1、Designation: E2696 09 (Reapproved 2013) An American National StandardStandard Practice forLife and Reliability Testing Based on the ExponentialDistribution1This standard is issued under the fixed designation E2696; the number immediately following the designation indicates the year oforiginal adopti
2、on 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 presents standard sampling procedures andtables for life and
3、 reliability testing in procurement, supply, andmaintenance quality control operations as well as in researchand development activities.1.2 This practice describes general procedures and defini-tions of terms used in life test sampling and describes specificprocedures and applications of the life te
4、st sampling plans fordetermining conformance to established reliability require-ments.1.3 This practice is an adaptation of the Quality Control andReliability Handbook H-108, “Sampling Procedures andTables for Life and Reliability Testing (Based on ExponentialDistribution),” U.S. Government Printing
5、 Office, April 29,1960.1.4 A system of units is not specified in this practice.1.5 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 dete
6、rmine the applica-bility of regulatory limitations prior to use.1.6 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendat
7、ions issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and StatisticsE2234 Practice for Sampling a Stream of Product by Attri-butes Indexed by AQLE2555 Practice for Factors and Procedures
8、for Applying theMIL-STD-105 Plans in Life and Reliability Inspection3. Terminology3.1 Definitions:3.1.1 See Terminology E456 for a more extensive listing ofterms in ASTM Committee E11 standards.3.1.2 consumers risk, ,nprobability that a lot havingspecified rejectable quality level will be accepted u
9、nder adefined sampling plan. E25553.1.2.1 DiscussionIn this practice, the consumers risk isthe probability of accepting lots with mean time to failure 1.3.1.2.2 DiscussionFor the procedures of 9.7 and 9.8, theconsumers risk may also be defined as the probability ofaccepting lots with unacceptable pr
10、oportion of lot failingbefore specified time, p1.3.1.3 life test, nprocess of placing one or more units ofproduct under a specified set of test conditions and measuringthe time until failure for each unit.3.1.4 mean time to failure, , n in life testing, the averagelength of life of items in a lot.3.
11、1.4.1 DiscussionAlso known as mean life.3.1.5 number of failures, nnumber of failures that haveoccurred at the time the decision as to lot acceptability isreached.3.1.5.1 DiscussionThe expected number of failures re-quired for decision is the average of the number of failuresrequired for decision wh
12、en life tests are conducted on a largenumber of samples drawn at random from the same exponen-tial distribution.3.1.6 producers risk, ,nprobability that a lot havingspecified acceptable quality level will be rejected under adefined sampling plan.3.1.6.1 DiscussionIn this practice, the producers risk
13、 isthe probability of rejecting lots with mean time to failure 0.3.1.6.2 DiscussionFor the procedures of 9.7 and 9.8, theproducers risk may also be defined as the probability ofrejecting lots with acceptable proportion of lot failing beforespecified time, p0.1This practice is under the jurisdiction
14、of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.40 on Reliability.Current edition approved April 1, 2013. Published April 2013. Originallyapproved in 2009. Last previous edition approved in 2009 as E2696 091. DOI:10.1520/E2696-09R13.2For referenced
15、 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 Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Consh
16、ohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Org
17、anization Technical Barriers to Trade (TBT) Committee.13.1.7 sequential life test, nlife test sampling plan wherebyneither the number of failures nor the time required to reach adecision are fixed in advance but instead decisions depend onthe accumulated results of the life test.3.1.8 unit of produc
18、t, nthat which is inspected to deter-mine its classification as defective or nondefective or to countthe number of defects. E22343.1.9 waiting time, nin life testing, the time elapsed fromthe start of testing until a decision is reached as to lotacceptability.3.1.9.1 DiscussionThe expected waiting t
19、ime required fordecision is the average of the waiting times required fordecision when life tests are conducted on a large number ofsamples drawn at random from the same exponential distribu-tion.4. Significance and Use4.1 This practice was prepared to meet a growing need forthe use of standard samp
20、ling procedures and tables for life andreliability testing in government procurement, supply, andmaintenance quality control (QC) operations as well as inresearch and development activities where applicable.4.2 A characteristic feature of most life tests is that theobservations are ordered in time t
21、o failure. If, for example, 20radio tubes are placed on life test, and tidenotes the time whenthe ith tube fails, the data occur in such a way that t1 t2 . tn. The same kind of ordered observations will occur whetherthe problem under consideration deals with the life of electricbulbs, the life of el
22、ectronic components, the life of ballbearings, or the length of life of human beings after they aretreated for a disease. The examples just given all involveordering in time.4.3 In destructive testing involving such situations as thecurrent needed to blow a fuse, the voltage needed to breakdown a co
23、ndenser, or the force needed to rupture a physicalmaterial, the test can often be arranged in such a way that everyitem in the sample is subjected to precisely the same stimulus(current, voltage, or stress). If this is done, then clearly theweakest item will be observed to fail first, the second wea
24、kestnext, and so forth. While the random variable consideredmostly in this guide is time to failure, it should be emphasized,however, that the methodology provided herein can be adaptedto the testing situations mentioned above when the randomvariable is current, voltage, stress, and so forth.4.4 Sec
25、tions 6 and 7 describe general procedures anddefinitions of terms used in life test sampling. Sections 8, 9,and 10 describe specific procedures and applications of the lifetest sampling plans for determining conformance to establishedreliability requirements.4.5 Whenever the methodology or choice of
26、 procedures inthe practice requires clarification, the user is advised to consulta qualified mathematical statistician, and reference should bemade to appropriate technical reports and other publications inthe field.5. Introduction5.1 The theory underlying the development of the life testsampling pl
27、ans of this section, including the operating charac-teristic curves, assumes that the measurements of the length oflife are drawn from an exponential distribution. Statistical testprocedures for determining the validity of the exponentialdistribution assumption have appeared in the technical statis-
28、tical journals. Professor Benjamin Epstein published a com-prehensive paper (in two parts) on this subject in the Februaryand May 1960 issues of Technometrics.3Part I of the papercontains descriptions of the mathematical and graphical pro-cedures as well as an extensive bibliography for referencepur
29、poses. Numerical examples illustrating the statistical pro-cedures are included in Part II of the paper.5.2 It is important to note that the life test sampling plans ofthis practice are not to be used indiscriminately simply becauseit is possible to obtain life test data. Only after the exponentiala
30、ssumption is deemed reasonable should the sampling plans beused.5.3 Sections 6 and 7 describe general procedures anddescription of life test sampling plans. Section 8 describesspecific procedures and applications of sampling plans whenlife tests are terminated upon the occurrence of a preassignednum
31、ber of failures, and Section 9 provides sampling planswhen life tests are terminated at a preassigned time. Section 10describes sequential life test sampling plans. Section 8 covers:(1) acceptance procedures; (2) expected duration of life testsand cost considerations in selection of sample sizes; an
32、d (3) lifetest plans for certain specified values of , , and 1/0. Section9 covers: (1) acceptance procedures; (2) life test plans forcertain specified values of , , 1/0, and T/0; and (3) life testplans based on proportion of lot failing before specified time.Section 10 covers: (1) acceptance procedu
33、res; (2) graphicalacceptance procedures; and (3) expected number and waitingtime required for decision.5.4 Operating characteristic (OC) curves for the life testsampling plans of 8.1 8.5, 9.1 9.5, and Section 10 areshown in Fig. A1.1 for the corresponding sampling plans inthese sections were matched
34、 with respect to their OC curves.The OC curves in Fig. A1.1 have been computed for the lifetest sampling plans of 8.1 8.5 but are equally applicable forthe sampling plans of 9.1 9.5 and Section 10.5.5 The procedures of this section are based on the premisethat the life tests are monitored continuous
35、ly. If the tests aremonitored only periodically, the values obtained from thetables and curves are only approximations.6. General Definitions of Life and Reliability Test Terms6.1 Discussion of Terms and Procedures:6.1.1 PurposeThis section provides definitions of termsrequired for the life test sam
36、pling plans and procedures ofSections 7 through 10.3Epstein, B., “Tests for the Validity of the Assumption that the UnderlyingDistribution of Life is Exponential,” Technometrics, Vol 2, February and May 1960,pp. 83101 and 167183.E2696 09 (2013)26.1.2 Life TestLife test is the process of placing the
37、“unitof product” under a specified set of test conditions andmeasuring the time it takes until failure.6.1.3 Unit of ProductThe unit of product is the entity ofproduct that may be placed on life test.6.1.4 Specifying FailureThe state that constitutes a failureshall be specified in advance of the lif
38、e test.6.1.5 Life Test Sampling PlanA life test sampling plan isa procedure that specifies the number of units of product froma lot that are to be tested and the criterion for determiningacceptability of the lot.6.1.6 Life Test Terminated upon Occurrence of PreassignedNumber of FailuresLife test sam
39、pling plans whereby testingis terminated when a preassigned termination number offailures, r, occur are given in Section 8 of this practice.6.1.7 Life Test Terminated at Preassigned TimeLife testsampling plans whereby testing is terminated when a preas-signed termination time, T, is reached are give
40、n in Section 9 ofthis practice.6.1.8 Sequential Life TestSequential life test is a life testsampling plan whereby neither the number of failures nor thetime required to reach a decision are fixed in advance but,instead, decisions depend on the accumulated results of the lifetest. Information on the
41、observed time to failure are accumu-lated over time and the results at any time determine the choiceof one among three possible decisions: (1) the lot meets theacceptability criterion, (2) the lot does not meet the acceptabil-ity criterion, or (3) the evidence is insufficient for eitherdecision (1)
42、or (2) and the test must continue. Sequential lifetest sampling plans are given in Section 10 of this practice andhave the advantage over the life test sampling plans mentionedin 6.1.6 and 6.1.7 in that, for the same OC curve, the expectedwaiting time and the expected number of failures required tor
43、each a decision as to lot acceptability are less for thesequential life tests.6.1.9 Expected Number of FailuresThe number of failuresrequired for decision is the number of failures that haveoccurred at the time the decision as to lot acceptability isreached. For the life test sampling plans mentione
44、d in 6.1.6,this number of failures is known in advance of the life test; but,for the sampling plans mentioned in 6.1.7 and 6.1.8, thisnumber cannot be predetermined. The expected number offailures required for decision is the average of the number offailures required for decision when life tests are
45、 conducted ona large number of samples drawn at random from the sameexponential distribution. The expected number of failures canbe predetermined for the sampling plans mentioned in 6.1.6 6.1.8.6.1.10 Expected Waiting TimeThe waiting time requiredfor decision is the time elapsed from the start of th
46、e life test tothe time decision is reached as to lot acceptability. The waitingtime required for decision cannot be predetermined for any ofthe sampling plans mentioned in 6.1.6 6.1.8. The expectedwaiting time required for decision is the average of the waitingtimes required for decision when life t
47、ests are conducted on alarge number of samples drawn at random from the sameexponential distribution. The expected waiting time can bepredetermined for the sampling plans mentioned in 6.1.6 6.1.8.6.2 Length of Life:6.2.1 Length of LifeThe terms “length of life” and “time tofailure” may be used inter
48、changeably and shall denote thelength of time it takes for a unit of product to fail after beingplaced on life test. The length of time may be expressed in anyconvenient time scale such as seconds, hours, days, and soforth.6.2.2 Mean Time to FailureThe terms “mean time tofailure” and “mean life” may
49、 be used interchangeably and shalldenote the mean (or equivalently, the average) length of life ofitems in the lot. Mean life is denoted by .6.2.3 Acceptable Mean LifeThe acceptable mean life, 0,is the minimum mean time to failure that is consideredsatisfactory.6.2.4 Unacceptable Mean LifeThe unacceptable meanlife, 1(1p0), is the minimum fraction of the lotthat may fail before time, T, and results in the lot beingconsidered unsatisfactory. The interval between p0and p1is azone of indifference in which there is a
