ASTM E2782-17(2022)
(Guide)Standard Guide for Measurement Systems Analysis (MSA)
Standard Guide for Measurement Systems Analysis (MSA)
ABSTRACT
This guide presents terminology, concepts, and selected methods and formulas useful for measurement systems analysis (MSA). Measurement systems analysis may be broadly described as a body of theory and methodology that applies to the non-destructive measurement of the physical properties of manufactured objects. This guide presents selected concepts and methods useful for describing and understanding the measurement process. This guide is not intended to be a comprehensive survey of this topic.
SIGNIFICANCE AND USE
4.1 Many types of measurements are made routinely in research organizations, business and industry, and government and academic agencies. Typically, data are generated from experimental effort or as observational studies. From such data, management decisions are made that may have wide-reaching social, economic, and political impact. Data and decision making go hand in hand and that is why the quality of any measurement is important—for data originate from a measurement process. This guide presents selected concepts and methods useful for describing and understanding the measurement process. This guide is not intended to be a comprehensive survey of this topic.
4.2 Any measurement result will be said to originate from a measurement process or system. The measurement process will consist of a number of input variables and general conditions that affect the final value of the measurement. The process variables, hardware and software and their properties, and the human effort required to obtain a measurement constitute the measurement process. A measurement process will have several properties that characterize the effect of the several variables and general conditions on the measurement results. It is the properties of the measurement process that are of primary interest in any such study. The term “measurement systems analysis” or MSA study is used to describe the several methods used to characterize the measurement process.
Note 1: Sample statistics discussed in this guide are as described in Practice E2586; control chart methodologies are as described in Practice E2587.
SCOPE
1.1 This guide presents terminology, concepts, and selected methods and formulas useful for measurement systems analysis (MSA). Measurement systems analysis may be broadly described as a body of theory and methodology that applies to the non-destructive measurement of the physical properties of manufactured objects.
1.2 Units—The system of units for this guide is not specified. Dimensional quantities in the guide are presented only as illustrations of calculation methods and are not binding on products or test methods treated.
1.3 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.
1.4 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.
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Designation: E2782 − 17 (Reapproved 2022) An American National Standard
Standard Guide for
Measurement Systems Analysis (MSA)
This standard is issued under the fixed designation E2782; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.1.1 Unless otherwise noted, terms relating to quality and
statistics are defined in Terminology E456.
1.1 This guide presents terminology, concepts, and selected
3.1.2 accepted reference value, n—a value that serves as an
methods and formulas useful for measurement systems analy-
agreed-upon reference for comparison, and which is derived
sis (MSA). Measurement systems analysis may be broadly
as: (1) a theoretical or established value, based on scientific
described as a body of theory and methodology that applies to
principles, (2) an assigned or certified value, based on experi-
the non-destructive measurement of the physical properties of
mental work of some national or international organization, or
manufactured objects.
(3) a consensus or certified value, based on collaborative
1.2 Units—The system of units for this guide is not speci-
experimental work under the auspices of a scientific or
fied. Dimensional quantities in the guide are presented only as
engineering group. E177
illustrations of calculation methods and are not binding on
3.1.3 calibration, n—process of establishing a relationship
products or test methods treated.
between a measurement device and a known standard value(s).
1.3 This standard does not purport to address all of the
3.1.4 gage, n—device used as part of the measurement
safety concerns, if any, associated with its use. It is the
process to obtain a measurement result.
responsibility of the user of this standard to establish appro-
priate safety, health, and environmental practices and deter- 3.1.5 measurement process, n—process used to assign a
mine the applicability of regulatory limitations prior to use.
number to a property of an object or other physical entity.
1.4 This international standard was developed in accor-
3.1.5.1 Discussion—The term “measurement system” is
dance with internationally recognized principles on standard-
sometimes used in place of measurement process. (See 3.1.7.)
ization established in the Decision on Principles for the
3.1.6 measurement result, n—number assigned to a property
Development of International Standards, Guides and Recom-
of an object or other physical entity being measured.
mendations issued by the World Trade Organization Technical
3.1.6.1 Discussion—Theword“measurement”isusedinthe
Barriers to Trade (TBT) Committee.
same sense as measurement result.
3.1.7 measurement system, n—the collection of hardware,
2. Referenced Documents
2 software, procedures and methods, human effort, environmen-
2.1 ASTM Standards:
tal conditions, associated devices, and the objects that are
E177 Practice for Use of the Terms Precision and Bias in
measured for the purpose of producing a measurement.
ASTM Test Methods
3.1.8 measurement systems analysis (MSA), n—any of a
E456 Terminology Relating to Quality and Statistics
number of specialized methods useful for studying a measure-
E2586 Practice for Calculating and Using Basic Statistics
ment system and its properties.
E2587 Practice for Use of Control Charts in Statistical
Process Control
3.2 Definitions of Terms Specific to This Standard:
3.2.1 appraiser, n—the person who uses a gage or measure-
3. Terminology
ment system.
3.1 Definitions:
3.2.2 discrimination ratio, n—statistical ratio calculated
from the statistics from a gage R&R study that measures the
number of 97 % confidence intervals, constructed from gage
This guide is under the jurisdiction of ASTM Committee E11 on Quality and
R&R variation, that fit within six standard deviations of true
Statistics and is the direct responsibility of Subcommittee E11.50 on Metrology.
Current edition approved May 15, 2022. Published May 2022. Originally
object variation.
approved in 2011. Last previous edition approved in 2017 as E2782 – 17. DOI:
3.2.3 distinct product categories, n—alternate meaning of
10.1520/E2782-17R22.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or the discrimination ratio.
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.2.4 gage consistency, n—constancy of repeatability vari-
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. ance over a period of time.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2782 − 17 (2022)
3.2.4.1 Discussion—Consistency means that the variation methods useful for describing and understanding the measure-
within measurements of the same object (or group of objects) ment process.This guide is not intended to be a comprehensive
under the same conditions by the same appraiser behaves in a survey of this topic.
state of statistical control as judged, for example, using a
4.2 Any measurement result will be said to originate from a
control chart. See Practice E2587.
measurementprocessorsystem.Themeasurementprocesswill
3.2.5 gage performance curve, n—curve that shows the consist of a number of input variables and general conditions
probability of gage acceptance of an object given its real value that affect the final value of the measurement. The process
or the probability that an object’s real measure meets a variables, hardware and software and their properties, and the
requirement given the measurement of the object. human effort required to obtain a measurement constitute the
measurement process. A measurement process will have sev-
3.2.6 gage R&R, n—combined effect of gage repeatability
eral properties that characterize the effect of the several
and reproducibility.
variables and general conditions on the measurement results. It
3.2.7 gage resolution, n—degree to which a gage can
isthepropertiesofthemeasurementprocessthatareofprimary
discriminate between differing objects.
interest in any such study. The term “measurement systems
3.2.7.1 Discussion—The smallest difference between two
analysis” or MSAstudy is used to describe the several methods
objects that a gage is capable of detecting is referred to as its
used to characterize the measurement process.
finiteresolutionproperty.Forexample,alinearscalegraduated
NOTE 1—Sample statistics discussed in this guide are as described in
Practice E2586; control chart methodologies are as described in Practice
in tenths of an inch is not capable of discriminating between
E2587.
objects that differ by less than 0.1 in. (0.25 cm).
3.2.8 gage stability, n—absence of a change, drift, or erratic
5. Characteristics of a Measurement System (Process)
behavior in bias over a period of time.
5.1 Measurement has been defined as “the assignment of
3.2.8.1 Discussion—Stability means that repeated measure-
numbers to material objects to represent the relations existing
ments of the same object (or average of a set of objects) under
among them with respect to particular properties. The number
the same conditions by the same appraiser behave in a state of
assigned to some particular property serves to represent the
statistical control as judged for example by using a control
relative amount of this property associated with the object
chart technique. See Practice E2587.
concerned.” (1)
3.2.9 linearity, n—difference or change in bias throughout
5.2 Ameasurement system may be described as a collection
theexpectedoperatingrangeofagageormeasurementsystem.
of hardware, software, procedures and methods, human effort,
environmental conditions, associated devices, and the objects
3.2.10 measurement error, n—error incurred in the process
that are measured for the purpose of producing a measurement.
of measurement.
In the practical working of the measurement system, these
3.2.10.1 Discussion—As used in this guide, measurement
factors combine to cause variation among measurements of the
error includes one or both of R&R types of error.
same object that would not be present if the system were
3.2.11 repeatability conditions, n—in a gage R&R study,
perfect. A measurement system can have varying degrees of
conditionsinwhichindependentmeasurementsareobtainedon
each of these factors, and in some cases, one or more factors
identical objects, or a group of objects, by the same operator
may be the dominant contributor to this variation.
using the same measurement system within short intervals of
5.2.1 A measurement system is like a manufacturing pro-
time.
cess for which the product is a supply of numbers called
3.2.11.1 Discussion—As used in this guide, repeatability is
measurement results. The measurement system uses input
often referred to as equipment variation or EV.
factors and a sequence of steps to produce a result. The inputs
3.2.12 reproducibility conditions, n— in a gage R&R study, are just varying degrees of the several factors described in 5.2
conditions in which independent test results are obtained with including the objects being measured. The sequence of process
the same method, on identical test items by different operators. steps are that which would be described in a method or
procedure for producing the measurement. Taken as a whole,
3.2.12.1 Discussion—As used in this guide, reproducibility
the various factors and the process steps work collectively to
is often referred to as appraiser variation or AV. This term is
form the measurement system/process.
also used in a broader sense in Practice E177.
5.3 An important consideration in analyzing any measure-
4. Significance and Use
ment process is its interaction with time. This gives rise to the
properties of stability and consistency. A system that is stable
4.1 Many types of measurements are made routinely in
and consistent is one that is predictable, within limits, over a
research organizations, business and industry, and government
period of time. Such a system has properties that do not
and academic agencies. Typically, data are generated from
deteriorate with time (at least within some set time period) and
experimentaleffortorasobservationalstudies.Fromsuchdata,
is said to be in a state of statistical control. Statistical control,
management decisions are made that may have wide-reaching
stability and consistency, and predictability have the same
social, economic, and political impact. Data and decision
making go hand in hand and that is why the quality of any
measurement is important—for data originate from a measure-
The boldface numbers in parentheses refer to the list of references at the end of
ment process. This guide presents selected concepts and this standard.
E2782 − 17 (2022)
meaning in this sense. Measurement system instability and
inconsistency will cause further added overall variation over a
period of time.
5.3.1 In general, instability is a common problem in mea-
surement systems. Mechanical and electrical components may
wear or degrade with time, human effort may exhibit increas-
ing fatigue with time, software and procedures may change
with time, environmental variables will vary with time, and so
forth. Thus, measurement system stability is of primary con-
cern in any ongoing measurement effort.
FIG. 2 Reproducibility Concept
5.4 There are several basic properties of measurement
systems that are widely recognized among practitioners. These
attached “reproducibility conditions” and shall be defined and
are repeatability, reproducibility, linearity, bias, stability,
interpreted by the user of a measurement system. (In Practice
consistency, and resolution. In studying one or more of these
E177, reproducibility includes interlaboratory variation.)
properties,thefinalresultofanysuchstudyissomeassessment
5.4.3 Bias is the difference between a standard or accepted
of the capability of the measurement system with respect to the
reference value for an object, often called a “master,” and the
property under investigation. Capability may be cast in several
average value of a sample of measurements of the object(s)
ways, and this may also be application dependent. One of the
under a fixed set of conditions (see Fig. 1).
primary objectives in any MSA effort is to assess variation
5.4.4 Linearity is the change in bias over the operational
attributabletothevariousfactorsofthesystem.Allofthebasic
range of the measurement system. If the bias is changing as a
properties assess variation in some form.
function of the object being measured, we would say that the
5.4.1 Repeatabilityisthevariationthatresultswhenasingle
system is not linear. Linearity can also be interpreted to mean
object is repeatedly measured in the same way, by the same
that an instrument response is linearly related to the character-
appraiser, under the same conditions (see Fig. 1). The term
istic being measured.
“precision” also denotes the same concept, but “repeatability”
5.4.5 Stability is variation in bias with time, usually a drift
is found more often in measurement applications. The term
or trend, or erratic behavior.
“conditions” is sometimes combined with repeatability to
5.4.6 Consistency is the change in repeatability with time.A
denote “repeatability conditions” (see Terminology E456).
system is consistent with time when the standard deviation of
5.4.1.1 The phrase “intermediate precision” is also used (for
the repeatability error remains constant. When a measurement
example, see Practice E177). The user of a measurement
system is stable and consistent, we say that it is a state of
system shall decide what constitutes “repeatability conditions”
statistical control.
or “intermediate precision conditions” for the given applica-
5.4.7 The resolution of a measurement system has to do
tion. Typically, repeatability conditions for MSA will be as
with its ability to discriminate between different objects. A
described in 5.4.1.
system with high resolution is one that is sensitive to small
5.4.2 Reproducibility is defined as the variation among
changesfromobjecttoobject.Inadequateresolutionmayresult
average values as determined by several appraisers when
in identical measurements when the same object is measured
measuring the same group of objects using identical measure-
several times under identical conditions. In this scenario, the
ment systems under the same conditions (see Fig. 2). In a
measurement device is not capable of picking up variation as a
broader sense, this may be taken as variation in average values
result of repeatability (under the
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E2782 − 17 E2782 − 17 (Reapproved 2022) An American National Standard
Standard Guide for
Measurement Systems Analysis (MSA)
This standard is issued under the fixed designation E2782; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
1.1 This guide presents terminology, concepts, and selected methods and formulas useful for measurement systems analysis
(MSA). Measurement systems analysis may be broadly described as a body of theory and methodology that applies to the
non-destructive measurement of the physical properties of manufactured objects.
1.2 Units—The system of units for this guide is not specified. Dimensional quantities in the guide are presented only as
illustrations of calculation methods and are not binding on products or test methods treated.
1.3 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.
1.4 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.
2. Referenced Documents
2.1 ASTM Standards:
E177 Practice for Use of the Terms Precision and Bias in ASTM Test Methods
E456 Terminology Relating to Quality and Statistics
E2586 Practice for Calculating and Using Basic Statistics
E2587 Practice for Use of Control Charts in Statistical Process Control
3. Terminology
3.1 Definitions:
3.1.1 Unless otherwise noted, terms relating to quality and statistics are defined in Terminology E456.
3.1.2 accepted reference value, n—a value that serves as an agreed-upon reference for comparison, and which is derived as: (1)
a theoretical or established value, based on scientific principles, (2) an assigned or certified value, based on experimental work of
some national or international organization, or (3) a consensus or certified value, based on collaborative experimental work under
the auspices of a scientific or engineering group. E177
3.1.3 calibration, n—process of establishing a relationship between a measurement device and a known standard value(s).
This guide is under the jurisdiction of ASTM Committee E11 on Quality and Statistics and is the direct responsibility of Subcommittee E11.50 on Metrology.
Current edition approved Jan. 1, 2017May 15, 2022. Published February 2017May 2022. Originally approved in 2011. Last previous edition approved in 20112017 as
ɛ1
E2782 – 1117. . DOI: 10.1520/E2782-17.10.1520/E2782-17R22.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or 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.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2782 − 17 (2022)
3.1.4 gage, n—device used as part of the measurement process to obtain a measurement result.
3.1.5 measurement process, n—process used to assign a number to a property of an object or other physical entity.
3.1.5.1 Discussion—
The term “measurement system” is sometimes used in place of measurement process. (See 3.1.7.)
3.1.6 measurement result, n—number assigned to a property of an object or other physical entity being measured.
3.1.6.1 Discussion—
The word “measurement” is used in the same sense as measurement result.
3.1.7 measurement system, n—the collection of hardware, software, procedures and methods, human effort, environmental
conditions, associated devices, and the objects that are measured for the purpose of producing a measurement.
3.1.8 measurement systems analysis (MSA), n—any of a number of specialized methods useful for studying a measurement system
and its properties.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 appraiser, n—the person who uses a gage or measurement system.
3.2.2 discrimination ratio, n—statistical ratio calculated from the statistics from a gage R&R study that measures the number of
97 % confidence intervals, constructed from gage R&R variation, that fit within six standard deviations of true object variation.
3.2.3 distinct product categories, n—alternate meaning of the discrimination ratio.
3.2.4 gage consistency, n—constancy of repeatability variance over a period of time.
3.2.4.1 Discussion—
Consistency means that the variation within measurements of the same object (or group of objects) under the same conditions by
the same appraiser behaves in a state of statistical control as judged, for example, using a control chart. See Practice E2587.
3.2.5 gage performance curve, n—curve that shows the probability of gage acceptance of an object given its real value or the
probability that an object’s real measure meets a requirement given the measurement of the object.
3.2.6 gage R&R, n—combined effect of gage repeatability and reproducibility.
3.2.7 gage resolution, n—degree to which a gage can discriminate between differing objects.
3.2.7.1 Discussion—
The smallest difference between two objects that a gage is capable of detecting is referred to as its finite resolution property. For
example, a linear scale graduated in tenths of an inch is not capable of discriminating between objects that differ by less than 0.1
in. (0.25 cm).
3.2.8 gage stability, n—absence of a change, drift, or erratic behavior in bias over a period of time.
3.2.8.1 Discussion—
Stability means that repeated measurements of the same object (or average of a set of objects) under the same conditions by the
same appraiser behave in a state of statistical control as judged for example by using a control chart technique. See Practice E2587.
3.2.9 linearity, n—difference or change in bias throughout the expected operating range of a gage or measurement system.
3.2.10 measurement error, n—error incurred in the process of measurement.
3.2.10.1 Discussion—
As used in this guide, measurement error includes one or both of R&R types of error.
3.2.11 repeatability conditions, n—in a gage R&R study, conditions in which independent measurements are obtained on identical
objects, or a group of objects, by the same operator using the same measurement system within short intervals of time.
E2782 − 17 (2022)
3.2.11.1 Discussion—
As used in this guide, repeatability is often referred to as equipment variation or EV.
3.2.12 reproducibility conditions, n— in a gage R&R study, conditions in which independent test results are obtained with the
same method, on identical test items by different operators.
3.2.12.1 Discussion—
As used in this guide, reproducibility is often referred to as appraiser variation or AV. This term is also used in a broader sense
in Practice E177.
4. Significance and Use
4.1 Many types of measurements are made routinely in research organizations, business and industry, and government and
academic agencies. Typically, data are generated from experimental effort or as observational studies. From such data, management
decisions are made that may have wide-reaching social, economic, and political impact. Data and decision making go hand in hand
and that is why the quality of any measurement is important—for data originate from a measurement process. This guide presents
selected concepts and methods useful for describing and understanding the measurement process. This guide is not intended to be
a comprehensive survey of this topic.
4.2 Any measurement result will be said to originate from a measurement process or system. The measurement process will consist
of a number of input variables and general conditions that affect the final value of the measurement. The process variables,
hardware and software and their properties, and the human effort required to obtain a measurement constitute the measurement
process. A measurement process will have several properties that characterize the effect of the several variables and general
conditions on the measurement results. It is the properties of the measurement process that are of primary interest in any such study.
The term “measurement systems analysis” or MSA study is used to describe the several methods used to characterize the
measurement process.
NOTE 1—Sample statistics discussed in this guide are as described in Practice E2586; control chart methodologies are as described in Practice E2587.
5. Characteristics of a Measurement System (Process)
5.1 Measurement has been defined as “the assignment of numbers to material objects to represent the relations existing among
them with respect to particular properties. The number assigned to some particular property serves to represent the relative amount
of this property associated with the object concerned.” (1)
5.2 A measurement system may be described as a collection of hardware, software, procedures and methods, human effort,
environmental conditions, associated devices, and the objects that are measured for the purpose of producing a measurement. In
the practical working of the measurement system, these factors combine to cause variation among measurements of the same object
that would not be present if the system were perfect. A measurement system can have varying degrees of each of these factors,
and in some cases, one or more factors may be the dominant contributor to this variation.
5.2.1 A measurement system is like a manufacturing process for which the product is a supply of numbers called measurement
results. The measurement system uses input factors and a sequence of steps to produce a result. The inputs are just varying degrees
of the several factors described in 5.2 including the objects being measured. The sequence of process steps are that which would
be described in a method or procedure for producing the measurement. Taken as a whole, the various factors and the process steps
work collectively to form the measurement system/process.
5.3 An important consideration in analyzing any measurement process is its interaction with time. This gives rise to the properties
of stability and consistency. A system that is stable and consistent is one that is predictable, within limits, over a period of time.
Such a system has properties that do not deteriorate with time (at least within some set time period) and is said to be in a state
of statistical control. Statistical control, stability and consistency, and predictability have the same meaning in this sense.
Measurement system instability and inconsistency will cause further added overall variation over a period of time.
5.3.1 In general, instability is a common problem in measurement systems. Mechanical and electrical components may wear or
degrade with time, human effort may exhibit increasing fatigue with time, software and procedures may change with time,
environmental variables will vary with time, and so forth. Thus, measurement system stability is of primary concern in any ongoing
measurement effort.
The boldface numbers in parentheses refer to the list of references at the end of this standard.
E2782 − 17 (2022)
5.4 There are several basic properties of measurement systems that are widely recognized among practitioners. These are
repeatability, reproducibility, linearity, bias, stability, consistency, and resolution. In studying one or more of these properties, the
final result of any such study is some assessment of the capability of the measurement system with respect to the property under
investigation. Capability may be cast in several ways, and this may also be application dependent. One of the primary objectives
in any MSA effort is to assess variation attributable to the various factors of the system. All of the basic properties assess variation
in some form.
5.4.1 Repeatability is the variation that results when a single object is repeatedly measured in the same way, by the same appraiser,
under the same conditions (see Fig. 1). The term “precision” also denotes the same concept, but “repeatability” is found more often
in measurement applications. The term “conditions” is sometimes combined with repeatability to denote “repeatability conditions”
(see Terminology E456).
5.4.1.1 The phrase “intermediate precision” is also used (for example, see Practice E177). The user of a measurement system shall
decide what constitutes “repeatability conditions” or “intermediate precision conditions” for the given application. Typically,
repeatability conditions for MSA will be as described in 5.4.1.
5.4.2 Reproducibility is defined as the variation among average values as determined by several appraisers when measuring the
same group of objects using identical measurement systems under the same conditions (see Fig. 2). In a broader sense, this may
be taken as variation in average values of samples, either identical or selected at random from one homogeneous population, among
several laboratories or as measured using several systems.
5.4.2.1 Reproducibility may include different equipment and measurement conditions. This broader interpretation has attached
“reproducibility conditions” and shall be defined and interpreted by the user of a measurement system. (In Practice E177,
reproducibility includes interlaboratory variation.)
5.4.3 Bias is the difference between a standard or accepted reference value for an object, often called a “master,” and the average
value of a sample of measurements of the object(s) under a fixed set of conditions (see Fig. 1).
5.4.4 Linearity is the change in bias over the operational range of the measurement system. If the bias is changing as a function
of the object being measured, we would say that the system is not linear. Linearity can also be interpreted to mean that an
instrument response is linearly related to the characteristic being measured.
5.4.5 Stability is variation in bias with time, usually a drift or trend, or erratic behavior.
5.4.6 Consistency is
...
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