ASTM E3076-18

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Designation: E3076 − 18
Standard Practice for
Determination of the Slope in the Linear Region of a Test
1
Record
This standard is issued under the fixed designation E3076; 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 mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
1.1 This practice presents an automated, objective linear-
fitting method for determining the slope of the linear portion of
2. Referenced Documents
a test record. The method assumes that there is a linear region
2
2.1 ASTM Standards:
early in the test record where the value of the y variable
E1942 Guide for Evaluating Data Acquisition Systems Used
increases roughly in proportion to the x variable and the slope
in Cyclic Fatigue and Fracture Mechanics Testing
of the record decreases after the linear region. The practice
E2443 Guide for Verifying Computer-Generated Test Re-
determines the best linear fit to the data based on the least
sults Through The Use Of Standard Data Sets
normalized residual and provides metrics for evaluating the
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2.2 ASTM Data Set:
quality of the test record and the quality of the resultant fit.
E3076-DS1(2018) File 01 Benchmark Data Set to Evaluate
1.2 Data quality metrics are applied that evaluate the level
Computer Implementation of the Algorithm in Standard
of noise and the digital resolution of the data to determine if the
E3076.
test record is adequate for a linear regression analysis. Fit
quality metrics use analysis of residuals in the vicinity of the fit
3. Terminology
range to determine if the test record is adequately linear and the
3.1 Definitions:
fit range is sufficiently large.
3.1.1 digital resolution, n—the precision of stored informa-
1.3 For test records that meet the data and fit quality metrics,
tion resulting from a discrete digital representation of analog
the practice determines a repeatable slope without the need for
data.
operator input that is independent of operator judgment. For
3.1.2 linear region, n—a region of the test record where the
test records that fail one or more of the quality metrics, it is
underlying physics indicate that the dependent variable would
recommended that the analyst evaluate the fit to determine if it
increase in proportion to the independent variable if there were
is acceptable.
no noise in the test record.
1.4 This practice represents a general purpose approach that
3.1.3 normalized, n—data with global minima of 0 and
is applicable for any test standard or method in which a linear
global maxima of 1 in x and y.
fit is desired. It is intended that this practice can be called upon
3.1.4 residual, n—the difference between the linear fit and
by standard test methods when slope must be determined.
the original test record y-values at a given x-value.
1.5 This standard does not purport to address all of the
3.1.5 test record, n—the basic raw data from a data set
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
4. Summary of Practice
priate safety, health, and environmental practices and deter-
4.1 This practice is intended for the analysis of test records
mine the applicability of regulatory limitations prior to use.
where the y variable increases roughly in proportion to the x
1.6 This international standard was developed in accor-
variable over a region early in the test record.
dance with internationally recognized principles on standard-
4.2 The linear-fitting algorithm utilizes analysis of residuals
ization established in the Decision on Principles for the
coupled with computational effort to numerically determine the
Development of International Standards, Guides and Recom-
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
1
This practice is under the jurisdiction of ASTM Committee E08 on Fatigue and contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Fracture and is the direct responsibility of Subcommittee E08.03 on Advanced Standards volume information, refer to the standard’s Document Summary page on
Apparatus and Techniques. the ASTM website.
3
Current edition approved Nov. 15, 2018. Published April 2019. DOI: 10.1520/ This data set is available for download from ASTM at https://www.astm.org/
E3076–18 COMMITTEE/E08.htm, under the heading, Additional Information.
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E3076 − 18
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most linear region in a giv
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