ASTM D4460-97

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Designation: D 4460 – 97
Standard Practice for
Calculating Precision Limits Where Values are Calculated
from Other Test Methods
This standard is issued under the fixed designation D 4460; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope 4.2 At the heart of statistical theory is the concept of a
frequency distribution of a random variable. The precision
1.1 This practice describes techniques for calculating preci-
limit of the random variable is determined by the standard
sion limits when values are calculated from two other methods
deviation of the variable. The standard deviation of a random
having precision limits.
variable that is the sum, difference, product, or quotient of two
1.2 This standard does not purport to address all of the
other random variables can be calculated simply so long as the
safety concerns, if any, associated with its use. It is the
individual variables are independent and the standard devia-
responsibility of the user of this standard to establish appro-
tions are small relative to their mean values. These restrictions
priate safety and health practices and determine the applica-
are usually met in ASTM methods. In those cases where these
bility of regulatory limitations prior to use.
restrictions are not met, other methods can be used. Only cases
2. Referenced Documents
complying with the restrictions are covered in this standard.
2.1 ASTM Standards:
5. Procedure
D 1188 Test Method for Bulk Specific Gravity and Density
5.1 The standard deviation on which precision limits for a
of Compacted Bituminous Mixtures Using Paraffin-Coated
test result are based can be calculated from the following
Specimens
equations:
D 2041 Test Method for Theoretical Maximum Specific
Gravity of Bituminous Paving Mixtures 2 2
s 5 s 1s
=
x 6 y x y
D 3203 Test Method for Percent Air Voids in Compacted
(1)
Dense and Open Bituminous Paving Mixtures
where:
E 177 Practice for Use of the Terms Precision and Bias in
s 5 standard deviation for determining precision lim-
x 6y
ASTM Test Methods
its of a test result for a new standard based on
3. Terminology Definitions
either an addition or subtraction of test results
from two other standards,
3.1 For definitions of terms used in this document, consult
s 5 standard deviation from precision statement of
x
Practice E 177, or a standard dictionary, or a statistical text
one of the standards on which new standard is
from Refs. (1, 2, and 3).
based, and
4. Significance and Use s 5 standard deviation from precision statement of
y
other standard on which new standard is based.
4.1 Precision limits for a test result which is calculated by
The distributions of the test results from the two standards
addition, subtraction, multiplication, or division of two other
should be independent.
test results that have valid precision limits can be calculated
directly. This saves the cost and delay of conducting an 2 2 2 2
s 5 y¯ s 1 x¯ s (2)
=
xy x y
interlaboratory study.
where:
s 5 standard deviation for determining precision limits
xy
This practice is under the jurisdiction of ASTM Committee D-4 on Road and
of test results for a new standard based on the
Paving Materials and is the direct responsibility of Subcommittee D04.94on
products of two other test results from two other
Statistical Procedures and Evaluation of Data.
standards,
Current edition approved Nov. 10, 1997. Published April 1998 Originally
s 5 standard deviation from precision statement of one
published as D 4460–85.
x
Annual Book of ASTM Standards, Vol 04.03.
of the standards on which new standard is based,
Annual Book of ASTM Standards, Vol 14.02.
x¯ 5 mean or average value of X variable,
The boldface numbers in parentheses refer to the list of references at the end of
this standard.
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D 4460
s , s , x¯, y¯ 5 definitions given above. (4)
x y
s 5 standard deviation from precision statement of other
y
standard on which new standard is based, and
An example in Appendix X1. illustrates how the equations
y¯ 5 mean or average value of Y variable.
are ap
...