot
analysis)areneeded.Thesamplemeanisgivenbytheformula:
andascatterplotshouldbeconstructed.Manyconclusionscan
n
be drawn or hypotheses constructed about the quality of the
x¯ 5 x /n (1)
F G
( i
i51
calibration of the instrument, the synchronization of the data,
where: and the precision of the analyzer or the reference system.
x¯ = the mean, 7.3.2.1 Trend Plot—Fig. 7 is an example of a trend plot,
th
x = the i measurement, and
showing the analyzer and reference system measurements
i
n = the number of measurements.
versusthelotnumberonthesamegraph.Providedthatproduct
variationissufficientlylargecomparedtotheprecisionofeach
The sample standard deviation s is given by:
d
of these measurements, one expects to see “tracking.” That is,
n
when the conventional measurement shows a decrease in ash,
s
...

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