Designation: E1169 − 14 An American National StandardStandard Practice forConducting Ruggedness Tests1This standard is issued under the fixed designation E1169; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers conducting ruggedness tests. Thepurpose of a ruggedness test is to identify those factors thatstrongly influence the measurements provided by a specific testmethod and to estimate how closely those factors need to becontrolled.1.2 This practice restricts itself to designs with two levelsper factor. The designs require the simultaneous change of thelevels of all of the factors, thus permitting the determination ofthe effects of each of the factors on the measured results.1.3 The system of units for this practice is not specified.Dimensional quantities in the practice are presented only asillustrations of calculation methods. The examples are notbinding on products or test methods treated.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and StatisticsE1325 Terminology Relating to Design of ExperimentsE1488 Guide for Statistical Procedures to Use in Developingand Applying Test MethodsF2082 Test Method for Determination of TransformationTemperature of Nickel-Titanium Shape Memory Alloysby Bend and Free Recovery3. Terminology3.1 Definitions—The terminology defined in TerminologyE456 applies to this practice unless modified herein.3.1.1 fractional factorial design, n—a factorial experimentin which only an adequately chosen fraction of the treatmentsrequired for the complete factorial experiment is selected to berun. E13253.1.2 level (of a factor), n—a given value, a specification ofprocedure or a specific setting of a factor. E13253.1.3 Plackett-Burman designs, n—a set of screening de-signs using orthogonal arrays that permit evaluation of thelinear effects of up to n=t–1 factors in a study of t treatmentcombinations. E13253.1.4 ruggedness, n—insensitivity of a test method to de-partures from specified test or environmental conditions.3.1.4.1 Discussion—An evaluation of the “ruggedness” of atest method or an empirical model derived from an experimentis useful in determining whether the results or decisions will berelatively invariant over some range of environmental variabil-ity under which the test method or the model is likely to beapplied.3.1.5 ruggedness test, n—a planned experiment in whichenvironmental factors or test conditions are deliberately variedin order to evaluate the effects of such variation.3.1.5.1 Discussion—Since there usually are many environ-mental factors that might be considered in a ruggedness test, itis customary to use a “screening” type of experiment designwhich concentrates on examining many first order effects andgenerally assumes that second order effects such as interactionsand curvature are relatively negligible. Often in evaluating theruggedness of a test method, if there is an indication that theresults of a test method are highly dependent on the levels ofthe environmental factors, there is a sufficient indication thatcertain levels of environmental factors must be included in thespecifications for the test method, or even that the test methoditself will need further revision.3.1.6 screening design, n—a balanced design, requiringrelatively minimal amount of experimentation, to evaluate thelower order effects of a relatively large number of factors interms of contributions to variability or in terms of estimates ofparameters for a model. E13253.1.7 test result, n—the value of a characteristic obtained bycarrying out a specified test method.3.2 Definitions of Terms Specific to This Standard:1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.20 on Test MethodEvaluation and Quality Control.Current edition approved May 1, 2014. Published May 2014. Originallyapproved in 1987. Last previous edition approved in 2013 as E1169 – 13a. DOI:10.1520/E1169-14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.1 factor, n—test variable that may affect either the resultobtained from the use of a test method or the variability of thatresult.3.2.1.1 Discussion—For experimental purposes, factorsmust be temporarily controllable.3.2.2 foldover, n—test runs, added to a two-level fractionalfactorial experiment, generated by duplicating the originaldesign by switching levels of one or more factors in all runs.3.2.2.1 Discussion—The most useful type of foldover iswith signs of all factors switched. The foldover runs arecombined with the initial test results. The combination allowsmain effects to be separated from interactions of other factorsthat are aliased in the original design.4. Summary of Practice4.1 Conducting a ruggedness test requires making system-atic changes in the variables, called factors, and then observingthe subsequent effect of those changes upon the test result ofeach run. Factors are features of the test method or of thelaboratory environment that are known to vary across labora-tories and are subject to control by the test method.4.2 The factors chosen for ruggedness testing are thosebelieved to have the potential to affect the results. However,since no limits may be provided in the standard for thesefactors, ruggedness testing is intended to evaluate this poten-tial.4.3 This practice recommends statistically designed experi-ments involving two levels of multiple factors. The steps to beconducted include:4.3.1 Identification of relevant factors;4.3.2 Selection of appropriate levels (two for each factor) tobe used in experiment runs;4.3.3 Display of treatment combinations in cyclic shiftedorder (see Annex A1 for templates), which assigns factors andlevels to runs;4.3.4 Execution of runs arranged in a random order;4.3.5 Statistical analysis to determine the effect of factors onthe test method results; and4.3.6 Possible revision of the test method as needed.5. Significance and Use5.1 A ruggedness test is a special application of a statisti-cally designed experiment. It is generally carried out when it isdesirable to examine a large number of possible factors todetermine which of these factors might have the greatest effecton the outcome of a test method. Statistical design enablesmore efficient and cost effective determination of the factoreffects than would be achieved if separate experiments werecarried out for each factor. The proposed designs are easy touse in developing the information needed for evaluatingquantitative test methods.5.2 In ruggedness testing, the two levels for each factor arechosen to use moderate separations between the high and lowsettings. In general, the size of effects, and the likelihood ofinteractions between the factors, will increase with increasedseparation between the high and low settings of the factors.5.3 Ruggedness testing is usually done within a singlelaboratory on uniform material, so the effects of changing onlythe factors are measured. The results may then be used to assistin determining the degree of control required of factorsdescribed in the test method.5.4 Ruggedness testing is part of the validation phase ofdeveloping a standard test method as described in GuideE1488. It is preferred that a ruggedness test precedes aninterlaboratory (round robin) study.6. Ruggedness Test Design6.1 Aseries of fractional factorial designs are recommendedfor use with ruggedness tests for determining the effects of thetest method variables (see Annex A1). All designs consideredhere have just two levels for each factor. They are known asPlackett-Burman designs (1).36.1.1 Choose the level settings so that the measured effectswill be reasonably large relative to measurement error. It issuggested that the high and low levels be set at the extremelimits that could be expected to exist between differentqualifying laboratories.6.2 Table 1 shows the recommended design for up to sevenfactors, each factor set at two levels. The level setting isindicated by either (-1) or (1) for low or high levels, respec-tively. For factors with non-ordered scales (categorical), thedesignation “low” or “high” is arbitrary.3The boldface numbers in parentheses refer to the list of references at the end ofthis standard.TABLE 1 Recommended Design for Up to Seven FactorsNOTE 1—For four factors, use Columns A, B, C, and E; for five factors, use Columns A, B, C, D, and F; for six factors, use Columns A, B, C, D, F,and G.PB Order Run # A B C D E F G Test Result1 111-11-1-12 -1111-3 -1111-114 1 -1 -1 1 1 1 -15 -1 1 -1 -1 1 1 16 1 -1 1 -1 -1 1 17 1 1 -1 1 -1 -1 18 -1-1-1-1-1-1-Ave +Ave -EffectE1169 − 1426.3 The design provides equal numbers of low and highlevel runs for every factor. In other words, the designs arebalanced. Also, for any factor, while it is at its high level, allother factors will be run at equal numbers of high and lowlevels; similarly, while it is at its low level, all other factors willbe run at equal numbers of high and low levels. In theterminology used by statisticians, the design is orthogonal.6.4 The difference between the average response of runs atthe high level and the average response of runs at the low levelof a factor is the “main effect” of that factor. When the effectof a factor is the same regardless of levels of other factors, thenthe main effect is the best estimate of the factor’s effect.6.5 If the effect of one factor depends on the level of anotherfactor, then these two factors interact. The interaction of twofactors can be thought of as the effect of a third factor for whichthe column of signs is obtained by multiplying the columns ofsigns for the two initial factors. For example, the eight signs forColumn C of Table 1, multiplied by the corresponding eightsigns in Column D, gives a column of signs for the interactionCD. The complication of the fractional factorial designspresented here is that main effects are confounded (aliased)with the two-factor interactions. Factors are aliased when theircolumns of signs are the negatives or positives of each other.For example, the column of signs for the interaction CD isidentical to minus the column of signs for Column A.6.6 To separate factor main effects from interactions, thedesign shall be increased with additional runs.A“foldover,” asshown in Table 2, is recommended to separate the main effectsfrom the aliased interactions. When the runs in Tables 1 and 2are combined, all main factors will no longer be aliased withtwo-factor interactions.6.7 Sensitivity of the experiment can be increased by theaddition of a second block of runs that replicates the first (thatis, runs with the same factor settings as the first block).Increasing the size of the experiment improves the precision offactor effects and facilitates the evaluation of statistical signifi-cance of the effects. However, the preference of this practice isto use a foldover rather than a repeat of the original design.6.8 The sequence of runs in Tables 1 and 2 is not intendedto be the actual sequence for carrying out the experiments. Theorder in which the runs of a ruggedness experiment are carriedout should be randomized to reduce the probability of encoun-tering any potential effects of unknown, time-related factors.Alternatively, optimum run orders to control the number ofrequired factor changes and the effect of linear time trends havebeen derived (2). In some cases, it is not possible to change allfactors in a completely random order. It is best if this limitationis understood before the start of the experiment. A statisticianmay be contacted for methods to deal with such situations.7. Ruggedness Test Calculations7.1 Estimate factor effects by calculating the differencebetween average responses at the high and the low levels.When the design is folded over, obtain the main effect of afactor by averaging effects from the design and its foldover.Estimate the corresponding confounded interactions by takinghalf the difference of the main effects.7.2 A half-normal plot is used to identify potentially statis-tically significant effects.7.2.1 Construct a half-normal plot by plotting the absolutevalues of effects on the X-axis, in order from smallest tolargest, against the half-normal plotting values given in AnnexA2 on the Y-axis. Effects for all columns in the design,including columns not used to assign levels to any realexperiment factor, are plotted. The half-normal plotting valuesdo not depend on data. They depend only on the half-normaldistribution and the number of effects plotted.7.2.2 A reference line in the half normal plot is providedwith slope 1/seffect, if an estimate of precision is available.Potentially significant effects are those that fall farthest to theright of the line.7.3 If an estimate of precision is available or can be derivedfrom the experiment, statistical tests of factor effects can bedetermined using the Student’s t-test. The t-test statistic for afactor is the effect divided by the standard error seffect, which isthe same for all factors with a balanced and orthogonal design.If the t-value is greater than the t-value corresponding to the0.05 significance level, the factor is statistically significant atlevel 0.05.7.3.1 If fewer factors are used with the design than themaximum number, then “effects” estimated for the unusedcolumns differ from zero only as a result of experimental error(or interactions of other factors). The root mean square ofunused effects is an estimate of the standard error of an effecthaving degrees of freedom equal to the number of unusedeffects averaged (3).7.3.2 The design may be replicated; that is, a second blockof runs using the same factor settings as the original design isrun. Then an estimate of the standard error of an effect is:TABLE 2 Foldover of Design Shown in Table 1PB Order Run # A B C D E F G Test Result1 -1-1-1 1 -1 1 12 1 -1 -1 -1 1 -1 13 1 -1-1- -4 -1 1 - 1-1 15 1 -1 1 1 -1 -1 -16 -1 1 -1 1 1 -1 -17 -1 -1 1 -1 1 1 -18 1111111Ave +Ave -EffectE1169 − 143seffect5Œ4srep2N 3 reps(1)with degrees of freedom of (N –1)×(reps – 1),where:N = number of runs in the design,reps = number of replicates of the design, andsrep= th