ASTM F1650-21

Standard Practice for Evaluating Tire Traction Performance Data Under Varying Test Conditions

ABSTRACT
This practice covers the required correction procedures for examining sequential control tire data for any systematic or bias (not random) variation due to changing test conditions that may influence absolute and also comparative performance of candidate tires, as they are tested over any short or extended time period. The procedures provided here may be used for any repetitive tire traction testing in any environment (for example, dry, wet, snow, ice) where test conditions are subject to change. This practice does not address the issue of rejecting outlier data points or test values that might occur among a set of otherwise acceptable data values obtained under identical test conditions in a short time period. Method A uses the initial operational conditions defined by the first control traction test as a reference point. The calculations correct all traction test performance parameters (for example, traction coefficients) to the initial level or condition of the pavement or other testing conditions, or both. With this method, corrections may be made after only a few candidate and control sets have been evaluated. Method B uses essentially the midpoint of any evaluation program, with the grand average traction test value as a reference point. This grand average value is obtained with higher precision than the initial control traction test average of Method A because it contains more values. However, Method B corrections cannot be made until the grand average value is established, which is normally at the end of any program.
SCOPE
1.1 This practice covers the required procedures for examining sequential control tire data for any variation due to changing test conditions. Such variations may influence absolute and also comparative performance of candidate tires, as they are tested over any short or extended time period. The variations addressed in this practice are systematic or bias variations and not random variations. See Appendix X1 for additional details.  
1.1.1 Two types of variation may occur: time or test sequence “trend variations,” either linear or curvilinear, and the less common transient or abrupt shift variations. If any observed variations are declared to be statistically significant, the calculation procedures are given to correct for the influence of these variations. This approach is addressed in Method A.  
1.2 In some testing programs, a policy is adopted to correct all candidate traction test data values without the application of a statistical routine to determine if a significant trend or shift is observed. This option is part of this practice and is addressed in Method B.  
1.3 The issue of rejecting outlier data points or test values that might occur among a set of otherwise acceptable data values obtained under identical test conditions in a short time period is not part of this practice. Specific test method or other outlier rejection standards that address this issue may be used on the individual data sets prior to applying this practice and its procedures.  
1.4 Although this practice applies to various types of tire traction testing (for example, dry, wet, snow, ice), the procedures as given in this practice may be used for any repetitive tire testing in an environment where test conditions are subject to change.  
1.5 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.  
1.6 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-Mar-2021
• ICS: 83.160.10 - Road vehicle tyres
• Technical Committee: F09 - Tires
• Drafting Committee: F09.20 - Vehicular Testing

Relations

• Refers: ASTM F2872-19 - Standard Specification for 225/75R16C 116/114S M+S Radial Light Truck Standard Reference Test Tire
• Effective Date: 01-Oct-2019
• Refers: ASTM E1136-19 - Standard Specification for P195/75R14 Radial Standard Reference Test Tire
• Effective Date: 01-Oct-2019
• Refers: ASTM F2493-18 - Standard Specification for P225/60R16 97S Radial Standard Reference Test Tire
• Effective Date: 01-Jan-2018
• Refers: ASTM E1136-17 - Standard Specification for P195/75R14 Radial Standard Reference Test Tire
• Effective Date: 01-Oct-2017
• Refers: ASTM F2872-16 - Standard Specification for 225/75R16C 116/114S M+S Radial Light Truck Standard Reference Test Tire
• Effective Date: 01-Nov-2016
• Refers: ASTM F2870-16 - Standard Specification for 315/70R22.5 154/150L Radial Truck Standard Reference Test Tire
• Effective Date: 01-Nov-2016
• Refers: ASTM E1136-14 - Standard Specification for P195/75R14 Radial Standard Reference Test Tire
• Effective Date: 15-Aug-2014
• Refers: ASTM F2493-14 - Standard Specification for P225/60R16 97S Radial Standard Reference Test Tire
• Effective Date: 01-Jun-2014
• Refers: ASTM E826-08(2013) - Standard Practice for Testing Homogeneity of a Metal Lot or Batch in Solid Form by Spark Atomic Emission Spectrometry
• Effective Date: 01-Apr-2013
• Refers: ASTM F2870-11 - Standard Specification for 315/70R22.5 154/150L Radial Truck Standard Reference Test Tire
• Effective Date: 01-Jan-2011
• Refers: ASTM F2871-11 - Standard Specification for 245/70R19.5 136/134M Radial Truck Standard Reference Test Tire
• Effective Date: 01-Jan-2011
• Refers: ASTM F2872-11 - Standard Specification for 225/75R16C 116/114S M+S Radial Light Truck Standard Reference Test Tire
• Effective Date: 01-Jan-2011
• Refers: ASTM F538-09 - Standard Terminology Relating to the Characteristics and Performance of Tires
• Effective Date: 15-Jun-2009
• Refers: ASTM E826-08 - Standard Practice for Testing Homogeneity of a Metal Lot or Batch in Solid Form by Spark Atomic Emission Spectrometry
• Effective Date: 01-May-2008
• Refers: ASTM F2493-08 - Standard Specification for P225/60R16 97S Radial Standard Reference Test Tire
• Effective Date: 01-May-2008

Overview

ASTM F1650-21: Standard Practice for Evaluating Tire Traction Performance Data Under Varying Test Conditions provides essential procedures for identifying, evaluating, and correcting systematic or bias variations in tire traction test data that arise when test conditions change. This standard is critical in ensuring the accuracy of test results, especially when comparing absolute and relative performance of different tire models over extended or short periods. It is applicable to repetitive tire traction testing performed in diverse environments, including dry, wet, snow, and ice, where variations in weather or surface conditions can directly impact the integrity of test data.

Key Topics

• Systematic and Bias Variation: This standard addresses time-related or sequence-based trends in test results, as well as abrupt changes (transient variations), excluding random variations and outlier rejection.
• Correction Methods:
  • Method A: Uses the initial operational conditions from the first control tire test as a benchmark. All subsequent test data are corrected back to this reference, allowing for corrections after a small sequence of tests.
  • Method B: Relies on the grand average of all control tire tests throughout the program as a benchmark. Corrections can only be made once data collection is complete, offering higher statistical precision due to the larger data set.
• Test Plan Structure: Involves periodic insertion of control tire tests among candidate tire tests, providing a framework for identifying and correcting variations.
• Statistical Evaluation: Guidance is provided for using statistical tests, such as correlation coefficients, to determine the significance of observed trends or shifts in control data.
• Reporting and Documentation: The practice specifies clear protocols for tabulating and annotating corrected and uncorrected data, ensuring traceability and transparency in reporting tire traction performance.

Applications

• Tire Manufacturers and Testing Facilities: This standard is vital for manufacturers and third-party labs conducting comparative performance testing under variable test conditions, ensuring product data reflects true performance capabilities.
• Product Development and R&D: Supports accurate benchmarking and validation of new tire designs by controlling for environmental and procedural variations during testing.
• Regulatory and Certification Bodies: Provides consistency for compliance testing and performance certification, aligning results with internationally recognized methodologies.
• Fleet and Vehicle Operators: Enables reliable assessment of tread technologies and tire choices for enhanced safety and performance across diverse operational environments.
• Quality Assurance and Data Integrity: Methodologies defined in ASTM F1650-21 uphold the validity of test-derived decisions in safety-critical applications.

Related Standards

• ASTM E501 - Specification for Standard Rib Tire for Pavement Skid-Resistance Tests
• ASTM E524 - Specification for Standard Smooth Tire for Pavement Skid-Resistance Tests
• ASTM E1136 - Specification for P195/75R14 Radial Standard Reference Test Tire
• ASTM F538 - Terminology Relating to the Characteristics and Performance of Tires
• ASTM F2493, F2870, F2871, F2872 - Specifications for various standard reference test tires

Practical Value

Implementing ASTM F1650-21 ensures the accuracy and comparability of tire traction performance data, regardless of environmental fluctuations during testing. By following the correction procedures in this standard, organizations can isolate tire performance from external variables, bolster the credibility of their test results, and maintain compliance with international best practices in tire testing. It is a critical tool for any entity involved in the technical evaluation of tire traction, from research and development to regulatory oversight and commercial product validation.

Keywords: tire traction testing, ASTM F1650-21, bias correction, data correction, test variation, performance benchmarking, systematic variation, vehicle safety.

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.
Designation: F1650 − 21
Standard Practice for
Evaluating Tire Traction Performance Data Under Varying
Test Conditions
This standard is issued under the fixed designation F1650; 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.
INTRODUCTION
Tiretractiontestingprogramsatprovinggroundsorotherexteriortestsitesareoftenextendedover
a period of days or weeks. During this time period test conditions may change due to a number of
varying factors, for example, temperature, rain or snow fall, surface texture, water depth, and wind
velocity and direction. If tire performance comparisons are to be made over any part of the test
program(ortheentireprogram)wherethesetestconditionvariationsareknownorsuspectedtoaffect
performance, the potential influence of these variations must be considered in any final evaluation of
traction performance.
1. Scope 1.4 Although this practice applies to various types of tire
traction testing (for example, dry, wet, snow, ice), the proce-
1.1 This practice covers the required procedures for exam-
dures as given in this practice may be used for any repetitive
ining sequential control tire data for any variation due to
tire testing in an environment where test conditions are subject
changing test conditions. Such variations may influence abso-
to change.
lute and also comparative performance of candidate tires, as
1.5 This standard does not purport to address all of the
they are tested over any short or extended time period. The
variations addressed in this practice are systematic or bias safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
variations and not random variations. See Appendix X1 for
additional details. priate safety, health, and environmental practices and deter-
mine the applicability of regulatory limitations prior to use.
1.1.1 Two types of variation may occur: time or test
sequence“trendvariations,”eitherlinearorcurvilinear,andthe 1.6 This international standard was developed in accor-
dance with internationally recognized principles on standard-
less common transient or abrupt shift variations. If any
observed variations are declared to be statistically significant, ization established in the Decision on Principles for the
Development of International Standards, Guides and Recom-
thecalculationproceduresaregiventocorrectfortheinfluence
of these variations. This approach is addressed in Method A. mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
1.2 In some testing programs, a policy is adopted to correct
allcandidatetractiontestdatavalueswithouttheapplicationof
2. Referenced Documents
astatisticalroutinetodetermineifasignificanttrendorshiftis
2.1 ASTM Standards:
observed. This option is part of this practice and is addressed
E501Specification for Standard Rib Tire for Pavement
in Method B.
Skid-Resistance Tests
1.3 The issue of rejecting outlier data points or test values
E524Specification for Standard Smooth Tire for Pavement
that might occur among a set of otherwise acceptable data
Skid-Resistance Tests
values obtained under identical test conditions in a short time
E826Practice for Testing Homogeneity of a Metal Lot or
period is not part of this practice. Specific test method or other
Batch in Solid Form by Spark Atomic Emission Spec-
outlier rejection standards that address this issue may be used
trometry
ontheindividualdatasetspriortoapplyingthispracticeandits
E1136Specification for P195/75R14 Radial Standard Refer-
procedures.
ence Test Tire
This practice is under the jurisdiction ofASTM Committee F09 on Tires and is
the direct responsibility of Subcommittee F09.20 on Vehicular Testing. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved April 1, 2021. Published April 2021. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
ε1
approved in 1995. Last previous edition approved in 2014 as F1650–98 (2014) . Standards volume information, refer to the standard’s Document Summary page on
DOI: 10.1520/F1650-21. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F1650 − 21
F538Terminology Relating to the Characteristics and Per- 4. Significance and Use
formance of Tires
4.1 Tire testing is conducted to make technical decisions on
F2493Specification for P225/60R16 97S Radial Standard
variousperformancecharacteristicsoftires,andgoodtechnical
Reference Test Tire
decisions require high quality test data. High quality test data
F2870 Specification for 315/70R22.5 154/150L Radial
are obtained with carefully designed and executed tests.
Truck Standard Reference Test Tire
However, even with the highest quality testing programs,
F2871 Specification for 245/70R19.5 136/134M Radial
unavoidabletimeortestsequencetrendsorotherperturbations
Truck Standard Reference Test Tire
may occur. The procedures as described in this practice are
F2872Specification for 225/75R16C 116/114S M+S Radial
therefore needed to correct for these unavoidable testing
Light Truck Standard Reference Test Tire
complications.
3. Terminology 5. Summary of Practice
5.1 This practice specifies certain test plans for testing
3.1 Definitions of Terms Specific to This Standard:
control tires. Testing begins with an initial test of the control
3.1.1 candidate tire (set), n—a test tire (or test tire set) that
tire or control tire set.Anumber of candidate tire traction tests
is part of an evaluation program; each candidate tire (set)
are then conducted, followed by a repeat test of the control tire
usually has certain unique design or other features that distin-
traction test. Additional candidate tire traction tests are con-
guish it from other candidate tires (sets) in the program. F538
ductedpriortothenextcontroltiretractiontest.Thissequential
3.1.2 control tire (set), n—a reference tire (or reference set)
procedure is repeated for the entire evaluation program.
repeatedly tested in a specified sequence, typically in conjunc-
5.2 Using control tire average measured performance
tion with a candidate tire (set), throughout an evaluation
parameters, the performance parameters of the candidate tires
program. F538
(sets) are corrected for any changes in test conditions. Two
correction procedures are described (MethodAand Method B)
3.1.2.1 Discussion—Control tires (sets) are used for adjust-
that use different reference points for data correction and as
ment of data sets generated from an evaluation program or the
such give different values for the corrected actual or absolute
statistical procedures used on data sets, or both, in order to
traction parameters. However, both test methods give the same
offset or reduce variation in test results. They can also be used
relativeratingsortractionperformanceindexes.SeeSection10
to improve the accuracy of candidate tire (set) data and to
formoredetails.Thetwotestmethodsaresummarizedinmore
detect variation in test equipment.
detail in Section 6 and Section 9. Both MethodsAand B have
3.1.3 reference tire (set), n—a special test tire (test tire set)
advantages and disadvantages.
that is used as a base value or benchmark in an evaluation
5.2.1 Method A uses the initial operational conditions de-
program; these tires usually have carefully controlled design
fined by the first control tire traction test as a reference point.
features to minimize variation. F538
The calculations correct all traction test performance param-
3.1.4 standard reference test tire, SRTT, n—a tire that is
eters (for example, traction coefficients) to the initial level or
commonly used as a control tire or surface monitoring tire and
condition of the pavement or other testing conditions, or both.
meets the requirements for one of the Specifications E1136,
With this test method, corrections may be made after only a
F2493, F2870, F2871,or F2872. F538
few candidate tire and control tire sets have been evaluated.
5.2.2 Method B uses essentially the midpoint of any evalu-
3.1.5 surface monitoring tire (set), n—a reference tire (or
ation program, with the grand average traction test value as a
reference set) used to evaluate changes in the test surface over
reference point. This grand average value is obtained with
a selected time period. F538
higherprecisionthantheinitialcontroltiretractiontestaverage
3.1.6 test (or testing), n—a technical procedure, method, or
of MethodA, since it contains more values. However, Method
guide performed on an object (or set of objects) that produces
B corrections cannot be made until the grand average value is
data; the data are used to evaluate or model properties or
established, which is normally at the end of any program.
characteristics of the object (or set of objects). F538
5.3 Annex A1 provides illustrations of several types of
3.1.7 test run, n—in tire testing, a single pass over a given
typical variation patterns for control tire data. It additionally
testsurface,ortheacquisitionofasequenceofdata,orboth,in
provides an example of the Method A correction calculations
theactoftestingatireortiresetunderselectedtestconditions.
required to evaluate a set of candidate test tires. Method B
F538
corrections follow the same general approach as illustrated in
Annex A1, with C used in place of C1.
avg
3.1.8 test tire (set), n—one or more tires, as required by the
test equipment or procedure to perform a test, producing a
5.4 Annex A2 provides a recommended technique for
single test result; the tires within a test tire set are usually
weighting the correction of the two or three candidate tire
nominally identical. F538
values (for example, T1, T2, T3) between each pair of control
tire values. This gives a slightly improved correction that may
3.1.9 traction test, n— in tire testing, a series of n test runs
be important in certain testing operations.
at a selected operational condition; a traction test is character-
ized by an average value for the measured performance 5.5 Appendix X1 provides a statistical model for the trac-
parameter. F538 tion measurement process. This may help the user of this
F1650 − 21
A
TABLE 1 Test Plans for Tire Performance Evaluation
practice to sort out the differences between fixed or bias
Plan A:
components of variation and random components of variation.
Test in the order: C1, T1, T2, C2, T3, T4, C3, T5, T6, C4, etc.
AppendixX1givesarationalefortheproceduresasoutlinedin
Plan B:
this practice.
Test in the order: C1, T1, T2, T3, C2, T4, T5, T6, C3, T7, T8,T9,
C4, etc.
5.6 AnnexA2 contains some background and details on the
A
Ci = average measured parameter (for n test runs) for a selected operational
propagation of error or test variation that occurs when correc-
condition for the ith control set test (that is, i=1,2,3,etc.)
tions are applied to the measured traction performance param-
Ti = average measured parameter (for n test runs) of a selected operational
condition for the ith candidate set test (that is, i=1,2,3,etc.).
eters and when traction performance indexes are calculated.
METHOD A—DATA CORRECTIONS BASED ON
INITIAL CONTROL TIRE TRACTION TEST
date tire set and each control tire set, except the first set, shall
be selected. The number of test runs depends on the test
6. Summary of Method A
method. Good testing procedure calls for as many test runs as
6.1 This method corrects the data obtained throughout the
possible. If direction of test is important on any test surface,
evaluation program to the initial conditions (test surface or
one half of the test runs shall be in each direction.
other, or both)“ reference point” at the beginning of the
7.4.1 Number of Test Runs: Initial Control Tire Set—The
program.The correction procedure (and calculation algorithm)
initial test for the control tire set, indicated by C1, is a key
for time trend variations is mathematically equivalent to that
value used for correction of candidate tire set performance
described in Practice E826. The procedure used for abrupt or
parameter values as testing proceeds. Therefore, the average
step changes is provisional and is subject to change as
performance parameters for C1 must be evaluated with a high
experience is gained. In this method the initial traction test
degreeofconfidenceandtherecommendednumberoftestruns
value for the control tire is a key data point. This method also
for C1 should be at least two times the number of test runs
allows for decisions on the need for any correction, based on a
selected in 7.4.
statistical analysis of the control tire data.
7.4.2 More than One Control Tire—Insometypesoftesting,
the control tire is damaged or changed by the testing to the
7. Procedure
extent that it ceases to function as a stable control. In such
7.1 Thetestprocedureisgivenintermsoftestingtiresetsof
situations it is necessary to use more than one control tire
four tires, that is, one tire on each of four vehicle positions. If
throughoutanyevaluationprogram.Insuchcasesacontroltire
only one tire is to be tested (trailer or other dynamometer
indicationschemesuchasC1-1,C1-2,C1-3,C2-4,C2-5,C2-6,
vehicle testing), follow the procedure as outlined with the
C3-1, etc., is suggested. In this scheme, C1-1=control tire 1,
understanding that the one tire replaces the tire set.
sequence use 1; C1-2=control tire 1, sequence use 2; .,
C2-4=control tire 2, sequence use 4, etc.
7.2 Assemble all the tire sets to be tested in any evaluation
program or for daily testing. Select the test speeds to be used
7.5 Table of Results—Prepare a table of test results and
and other operational test conditions as well as the order in
record all data with columns for:
which the candidate tire sets are to be tested.
7.5.1 Test sequence number, a sequential indication from 1
7.2.1 For any selected order, a test plan is established with
to m, of all the tests for any program of evaluation,
reference tire (set) designated as a control tire set tested at
7.5.2 Tire set identification,
regular intervals among the selected candidate tire sets. Select
7.5.3 Speed or other selected operational test condition(s),
the number of test runs or replicates for both control and
and
candidatetiresets.Acompletetestforatiresetisdefinedasthe
7.5.4 Average value (for n test runs) for the measured
total of p traction tests, one at each selected operational test
parameter for that operational condition.
condition, with n replicate test runs for each operational
7.6 Bothcontrolandcandidatetiresetdatashallbeincluded
condition (for example, speed and surface type).
in the table in the order as tested. If deemed important, a
7.2.2 Tests with a surface monitoring tire may also be
separate table of ambient temperature, wind direction, wind
conducted on a regular basis in addition to the control tire.
velocity,orotherweatherinformationalsoshallbepreparedon
7.3 Test Sequence—The control tires may be standard tires
a selected time (hourly) basis.
as specified in Specifications E501, E524, E1136, and F2493,
or a tire set similar in design and performance level to the 8. Calculations for Corrected Traction Performance Data
candidate tire sets. Conduct a complete test for the control tire
8.1 Preliminary Control Tire Set Data Review—The deci-
sets in relation to the candidate tire sets as given in Table 1.
sion to correct data, for any part of the test program where
Twotestplansaregiven:PlanA,inwhich(excludingtheinitial
candidate tire set comparisons are to be made, is based on the
control tire set) candidate tire sets constitute 67% of the tires
timeortestsequenceresponseofthecontroltireparametersfor
tested, and Plan B, in which candidate tire sets constitute 75%
each speed or other selected operational test condition. Cor-
of the tires tested.
rections may also be made for the entire test program. If a
7.4 Number of Test Runs at Each Speed or Operational significant trend is found or if significant transient perturba-
Condition—The number of test runs or replicates, n, for each tions are found, corrections are made for candidate tire set
speed or other selected operational condition for each candi- traction performance parameters.
F1650 − 21
8.2 Evaluating the Control Tire Data—Using the data lationcoefficientisgreaterthanthetabulatedcriticalvalue,the
table(s) generated in accordance with the procedures outlined calculated coefficient is significant and corrections are applied
in 7.5, plot the average control tire traction test parameter (that
to the candidate tire data in accordance with 8.5.
is, for C1 to Ci) at each speed or other operational condition,
8.3.2 If the correlation coefficient is not significant, no
as a function of the test sequence number for the control set or
corrections are required and the original candidate tire set
the “test time” period (hours) that has elapsed for each control
performance data may be used for evaluation.
tire test. For a good evaluation of potential drift, at least five
8.4 Evaluating the Significance of Transient Variations—
control set values (that is, C1 to C5 as defined in Table 1)
The procedure outlined for a decision on the existence of a
should be available; six or more is better.
transient or shift variation is given as a recommended ap-
8.2.1 The plot of average control traction test parameter
proach. Transient variations are one of two types: (1) After
versus test sequence number or time period is examined for
several control tire values with an established trend, an abrupt
two types of response: (1) any upward or downward drift or
change in one or more control tire traction parameter values
trend and (2) the less common occurrence of any transient or
occurs(thisisfollowedbyareturntotheestablishedtrend);or
step change of either a temporary or permanent value shift.
(2)afteranestablishedtrendisobserved,anabruptshiftoccurs
AnnexA1 gives some typical control tire versus test sequence
number plots. Since the time drift may be nonlinear, a and a new trend is established with no return to the original
level.
transformation may be applied to the data to permit a linear
regression analysis to be conducted. A curvilinear time trend
8.4.1 The significance of the shift is established by compar-
can be converted into a relationship that very closely approxi-
ing the magnitude of the step with the standard error of the
mates linearity on the basis of the logarithmic transformation
estimate (or the standard deviation) of the control tire traction
of both the test sequence number and the average parameter
valuesabouttheregressionline.Calculatethestandarderrorof
test value.
theestimate(SE)fortheactualorlogtransformeddata(see8.2
8.2.2 The calculated correlation coefficient, R , from the
(calc) and 8.3) according to the type of transient shift. All of the
transformeddatalinearregressionanalysisisusedtodetermine
calculations as outlined below must be performed on the same
if the trend or drift is significant. If the calculated coefficient is
basis, that is, all with actual values or all with transformed
significant, a correction of the candidate tire set traction
values.
parametervaluesismade.Correctionforanysignificantdriftis
8.4.2 For a Type 1 Shift—With any typical statistical
made on a basis that allows for any overall curvilinear trend
software,calculatetheSEfortheregressionlinefittedtoallthe
(see 8.5).
data points, omitting the shifted or transient offset points.
8.3 Evaluating the Significance of Drift—For the linear or
Designate this as SE(MR), the main regression standard error
log transformed traction parameter versus linear or log trans-
of estimate. If there are several (four or more) offset points,
formed test sequence number plot, evaluate the correlation
calculate the SE for the regression line fitted to these points.
coefficient, R , using any typical software or spreadsheet
(calc) Designate this as SE(O), the offset point standard error of
statistical calculation algorithm.
estimate.Iftherearethreeorfeweroffsetpoints,calculatetheir
8.3.1 Determine if R is significant for the control tire
(calc) average; designate this as OP .
avg
traction parameter by referring to Table 2, a table of 95%
8.4.3 For a Type 2 Shift—With any statistical software,
confidence level “critical” correlation coefficient values, R ,
(crit)
calculate the SE of each of the two regression trend lines
for varying degrees of freedom (DF). If the calculated corre-
(actualvaluesortransformed).DesignatetheseasSE(1)forthe
first trend line and SE(2) for the second line.
A
TABLE 2 Critical Values of Correlation Coefficient
8.4.4 Significance of Transient Shift—The significance is
DF R(crit)
determined by comparing the magnitude of the shift or offset
1 0.997
with the magnitude of the standard errors in question.
2 0.950
8.4.4.1 Significance For a Type 1 Shift—If there are four or
3 0.878
40.811
more offset points, the shift is significant if the difference
5 0.754
between the offset regression line and the main regression line
6 0.706
7 0.666 (at the shift point) is greater than the sum [2 SE(MR)+2
8 0.631
SE(O)], that is, greater than the sum of the two standard
9 0.602
deviation limits (2 σ limits) about each regression line. If there
10 0.576
12 0.532
are three or fewer offset points, the shift is significant if the
14 0.497
differencebetweenOP andthevalueoftheregressionlineat
avg
16 0.468
the initial point of offset is greater than [4 SE(MR)].
18 0.443
20 0.422
8.4.4.2 Significance For a Type 2 Shift—The shift is signifi-
25 0.380
cant if the difference between the two regression lines at the
30 0.349
A point of initial offset is greater than the sum [2 SE(1)+2
Critical values for the correlation coefficient, R(crit) at the 95 % confidence level
or at p = 0.05 are given as a function of the degrees of freedom, DF.The value for SE(2)].
DF is equal to (N − 2), where N is the number of pairs of data, number of log
8.4.5 If significant transient shifts are found, corrections are
(average parameter) values, plotted for the control set, that is, Ci.
made in accordance with 8.5.
F1650 − 21
8.5 Making the Corrections—For each speed or other op- METHOD B—CORRECTIONS BASED ON AVERAGE
erational condition, arrange the control tire set average (mea- OF CONTROL TIRE TRACTION TESTS
sured) traction test values in chronological or test sequence
9. Summary of Method B
order, that is, C1, C2, C3, . Ci. Normal correction procedure
is defined on the basis of equivalent corrections to each 9.1 This method corrects the data obtained throughout the
candidate tire in the interval between two successive control evaluation program using the same basic calculation algorithm
tire traction tests (see 8.5.1). An alternative correction proce- as for MethodA, with one important difference.The candidate
dure using a weighting technique for the first and second tire traction values are corrected to a “reference point” char-
candidate tires between successive control tires (PlanA) or the acterized by the grand average traction test value (averaged
first,second,andthird(PlanB),isgivenasanoptioninAnnex over all control tire traction test values). This method also
A2.Thisoptionalcorrectionproceduremaybemoreimportant applies the corrections to all candidate tire traction test data
for Plan B testing with three candidate tires between each values.Nostatisticaltestsofsignificancefortrendsortransient
successive set of control tires. For the normal procedure, shifts are required. See Appendix X2 for some background on
compute the “correction” factors, Fj, as follows: how making corrections influences the 62 σ limits on candi-
date tire relative performance as outlined in Section 10.
F1 5 ~C11C2!/2C1
9.2 The test procedure for Method B is exactly as given in
F2 5 C21C3 /2C1
~ !
Section 7 of this practice. Follow all instructions as given in
F3 5 C31C4 /2C1
~ !
this section.
F4 5 C41C5 /2C1 (1)
~ !
9.3 Making the Corrections—For each speed or other op-
F5 5 ~C51C6!/2C1
erational condition, arrange the control tire set average (mea-
… sured) traction test values in chronological or test sequence
order, C1, C2, C3, . Ci. Compute the “correction” factors, Fj,
Fj 5 Ci1Ci11 /2C1
~ !
as follows:
8.5.1 Divide the measured candidate tire set performance
F1 5 C11C2 /2C ,
~ !
avg
parameter values by the appropriate “correction” factor to
F2 5 ~C21C3!/2C ,
obtain the “corrected value” for the candidate tire set perfor- avg
mance parameter. The appropriate correction factor is that
F3 5 ~C31C4!/2C ,
avg
factor calculated from the control tire (C values) that brackets
F4 5 C41C5 /2C , (3)
~ !
avg
the measured candidate tire parameter values within the test
F5 5 C51C6 /2C ,
~ !
avg
sequence (time) span for the two C values. Thus, apply the
…
Factor F1 to the candidate tire test values between C1 and C2;
apply F2 to the candidate tire test values between C2 and C3,
Fj 5 ~Ci1Ci11!/2C
avg
etc. The following equations give the general expression for
where:
the“ corrected parameter” values for Plan A, in terms of the
C = average of all Ci values in any program.
measuredparametervaluesandthevalueofFj.Expressionsfor avg
the other “corrected parameter” values have the same calcula-
9.3.1 Divide the measured candidate tire set performance
tion procedure, for example:
parameter values by the appropriate “correction” factor to
obtain the “corrected value” for the candidate tire set perfor-
~Corr! ParameterCandidateSet15
“asmeasured” ParameterCandidateSet1/F1 mance parameter. The appropriate correction factor is that
factor calculated from the control tire (C values) that brackets
Corr ParameterCandidateSet25
~ !
the measured candidate tire parameter values within the test
“asmeasured” ParameterCandidateSet2/F1
sequence (time) span for the two C values. Thus, apply the
~Corr! ParameterCandidateSet35 (2)
Factor F1 to the candidate tire test values between C1 and C2;
apply F2 to the candidate tire test values between C2 and C3;
“asmeasured” ParameterCandidateSet3/F2
etc. The following equations give the general expression for
Corr ParameterCandidateSet45
~ !
the“ corrected parameter” values for Plan A in terms of the
“asmeasured” ParameterCandidateSet4/F2
measuredparametervaluesandthevalueofFj.Expressionsfor
…
the other “corrected parameter” values have the same calcula-
Corr ParameterCandidateSetM5 tion procedure:
~ !
“asmeasured” ParameterCandidateSetM/Fj
Corr ParameterCandidateSet15
~ !
“asmeasured” ParameterCandidateSet1/F1,
8.5.2 Tabulate the corrected candidate parameter values as
an additional column in the table format as outlined in 7.5.
~Corr! ParameterCandidateSet25
Indicate on the table that Method A correction was used. “asmeasured” ParameterCandidateSet2/F1,
F1650 − 21
Corr ParameterCandidateSet35 (4) TPI 5 TPparameter i /TPparameter refstd 100 (5)
~ ! @ ~ ! ~ !#
“asmeasured” ParameterCandidateSet3/F2, and
~Corr! ParameterCandidateSet45
where:
“asmeasured” ParameterCandidateSet4/F2,
TP parameter (i) = corrected or original average trac-
… tion performance parameter for
the te
...

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.
´1
Designation: F1650 − 98 (Reapproved 2014) F1650 − 21
Standard Practice for
Evaluating Tire Traction Performance Data Under Varying
Test Conditions
This standard is issued under the fixed designation F1650; 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.
ε NOTE—Editorially corrected Subsection X2.4 in April 2014.
INTRODUCTION
Tire traction testing programs at proving grounds or other exterior test sites are often extended over
a period of days or weeks. During this time period test conditions may change due to a number of
varying factors, for example, temperature, rain or snow fall, surface texture, water depth, and wind
velocity and direction. If tire performance comparisons are to be made over any part of the test
program (or the entire program) where these test condition variations are known or suspected to affect
performance, the potential influence of these variations must be considered in any final evaluation of
traction performance.
1. Scope
1.1 This practice covers the required procedures for examining sequential control tire data for any variation due to changing test
conditions. Such variations may influence absolute and also comparative performance of candidate tires, as they are tested over
any short or extended time period. The variations addressed in this practice are systematic or bias variations and not random
variations. See Appendix X1 for additional details.
1.1.1 Two types of variation may occur: time or test sequence “trend variations,” either linear or curvilinear, and the less common
transient or abrupt shift variations. If any observed variations are declared to be statistically significant, the calculation procedures
are given to correct for the influence of these variations. This approach is addressed in Method A.
1.2 In some testing programs, a policy is adopted to correct all candidate traction test data values without the application of a
statistical routine to determine if a significant trend or shift is observed. This option is part of this practice and is addressed in
Method B.
1.3 The issue of rejecting outlier data points or test values that might occur among a set of otherwise acceptable data values
obtained under identical test conditions in a short time period is not part of this practice. Specific test method or other outlier
rejection standards that address this issue may be used on the individual data sets prior to applying this practice and its procedures.
1.4 Although this practice applies to various types of tire traction testing (for example, dry, wet, snow, ice), the procedures as given
in this practice may be used for any repetitive tire testing in an environment where test conditions are subject to change.
This practice is under the jurisdiction of ASTM Committee F09 on Tires and is the direct responsibility of Subcommittee F09.20 on Vehicular Testing.
Current edition approved Jan. 1, 2014April 1, 2021. Published February 2014April 2021. Originally approved in 1995. Last previous edition approved in 20052014 as
ε1
F1650 – 98 (2005).(2014) . DOI: 10.1520/F1650-98R14E01.10.1520/F1650-21.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F1650 − 21
1.5 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 safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.6 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:
E501 Specification for Standard Rib Tire for Pavement Skid-Resistance Tests
E524 Specification for Standard Smooth Tire for Pavement Skid-Resistance Tests
E826 Practice for Testing Homogeneity of a Metal Lot or Batch in Solid Form by Spark Atomic Emission Spectrometry
E1136 Specification for P195/75R14 Radial Standard Reference Test Tire
F538 Terminology Relating to the Characteristics and Performance of Tires
F2493 Specification for P225/60R16 97S Radial Standard Reference Test Tire
F2870 Specification for 315/70R22.5 154/150L Radial Truck Standard Reference Test Tire
F2871 Specification for 245/70R19.5 136/134M Radial Truck Standard Reference Test Tire
F2872 Specification for 225/75R16C 116/114S M+S Radial Light Truck Standard Reference Test Tire
3. Terminology
3.1 Descriptions of Terms Specific to This Standard—Descriptions of terms particular to this practice are listed either as principal
terms or under principal terms as derived terms.
3.1 Discussion: Definitions of Terms Specific to This Standard:
3.2.1 The terminology in this section is currently under review by Subcommittee F09.94 on Terminology. This terminology is
subject to change and should be considered tentative.
3.1.1 candidate tire (set), n—a test tire (or test tire set) that is part of an evaluation program; each candidate tire (set) usually has
certain unique design or other features that distinguish it from other candidate tires (sets) in the program. F538
3.1.2 control tire (set), n—a reference tire (or reference set) repeatedly tested in a specified sequence throughout an evaluation
program, that is used for data adjustment or statistical procedures, or both, to offset or reduce testing variation and improve the
accuracy of candidate tire (set) evaluation or detect test equipment variation, or both. sequence, typically in conjunction with a
candidate tire (set), throughout an evaluation program. F538
3.1.2.1 Discussion—
Control tires (sets) are used for adjustment of data sets generated from an evaluation program or the statistical procedures used
on data sets, or both, in order to offset or reduce variation in test results. They can also be used to improve the accuracy of candidate
tire (set) data and to detect variation in test equipment.
3.1.3 reference tire (set), n—a special test tire (test tire set) that is used as a base value or benchmark in an evaluation program;
these tires usually have carefully controlled design features to minimize variation. F538
3.1.4 standard reference test tire, SRTT, n—a tire that is commonly used as a control tire or surface monitoring tire and meets the
requirements of Specification for one of the Specifications E1136, F2493commonly, F2870used, F2871as a control tire , or
F2872surface monitoring tire. . F538
3.1.5 surface monitoring tire (set), n—a reference tire (or reference set),set) used to evaluate changes in the test surface over a
selected time period. F538
3.1.6 test, test (or testing), n—a technical procedure procedure, method, or guide performed on an object (or set of objects) using
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.
F1650 − 21
specified equipment, that produces data; the data are used to evaluate or model selected properties or characteristics of the object
(or set of objects). F538
3.1.7 test run, n—in tire testing, a single pass (overover a given test surface) or sequence of data acquisition, surface, or the
acquisition of a sequence of data, or both, in the act of testing a tire or tire set under selected test conditions. F538
3.2.9 test tire, n—a tire used in a test.
3.1.8 test tire set,(set), n—one or more tires, as required by the test equipment or procedure,procedure to perform a test, producing
a single set of results; these tires test result; the tires within a test tire set are usually nominally identical. F538
3.1.9 traction test, n— in tire testing, a series of n test runs at a selected operational condition; a traction test is characterized by
an average value for the measured performance parameter. F538
4. Significance and Use
4.1 Tire testing is conducted to make technical decisions on various performance characteristics of tires, and good technical
decisions require high quality test data. High quality test data are obtained with carefully designed and executed tests. However,
even with the highest quality testing programs, unavoidable time or test sequence trends or other perturbations may occur. The
procedures as described in this practice are therefore needed to correct for these unavoidable testing complications.
5. Summary of Practice
5.1 This practice specifies certain test plans for testing control tires. Testing begins with an initial test of the control tire or control
tire set. A number of candidate tire traction tests are then conducted, followed by a repeat test of the control tire traction test.
Additional candidate tire traction tests are conducted prior to the next control tire traction test. This sequential procedure is repeated
for the entire evaluation program.
5.2 Using control tire average measured performance parameters, the performance parameters of the candidate tires (sets) are
corrected for any changes in test conditions. Two correction procedures are described (Method A and Method B) that use different
reference points for data correction and as such give different values for the corrected actual or absolute traction parameters.
However, both test methods give the same relative ratings or traction performance indexes. See Section 10 for more details. The
two test methods are summarized in more detail in Section 6 and Section 9. Both Methods A and B have advantages and
disadvantages.
5.2.1 Method A uses the initial operational conditions defined by the first control tire traction test as a reference point. The
calculations correct all traction test performance parameters (for example, traction coefficients) to the initial level or condition of
the pavement or other testing conditions, or both. With this test method, corrections may be made after only a few candidate tire
and control tire sets have been evaluated.
5.2.2 Method B uses essentially the midpoint of any evaluation program, with the grand average traction test value as a reference
point. This grand average value is obtained with higher precision than the initial control tire traction test average of Method A,
since it contains more values. However, Method B corrections cannot be made until the grand average value is established, which
is normally at the end of any program.
5.3 Annex A1 provides illustrations of several types of typical variation patterns for control tire data. It additionally provides an
example of the Method A correction calculations required to evaluate a set of candidate test tires. Method B corrections follow the
same general approach as illustrated in Annex A1, with C used in place of C1.
avg
5.4 Annex A2 provides a recommended technique for weighting the correction of the two or three candidate tire values (for
example, T1, T2, T3) between each pair of control tire values. This gives a slightly improved correction that may be important in
certain testing operations.
5.5 Appendix X1 provides a statistical model for the traction measurement process. This may help the user of this practice to sort
out the differences between fixed or bias components of variation and random components of variation. Appendix X1 gives a
rationale for the procedures as outlined in this practice.
F1650 − 21
5.6 Annex A2 contains some background and details on the propagation of error or test variation that occurs when corrections are
applied to the measured traction performance parameters and when traction performance indexes are calculated.
METHOD A—DATA CORRECTIONS BASED ON INITIAL CONTROL TIRE TRACTION TEST
6. Summary of Method A
6.1 This method corrects the data obtained throughout the evaluation program to the initial conditions (test surface or other, or
both)“ reference point” at the beginning of the program. The correction procedure (and calculation algorithm) for time trend
variations is mathematically equivalent to that described in Practice E826. The procedure used for abrupt or step changes is
provisional and is subject to change as experience is gained. In this method the initial traction test value for the control tire is a
key data point. This method also allows for decisions on the need for any correction, based on a statistical analysis of the control
tire data.
7. Procedure
7.1 The test procedure is given in terms of testing tire sets of four tires, that is, one tire on each of four vehicle positions. If only
one tire is to be tested (trailer or other dynamometer vehicle testing), follow the procedure as outlined with the understanding that
the one tire replaces the tire set.
7.2 Assemble all the tire sets to be tested in any evaluation program or for daily testing. Select the test speeds to be used and other
operational test conditions as well as the order in which the candidate tire sets are to be tested.
7.2.1 For any selected order, a test plan is established with reference tire(s) tire (set) designated as a control tire set tested at regular
intervals among the selected candidate tire sets. Select the number of test runs or replicates for both control and candidate tire sets.
A complete test for a tire set is defined as the total of p traction tests, one at each selected operational test condition, with n replicate
test runs for each operational condition (for example, speed and surface type).
7.2.2 Tests with a surface monitoring tire may also be conducted on a regular basis in addition to the control tire.
7.3 Test Sequence—The control tires may be standard tires as specified in Specifications E501, E524, and E1136, and F2493, or
a tire set similar in design and performance level to the candidate tire sets. Conduct a complete test for the control tire sets in
relation to the candidate tire sets as given in Table 1. Two test plans are given: Plan A, in which (excluding the initial control tire
set) candidate tires tire sets constitute 67 % of the tires tested, and Plan B, in which candidate tires tire sets constitute 75 % of the
tires tested.
7.4 Number of Test Runs at Each Speed or Operational Condition—The number of test runs or replicates, n, for each speed or
other selected operational condition for each candidate tire set and each control tire set, except the first set, shall be selected. The
number of test runs depends on the test method. Good testing procedure calls for as many test runs as possible. If direction of test
is important on any test surface, one half of the test runs shall be in each direction.
7.4.1 Number of Test Runs: Initial Control Tire Set—The initial test for the control, control tire set, indicated by C1, is a key value
used for correction of candidate tire set performance parameter values as testing proceeds. Therefore, the average performance
parameters for C1 must be evaluated with a high degree of confidence and the recommended number of test runs for C1 should
be at least two times the number of test runs selected in 7.4.
A
TABLE 1 Test Plans for Tire Performance Evaluation
Plan A:
Test in the order: C1, T1, T2, C2, T3, T4, C3, T5, T6, C4, etc.
Plan B:
Test in the order: C1, T1, T2, T3, C2, T4, T5, T6, C3, T7, T8,T9,
C4, etc.
A
Ci = average measured parameter (for n test runs) for a selected operational
condition for the ith control set test (that is, i = 1, 2, 3, etc.)
Ti = average measured parameter (for n test runs) of a selected operational
condition for the ith candidate set test (that is, i = 1, 2, 3, etc.).
F1650 − 21
7.4.2 More than One Control Tire—In some types of testing, the control tire is damaged or changed by the testing to the extent
that it ceases to function as a stable control. In such situations it is necessary to use more than one control tire throughout any
evaluation program. In such cases a control tire indication scheme such as C1-1, C1-2, C1-3, C2-4, C2-5, C2-6, C3-1, etc., is
suggested. In this scheme, C1-1 = control tire 1, sequence use 1; C1-2 = control tire 1, sequence use 2; . ., C2-4 = control tire 2,
sequence use 4, etc.
7.5 Table of Results—Prepare a table of test results and record all data with columns for:
7.5.1 Test sequence number, a sequential indication from 1 to m, of all the tests for any program of evaluation,
7.5.2 Tire set identification,
7.5.3 Speed or other selected operational test condition(s), and
7.5.4 Average value (for n test runs) for the measured parameter for that operational condition.
7.6 Both control and candidate tire set data shall be included in the table in the order as tested. If deemed important, a separate
table of ambient temperature, wind direction, wind velocity, or other weather information also shall be prepared on a selected time
(hourly) basis.
8. Calculations for Corrected Traction Performance Data
8.1 Preliminary Control Tire Set Data Review—The decision to correct data, for any part of the test program where candidate tire
set comparisons are to be made, is based on the time or test sequence response of the control tire parameters for each speed or
other selected operational test condition. Corrections may also be made for the entire test program. If a significant trend is found
or if significant transient perturbations are found, corrections are made for candidate tire set traction performance parameters.
8.2 Evaluating the Control Tire Data—Using the data table(s) generated in accordance with the procedures outlined in 7.5, plot
the average control tire traction test parameter (that is, for C1 to Ci) at each speed or other operational condition, as a function
of the test sequence number for the control set or the “test time” period (hours) that has elapsed for each control tire test. For a
good evaluation of potential drift, at least five control set values (that is, C1 to C5 as defined in Table 1) should be available; six
or more is better.
8.2.1 The plot of average control traction test parameter versus test sequence number or time period is examined for two types
of response: (1) any upward or downward drift or trend and (2) the less common occurrence of any transient or step change of
either a temporary or permanent value shift. Annex A1 gives some typical control tire versus test sequence number plots. Since
the time drift may be nonlinear, a transformation may be applied to the data to permit a linear regression analysis to be conducted.
A curvilinear time trend can be converted into a relationship that very closely approximates linearity on the basis of the logarithmic
transformation of both the test sequence number and the average parameter test value.
8.2.2 The calculated correlation coefficient, R , from the transformed data linear regression analysis is used to determine if the
(calc)
trend or drift is significant. If the calculated coefficient is significant, a correction of the candidate tire set traction parameter values
is made. Correction for any significant drift is made on a basis that allows for any overall curvilinear trend (see 8.5).
8.3 Evaluating the Significance of Drift—For the linear or log transformed traction parameter versus linear or log transformed test
sequence number plot, evaluate the correlation coefficient, R , using any typical software or spreadsheet statistical calculation
(calc)
algorithm.
8.3.1 Determine if R is significant for the control tire traction parameter by referring to Table 2, a table of 95 % confidence
(calc)
level “critical” correlation coefficient values, R , for varying degrees of freedom (DF). If the calculated correlation coefficient
(crit)
is greater than the tabulated critical value, the calculated coefficient is significant and corrections are applied to the candidate tire
data in accordance with 8.5.
8.3.2 If the correlation coefficient is not significant, no corrections are required and the original candidate tire set performance data
may be used for evaluation.
F1650 − 21
A
TABLE 2 Critical Values of Correlation Coefficient
DF R(crit)
1 0.997
2 0.950
3 0.878
4 0.811
5 0.754
6 0.706
7 0.666
8 0.631
9 0.602
10 0.576
12 0.532
14 0.497
16 0.468
18 0.443
20 0.422
25 0.380
30 0.349
A
Critical values for the correlation coefficient, R(crit) at the 95 % confidence level
or at p = 0.05 are given as a function of the degrees of freedom, DF. The value for
DF is equal to (N − 2), where N is the number of pairs of data, number of log
(average parameter) values, plotted for the control set, that is, Ci.
8.4 Evaluating the Significance of Transient Variations—The procedure outlined for a decision on the existence of a transient or
shift variation is given as a recommended approach. Transient variations are one of two types: (1) After several control tire values
with an established trend, an abrupt change in one or more control tire traction parameter values occurs (this is followed by a return
to the established trend); or (2) after an established trend is observed, an abrupt shift occurs and a new trend is established with
no return to the original level.
8.4.1 The significance of the shift is established by comparing the magnitude of the step with the standard error of the estimate
(or the standard deviation) of the control tire traction values about the regression line. Calculate the standard error of the estimate
(SE) for the actual or log transformed data (see 8.2 and 8.3) according to the type of transient shift. All of the calculations as
outlined below must be performed on the same basis, that is, all with actual values or all with transformed values.
8.4.2 For a Type 1 Shift—With any typical statistical software, calculate the SE for the regression line fitted to all the data points,
omitting the shifted or transient offset points. Designate this as SE(MR), the main regression standard error of estimate. If there
are several (four or more) offset points, calculate the SE for the regression line fitted to these points. Designate this as SE(O), the
offset point standard error of estimate. If there are three or fewer offset points, calculate their average; designate this as OP .
avg
8.4.3 For a Type 2 Shift—With any statistical software, calculate the SE of each of the two regression trend lines (actual values
or transformed). Designate these as SE(1) for the first trend line and SE(2) for the second line.
8.4.4 Significance of Transient Shift—The significance is determined by comparing the magnitude of the shift or offset with the
magnitude of the standard errors in question.
8.4.4.1 Significance For a Type 1 Shift—If there are four or more offset points, the shift is significant if the difference between
the offset regression line and the main regression line (at the shift point) is greater than the sum [2 SE(MR) + 2 SE(O)], that is,
greater than the sum of the two standard deviation limits (2 σ limits) about each regression line. If there are three or fewer offset
points, the shift is significant if the difference between OP and the value of the regression line at the initial point of offset is
avg
greater than [4 SE(MR)].
8.4.4.2 Significance For a Type 2 Shift—The shift is significant if the difference between the two regression lines at the point of
initial offset is greater than the sum [2 SE(1) + 2 SE(2)].
8.4.5 If significant transient shifts are found, corrections are made in accordance with 8.5.
8.5 Making the Corrections—For each speed or other operational condition, arrange the control tire set average (measured)
traction test values in chronological or test sequence order, that is, C1, C2, C3, . Ci. Normal correction procedure is defined on
the basis of equivalent corrections to each candidate tire in the interval between two successive control tire traction tests (see 8.5.1).
An alternative correction procedure using a weighting technique for the first and second candidate tires between successive control
F1650 − 21
tires (Plan A) or the first, second, and third (Plan B), is given as an option in Annex A2. This optional correction procedure may
be more important for Plan B testing with three candidate tires between each successive set of control tires. For the normal
procedure, compute the “correction” factors, Fj, as follows:
F15 ~C11C2!/2C1
F25 C21C3 /2C1
~ !
F35 C31C4 /2C1
~ !
F45 ~C41C5!/2C1 (1)
F55 ~C51C6!/2C1
…
Fj 5 Ci1Ci11 /2C1
~ !
8.5.1 Divide the measured candidate tire set performance parameter values by the appropriate “correction” factor to obtain the
“corrected value” for the candidate tire set performance parameter. The appropriate correction factor is that factor calculated from
the control tire (C values) that brackets the measured candidate tire parameter values within the test sequence (time) span for the
two C values. Thus, apply the Factor F1 to the candidate tire test values between C1 and C2; apply F2 to the candidate tire test
values between C2 and C3, etc. The following equations give the general expression for the“ corrected parameter” values for Plan
A, in terms of the measured parameter values and the value of Fj. Expressions for the other “corrected parameter” values have the
same calculation procedure, for example:
~Corr! Parameter Candidate Set 15
“as measured” Parameter Candidate Set1/F1
Corr Parameter Candidate Set 25
~ !
“as measured” Parameter Candidate Set2/F1
~Corr! Parameter Candidate Set 35 (2)
“as measured” Parameter Candidate Set3/F2
Corr Parameter Candidate Set 45
~ !
“as measured” Parameter Candidate Set4/F2
…
Corr Parameter Candidate SetM5
~ !
“as measured” Parameter Candidate SetM/Fj
8.5.2 Tabulate the corrected candidate parameter values as an additional column in the table format as outlined in 7.5. Indicate
on the table that Method A correction was used.
METHOD B—CORRECTIONS BASED ON AVERAGE OF CONTROL TIRE TRACTION TESTS
9. Summary of Method B
9.1 This method corrects the data obtained throughout the evaluation program using the same basic calculation algorithm as for
Method A, with one important difference. The candidate tire traction values are corrected to a “reference point” characterized by
the grand average traction test value (averaged over all control tire traction test values). This method also applies the corrections
to all candidate tire traction test data values. No statistical tests of significance for trends or transient shifts are required. See
Appendix X2 for some background on how making corrections influences the 62 σ limits on candidate tire relative performance
as outlined in Section 10.
9.2 The test procedure for Method B is exactly as given in Section 7 of this practice. Follow all instructions as given in this section.
9.3 Making the Corrections—For each speed or other operational condition, arrange the control tire set average (measured)
traction test values in chronological or test sequence order, C1, C2, C3, . Ci. Compute the “correction” factors, Fj, as follows:
F15 ~C11C2!/2C ,
avg
F25 C21C3 /2C ,
~ !
avg
F35 C31C4 /2C ,
~ !
avg
F1650 − 21
F45 C41C5 /2C , (3)
~ !
avg
F55 C51C6 /2C ,
~ !
avg
…
Fj 5~Ci1Ci11!/2C
avg
where:
C = average of all Ci values in any program.
avg
9.3.1 Divide the measured candidate tire set performance parameter values by the appropriate “correction” factor to obtain the
“corrected value” for the candidate tire set performance parameter. The appropriate correction factor is that factor calculated from
the control tire (C values) that brackets the measured candidate tire parameter values within the test sequence (time) span for the
two C values. Thus, apply the Factor F1 to the candidate tire test values between C1 and C2; apply F2 to the candidate tire test
values between C2 and C3; etc. The following equations give the general expression for the“ corrected parameter” values for Plan
A in terms of the measured parameter values and the value of Fj. Expressions for the other “corrected parameter” values have the
same calculation procedure:
~Corr! Parameter Candidate Set 15
“as measured” Parameter Candidate Set1/F1,
Corr Parameter Candidate Set 25
~ !
“as measured” Parameter Candidate Set2/F1,
~Corr! Parameter Candidate Set 35 (4)
“as measured” Parameter Candidate Set3/F2, and
Corr Parameter Candidate
...