ASTM D4460-97(2015)

Standard Practice for Calculating Precision Limits Where Values are Calculated from Other Test Methods

SIGNIFICANCE AND USE
4.1 Precision limits for a test result that is calculated by addition, subtraction, multiplication, or division of two other test results that have valid precision limits can be calculated directly. This saves the cost and delay of conducting an interlaboratory study.  
4.2 At the heart of statistical theory is the concept of a frequency distribution of a random variable. The precision limit of the random variable is determined by the standard deviation of the variable. The standard deviation of a random variable that is the sum, difference, product, or quotient of two other random variables can be calculated simply so long as the individual variables are independent and the standard deviations are small relative to their mean values. These restrictions are usually met in ASTM methods. In those cases where these restrictions are not met, other methods can be used. Only cases complying with the restrictions are covered in this standard.
SCOPE
1.1 This practice covers techniques for calculating precision limits when values are calculated from two other methods having precision limits.  
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 and health practices and determine the applicability of regulatory limitations prior to use.

General Information

• Status: Historical
• Publication Date: 31-Dec-2014
• ICS: 93.080.20 - Road construction materials
• Technical Committee: D04 - Road and Paving Materials
• Drafting Committee: D04.94 - Statistical Procedures and Evaluation of Data

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: D4460 − 97 (Reapproved 2015)
Standard Practice for
Calculating Precision Limits Where Values are Calculated
from Other Test Methods
This standard is issued under the fixed designation D4460; 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 test results that have valid precision limits can be calculated
directly. This saves the cost and delay of conducting an
1.1 This practice covers techniques for calculating precision
interlaboratory study.
limits when values are calculated from two other methods
having precision limits.
4.2 At the heart of statistical theory is the concept of a
frequency distribution of a random variable. The precision
1.2 This standard does not purport to address all of the
limit of the random variable is determined by the standard
safety concerns, if any, associated with its use. It is the
deviation of the variable. The standard deviation of a random
responsibility of the user of this standard to establish appro-
variable that is the sum, difference, product, or quotient of two
priate safety and health practices and determine the applica-
other random variables can be calculated simply so long as the
bility of regulatory limitations prior to use.
individual variables are independent and the standard devia-
2. Referenced Documents
tions are small relative to their mean values. These restrictions
are usually met in ASTM methods. In those cases where these
2.1 ASTM Standards:
restrictions are not met, other methods can be used. Only cases
D1188 TestMethodforBulkSpecificGravityandDensityof
complying with the restrictions are covered in this standard.
Compacted Bituminous Mixtures Using Coated Samples
D2041 Test Method for Theoretical Maximum Specific
5. Procedure
Gravity and Density of Bituminous Paving Mixtures
D3203 Test Method for Percent Air Voids in Compacted
5.1 The standard deviation on which precision limits for a
Dense and Open Bituminous Paving Mixtures
test result are based can be calculated from the following
E177 Practice for Use of the Terms Precision and Bias in
equations:
ASTM Test Methods
2 2
σ 5 =σ 1σ (1)
x6y x y
3. Definitions
where:
3.1 For definitions of terms used in this document, consult
σ = standard deviation for determining precision limits of
3,4,5 x6y
Practice E177, or a standard dictionary, or a statistical text.
a test result for a new standard based on either an
addition or subtraction of test results from two other
4. Significance and Use
standards,
4.1 Precision limits for a test result that is calculated by
σ = standard deviation from precision statement of one of
x
addition, subtraction, multiplication, or division of two other
the standards on which new standard is based, and
σ = standard deviation from precision statement of other
y
1 standard on which new standard is based.
This practice is under the jurisdiction of ASTM Committee D04 on Road and
Paving Materials and is the direct responsibility of Subcommittee D04.94 on
The distributions of the test results from the two standards
Statistical Procedures and Evaluation of Data.
should be independent.
Current edition approved Jan. 1, 2015. Published February 2015. Originally
approved in 1985. Last previous edition approved in 2009 as D4460 – 97 (2009).
2 2 2 2
σ 5 = y¯ σ 1x¯ σ (2)
DOI: 10.1520/D4460-97R15.
xy x y
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
where:
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
Standards volume information, refer to the standard’s Document Summary page on
σ = standard deviation for determining precision limits of
xy
the ASTM website.
test results for a new standard based on the products of
Geary, R. C., “The Frequency Distribution of a Quotient,” Journal of the Royal
two other test results from two other standards,
Statistical Society, Vol 93, 1930, pp. 442–446.
Fieller,E.C.,“TheDistributionoftheIndexinaNormalBivariatePopulation,” σ = standard deviation from precision statement of one of
x
Biometrika, Vol 24, 1932, pp. 428–440.
the standards on which new standard is based,
Ku, H. H., “Notes on the Use of Propagation of Error Formulas,” Journal of
x¯ = mean or average value of X variable,
Research of the National Bureau of Standards, Vol 70C, No. 4, 1966, pp. 331–341.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700
...

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: D4460 − 97 (Reapproved 2009) D4460 − 97 (Reapproved 2015)
Standard Practice for
Calculating Precision Limits Where Values are Calculated
from Other Test Methods
This standard is issued under the fixed designation D4460; 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 practice covers techniques for calculating precision limits when values are calculated from two other methods having
precision limits.
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 and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2.1 ASTM Standards:
D1188 Test Method for Bulk Specific Gravity and Density of Compacted Bituminous Mixtures Using Coated Samples
D2041 Test Method for Theoretical Maximum Specific Gravity and Density of Bituminous Paving Mixtures
D3203 Test Method for Percent Air Voids in Compacted Dense and Open Bituminous Paving Mixtures
E177 Practice for Use of the Terms Precision and Bias in ASTM Test Methods
3. Definitions
3,4,5
3.1 For definitions of terms used in this document, consult Practice E177, or a standard dictionary, or a statistical text.
4. Significance and Use
4.1 Precision limits for a test result that is calculated by addition, subtraction, multiplication, or division of two other test results
that have valid precision limits can be calculated directly. This saves the cost and delay of conducting an interlaboratory study.
4.2 At the heart of statistical theory is the concept of a frequency distribution of a random variable. The precision limit of the
random variable is determined by the standard deviation of the variable. The standard deviation of a random variable that is the
sum, difference, product, or quotient of two other random variables can be calculated simply so long as the individual variables
are independent and the standard deviations are small relative to their mean values. These restrictions are usually met in ASTM
methods. In those cases where these restrictions are not met, other methods can be used. Only cases complying with the restrictions
are covered in this standard.
5. Procedure
5.1 The standard deviation on which precision limits for a test result are based can be calculated from the following equations:
2 2
σ 5=σ 1σ (1)
x6y x y
where:
σ = standard deviation for determining precision limits of a test result for a new standard based on either an addition or
x6y
subtraction of test results from two other standards,
This practice is under the jurisdiction of ASTM Committee D04 on Road and Paving Materials and is the direct responsibility of Subcommittee D04.94 on Statistical
Procedures and Evaluation of Data.
Current edition approved Dec. 1, 2009Jan. 1, 2015. Published January 2010February 2015. Originally approved in 1985. Last previous edition approved in 20052009 as
D4460 – 97 (2005).(2009). DOI: 10.1520/D4460-97R09.10.1520/D4460-97R15.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Geary, R. C., “The Frequency Distribution of a Quotient,” Journal of the Royal Statistical Society, Vol 93, 1930, pp. 442–446.
Fieller, E. C., “The Distribution of the Index in a Normal Bivariate Population,” Biometrika, Vol 24, 1932, pp. 428–440.
Ku, H. H., “Notes on the Use of Propagation of Error Formulas,” Journal of Research of the National Bureau of Standards, Vol 70C, No. 4, 1966, pp. 331–341.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D4460 − 97 (2015)
σ = standard deviation from precision statement of one of the standards on which new standard is based, and
x
σ = standard deviation from precision statement of other standard on which new standard is based.
y
The distributions of the test results from the two standards should be independent.
2 2 2 2
σ 5= y¯ σ 1x¯ σ (2)
xy x y
2 2 2 2
σ 5= y¯ σ 1x¯ σ (2)
xy x y
where:
σ = standard deviation for determining precision limits of test results for a ne
...