Designation: F1263 − 11Standard Guide forAnalysis of Overtest Data in Radiation Testing of ElectronicParts1This standard is issued under the fixed designation F1263; 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 guide covers the use of overtesting in order toreduce the required number of parts that must be tested to meeta given quality acceptance standard. Overtesting is testing asample number of parts at a stress level higher than theirspecification stress in order to reduce the amount of necessarydata taking. This guide discusses when and how overtestingmay be applied to forming probabilistic estimates for thesurvival of electronic piece parts subjected to radiation stress.Some knowledge of the probability distribution governing thestress-to-failure of the parts is necessary, although exactknowledge may be replaced by over-conservative estimates ofthis distribution.2. Referenced Documents2.1 Military Standards:MIL-PRF 19500 Semiconductor Devices, General Specifi-cations for2MIL-PRF 38535 Integrated Circuits (Microcircuit Manufac-turing)23. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 Confidence—the probability, C, that at least a fraction,P, of the electronic parts from a test lot will survive in actualservice; since radiation testing of electronic parts is generallydestructive, this probability must be calculated from tests onselected specimens from the lot.3.1.2 Rejection Confidence—the probability, R, that a lotwill be rejected based on destructive tests of selected speci-mens if more than a specified fraction, P, of the parts in the lotwill fail in actual service.3.1.3 Discussion of Preceding Terms—Strictly speaking,most lot acceptance tests (be they testing by attributes orvariables) do not guarantee survivability, but rather that infe-rior lots, where the survival probability of the parts is less thanprobability, P, will be rejected with confidence, C. In order toinfer a true confidence, it would require a Bayes Theoremcalculation. In many cases, the distinction between confidenceand rejection confidence is of little practical importance.However, in other cases (typically when a large number of lotsare rejected) the distinction between these two kinds ofconfidence can be significant. The formulas given in this guideapply whether one is dealing with confidence or rejectionconfidence.4. Summary of Guide4.1 This guide is intended to primarily apply to sampling byattribute plans typified by Lot Tolerance Percent Defective(LTPD) tables given in MIL-PRF 38535 and MIL-PRF 19500,and contains the following:4.1.1 An equation for estimating the effectiveness of over-testing in terms of increased probability of survival,4.1.2 An equation for the required amount of overtestinggiven a necessary survival probability, and4.1.3 Cautions and limitations on the method.5. Significance and Use5.1 Overtesting should be done when (a) testing by vari-ables is impractical because of time and cost considerations orbecause the probability distribution of stress to failure cannotbe estimated with sufficient accuracy, and (b) an unrealisticallylarge number of parts would have to be tested at the specifi-cation stress for the necessary confidence and survival prob-ability.6. Interferences6.1 Probability Distributions—In overtesting, a knowledgeof the probability distribution governing stress to failure isrequired, though it need not be specified with the sameaccuracy necessary for testing by variables. For bipolar tran-sistors exposed to neutron radiation, the failure mechanism isusually gain degradation and the stress to failure is known to1This guide is under the jurisdiction ofASTM Committee F01 on Electronicsandis the direct responsibility of Subcommittee F01.11 on Nuclear and Space RadiationEffects.Current edition approved June 1, 2011. Published July 2011. Originally approvedin 1989. Last previous edition approved in 2005 as F1263 – 99(2005). DOI:10.1520/F1263-11.2Available from Standardization Documents Order Desk, Bldg. 4 Section D, 700Robbins Ave., Philadelphia, PA 19111-5094, Attn: NPODS.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1follow a lognormal distribution.3For bipolar transistors ex-posed to total dose the use of the lognormal distribution is alsofairly accurate.4For more complex electronics and other kindsof radiation stress, the lognormal distribution is widely used inestimating the failure probabilities of electronic piece parts,and therefore this standard governs the use of a lognormaldistribution. However, caution should be exercised when theprobability distribution of stress to failure is not well estab-lished. Nevertheless, even if the lognormal distribution doesnot strictly apply, the equations given in Section 7 will hold aslong as a sufficiently conservative estimate was made of thevariability of the parts within the stress range of interest.56.2 Time Dependent Post Radiation Effects—In total dosetesting annealing and rebound effects can affect the results.7. Equations and Tabulations for Overtesting7.1 Let RTand RSbe the respective overtest (radiation levelat which the test is performed) and specification stresses(specification radiation level). Let sln(max) be an estimatedmaximum standard deviation in the natural logarithms of thestress to failure, and let PTand PSbe the respective survivalprobabilities with confidence, C, at the overtest and stresslevels. Then,PS5FFF¯~PT!1ln~RT/RS!sln~max!G, (1)where:F = the cumulative standard normal probability distribu-tion, andF¯= the anti-function of F where F¯[F(X)] = X.Most probability texts tabulate the cumulative standardnormal probability distribution function, F, and its antifunction(sometimes denoted by Zp).7.1.1 When PSis given and PTis known, the overtest factoris:RT/RS5exp$sln~max! @F¯~PS!2F¯~PT!#% (2)7.2 For neutrons, 0.5 is a good estimate of sln(max).5,67.2.1 Example:Suppose bipolar transistors are tested at a neutron fluencethree times the specification fluence and it is determined thatwith 90 % confidence, at least 80 % of the transistors willsurvive the overtest fluence. Then from Eq 1, at the specifica-tion fluence, with 90 % confidence, the survival probability isas follows:

[email protected]¯~PT!1ln~3!/0.5#

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[email protected]#50.999,where we used the following facts governing the normaldistribution:Standard probability tables such as those shown in M.G.Natrella, “Experimental Statistics,” NBS Handbook 91, U.S.Dept. of Commerce (1966) shows that F¯(0.8) = 0.84. The 80percentile point of the distribution is 0.84 standard deviationsabove the mean of the distribution (80 % of the distribution isbelow 0.84 standard deviations above the mean).The number 3.04 is approximately the 99.9 percentile ofthe distribution. This result means that lots will be rejected with90 % confidence unless 99.9 % of these parts survive one timesthe specification fluence. The three times overtest has thusraised the requirement on the lot quality to a value whichwould otherwise require testing an excessively large number ofparts.57.3 Table 1 gives examples of the estimated survival prob-ability as a function of R, where R depends on the overtestfactor and the estimated maximum logarithmic standard devia-tion in stress-to-failure as follows:R5ln~RT/RS!sln~max!(3)7.3.1 Sample Use of Table 1:If an overtest were performed with R = 1.5, and if it is knownthat a certain part type has stresses-to-failure that never vary upor down by more than a factor of 4, that is sln(max) = ln(4),then the overtest level would be 1.5 =ln(RT/RS)⁄ln4 and RT/RS=e1.5ln4= 8 or 41.5= 8 times the specification level. If it weredetermined that with 90 % confidence, C, 80 % of the partswould survive the overtest level, then since the table shows thatat the specification level, with confidence, C, the table showsthat 0.990400 or an estimated 99 % of the parts would survive.Alternatively, given the data at the specification level, thedesired part survivability and a factor that bounds the variabil-ity of the parts, this table can be used to determine an overtestlevel.7.3.2 Cautions for Using Table 1:Be aware that clearly a survival probability of 1.0 is3Messenger, G. C., Steele, E. L., “Statistical Modeling of SemiconductorDevices for the TREE Environment,’’ Transactions on Nuclear Science NS-15,1968, p. 4691.4Stanley, A. G., Martin, K. E., and Price, W. E., “Hardness Assurance for TotalDose Radiation—Final Report,’’ No. 730-2, Jet Propulsion Laboratory, Pasadena,CA 1977.5Namenson, A. I., “Hardness Assurance and Overtesting,’’ IEEE Transactionson Nuclear Science NS-29, 1982, p. 1821.6Namenson, A. I., “Statistical Treatment of Damage Factors for SemiconductorDevices,’’ IEEE Transactions on Nuclear Science NS-26, 1979, p. 4691.TABLE 1 Survival Probability at Specification Level Versus R and Survival Probability at Overtest LevelSpecification Level Probability for:Overtest LevelProbabilityR =0.5 R =1.0 R =1.5 R =2.0 R =3.0 R =5.00.50 0.691462 0.841345 0.933193 0.977250 0.998650 1.0000000.80 0.910140 0.967235 0.990400 0.997756 0.999939 1.0000000.90 0.962588 0.988742 0.997295 0.999484 0.999991 1.0000000.95 0.984016 0.995913 0.999169 0.999866 0.999998 1.000000F1263 − 112unrealistic, and where it appears, the table should be inter-preted to mean that there would be no point in going to a higherlevel of overtest than the one indicated in the table. In general,very high probabilities of survival should not be taken literallybecause errors in the assumed probability distribution, unex-pected results, maverick parts, simulation fidelity, and humanerror, all affect a practical situation.An experienced user wouldhave some idea of the maximum credible survivability for theparticular application. It is suggested here that probabilities ofover 0.999999 are not credible unless massive experienceshows that tests, part processing, and the personnel are reliableto at least that level of confidence. Nevertheless, if a very highlevel of survival is predicted, the information suggests that anyweak point in a system is most likely somewhere else.8. Keywords8.1 confidence; rejection; overtest data; statistical analysisASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. 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[email protected] (e-mail); or through the ASTM website(www.astm.org). Permission rights to photocopy the standard may also be secured from the ASTM website (www.astm.org/COPYRIGHT/).F1263 − 113