1、Designation: E 1169 07Standard Practice forConducting Ruggedness Tests1This standard is issued under the fixed designation E 1169; 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 i
2、ndicates the year of last reapproval. Asuperscript epsilon (e) 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 provid
3、ed 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
4、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 ad
5、dress 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:2E 456 Termin
6、ology Relating to Quality and StatisticsE 1325 Terminology Relating to Design of ExperimentsE 1488 Guide for Statistical Procedures to Use in Develop-ing and Applying Test MethodsF 2082 Test Method for Determination of TransformationTemperature of Nickel-Titanium Shape Memory Alloys byBend and Free
7、Recovery3. Terminology3.1 DefinitionsThe terminology defined in TerminologyE 456 applies to this practice unless modified herein.3.1.1 ruggedness, ninsensitivity of a test method to de-partures from specified test or environmental conditions.3.1.1.1 DiscussionAn evaluation of the “ruggedness” of ate
8、st 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.3.1.2 ruggedness test, na planned experiment i
9、n whichenvironmental factors or test conditions are deliberately variedin order to evaluate the effects of such variation.3.1.2.1 DiscussionSince there usually are many environ-mental factors that might be considered in a ruggedness test, itis customary to use a “screening” type of experiment design
10、which 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
11、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.3.2 Definitions of Terms Specific to This Standard:3.2.1 facto
12、r, ntest variable that may affect either the resultobtained from the use of a test method or the variability of thatresult.3.2.1.1 DiscussionFor experimental purposes, factorsmust be temporarily controllable.3.2.2 foldover, ntest runs, added to a two-level fractionalfactorial experiment, generated b
13、y duplicating the originaldesign by switching levels of one or more factors in all runs.3.2.2.1 DiscussionThe 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 intera
14、ctions of other factorsthat are aliased in the original design.1This practice is under the jurisdiction of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.20 on Test MethodEvaluation and Quality Control.Current edition approved Aug. 1, 2007. Published
15、 October 2007. Originallyapproved in 1987. Last previous edition approved in 2002 as E 1169 02.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Documen
16、t Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.4. Summary of Practice4.1 Conducting a ruggedness test requires making system-atic changes in the variables, called factors, that are associatedwith th
17、e test method and then observing the subsequent effectof those changes upon the test result of each run.4.2 The factors chosen for ruggedness testing are thosebelieved to have the potential to affect the results. However,since no control limits are provided in the standard for thesefactors, ruggedne
18、ss 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 use
19、d 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
20、.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
21、 the greatest effecton the outcome of a test method. Statistical design enablesmore accurate determination of the factor effects than would beachieved if separate experiments were carried out for eachfactor. The proposed designs are easy to use and are efficient indeveloping the information needed f
22、or evaluating quantitativetest 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 betw
23、een 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 t
24、est method.5.4 Ruggedness testing is part of the validation phase ofdeveloping a standard test method as described in GuideE 1488. It is preferred that a ruggedness test precedes aninterlaboratory (round robin) study.6. Ruggedness Test Design6.1 Aseries of fractional factorial designs are recommende
25、dfor 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 r
26、elative 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
27、 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.6.3 The design provides equal numbers of low and highlevel runs for every factor. In other words, the designs arebalanced. Also, for any factor
28、, 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 be
29、tween 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 factors effect.6.5 If th
30、e 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 eig
31、ht signs for3The boldface numbers in parentheses refer to the list of references at the end ofthis standard.TABLE 1 Recommended Design for Up to Seven FactorsNOTEFor four factors, use ColumnsA, B, C, and E; for five factors, use ColumnsA, B, C, D, and F; for six factors, use ColumnsA, B, C, D, F, an
32、d G.PB Order Run # A B C D E F G Test Result1 111-11-1-12 -1111-3 1-1111-114 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 -EffectE1169072Column C of Table 1, multiplied by the corresponding eightsigns in Column D, gives a column of signs for the inter
33、actionCD. 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
34、 CD isidentical to minus the column of signs for Column A.6.6 To separate factor effects from interactions, the designshall be increased with additional runs. A “foldover,” as shownin Table 2, is recommended to separate the main effects fromthe aliased interactions. When the runs in Tables 1 and 2 a
35、recombined, 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 experime
36、nt 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 s
37、equence 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 fac
38、tor 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 situ
39、ations.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 c
40、onfounded 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
41、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 numbe
42、r 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 ex
43、periment, statistical tests of factor effects can bedetermined using the Students 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 correspond
44、ing 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). Th
45、e 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 est
46、imate of the standard error of an effect is:seffect54sr2N 3 reps(1)with degrees of freedom of (N 1)3 (reps 1),where:N = number of runs in the design,reps = number of replicates of the design, andsr= the estimated standard deviation of the test results.7.3.2.1 An example showing calculation of sr2and
47、 seffectisgiven in 8.2.8. Example of a Replicated Ruggedness Experiment8.1 An example of a seven-factor ruggedness experimentcomes from a study done for Test Method F 2082. This testmethod determines a transformation temperature for nickel-titanium shape memory alloys. The factors of interest areque
48、nch method, bath temperature at deformation, equilibriumtime, bending strain, pin spacing, linear variable differentialTABLE 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 -
49、1 -1 1 -1 1 1 -18 1111111Ave +Ave -EffectE1169073transducer (LVDT) probe weight, and heating rate. Table 3provides the levels of factors chosen in this example.8.2 After all tests are completed, the transformation tem-perature results are entered in Table 4 in the Rep 1 and Rep 2Test Result columns.8.2.1 Factor main effects are then calculated using theaverage values (Rep Ave) of each design point for the tworeplicates.At the bottom of each column are the averages of thereplicate averages corresponding to the (1) and the averages ofthe replicate averages corresponding
