1、Designation: E2555 07 (Reapproved 2018) An American National StandardStandard Practice forFactors and Procedures for Applying the MIL-STD-105 Plansin Life and Reliability Inspection1This standard is issued under the fixed designation E2555; the number immediately following the designation indicates
2、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 presents a procedure and related t
3、ables offactors for adapting Practice E2234 (equivalent to MIL-STD-105) sampling plans to acceptance sampling inspection whenthe item quality of interest is life length or reliability. Factorsare provided for three alternative criteria for lot evaluation:mean life, hazard rate, and reliable life. In
4、spection of thesample is by attributes with testing truncated at the end of someprearranged period of time. The Weibull distribution, togetherwith the exponential distribution as a special case, is used asthe underlying statistical model.1.2 A system of units is not specified by this practice.1.3 Th
5、is 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, health, and environmental practices and deter-mine the applicability of regulatory limitations prior to use.1.4 T
6、his 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-mendations issued by the World Trade Organization TechnicalBarriers to Trad
7、e (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 AQL2.2 Other Documents:MIL-STD-105E Sampling Procedures and Tables for In-spection by Attributes33. Terminology3.1
8、 Definitions:3.1.1 The terminology defined in Terminology E456 appliesto this practice unless modified herein.3.1.2 acceptance quality level (AQL), nquality limit that isthe worst tolerable process average when a continuing series oflots is submitted for acceptance sampling. E22343.1.2.1 DiscussionT
9、his term is often referred to as the“acceptance quality limit.”3.1.2.2 DiscussionThis definition supersedes that given inMIL-STD-105E.3.1.2.3 DiscussionA sampling plan and an AQL are cho-sen in accordance with the risk assumed. Use of a value ofAQL for a certain defect or group of defects indicates
10、that thesampling plan will accept the great majority of the lots orbatches provided the process average level of percent defective(or defects per hundred units) in these lots or batches are nogreater than the designated value of AQL. Thus, the AQL is adesignated value of percent defective (or defect
11、s per hundredunits) for which lots will be accepted most of the time by thesampling procedure being used. The sampling plans providedherein are so arranged that the probability of acceptance at thedesignated AQL value depends upon the sample size, beinggenerally higher for large samples than for sma
12、ll ones, for agiven AQL. The AQL alone does not identify the chances ofaccepting or rejecting individual lots or batches but moredirectly relates to what might be expected from a series of lotsor batches, provided the steps indicated in this refer to theoperating characteristic curve of the plan to
13、determine therelative risks.1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.40 on Reliability.Current edition approved April 1, 2018. Published May 2018. Originallyapproved in 2007. Last previous version appr
14、oved in 2012 as E2555 07 (2012).DOI: 10.1520/E2555-07R18.2For 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 Document Summary page onthe ASTM website.3MIL
15、-STD-105E is also commonly referred to as “MIL-STD-105.” It is virtuallyidentical in content to its predecessor, MIL-STD-105D. These documents are out ofprint.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard
16、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 Organization Technical Barriers to Trade (TBT) Committee.13.1.3 cons
17、umers risk, nprobability that a lot havingspecified rejectable quality level will be accepted under adefined sampling plan.3.1.4 double sampling plan, na multiple sampling plan inwhich up to two samplings can be taken and evaluated toaccept or reject a lot.3.1.5 limiting quality level (LQL), nqualit
18、y level having aspecified consumers risk for a given sampling plan.3.1.6 lot, na definite quantity of a product or materialaccumulated under conditions that are considered uniform forsampling purposes.3.1.6.1 DiscussionThe lot for sampling may differ from acollection of units designated as a batch f
19、or other purposes, forexample, production, shipment, and so forth.3.1.7 multiple sampling plan, na sampling plan in whichsuccessive samples from a lot are drawn and after each sampleis inspected a decision is made to accept the lot, reject the lot,or to take another sample, based on quality level of
20、 thecombined samples.3.1.7.1 DiscussionWhen the quality is much less or muchmore than the AQL, the decision can be made on the firstsample, which is smaller than that of a single sampling planwith equivalent acceptance quality level. For samples that areclose to theAQLin quality, additional samples
21、are required andthe total sample size will be larger than the correspondingsingle sampling plan.3.1.8 sample, ngroup of items, observations, test results,or portions of material taken from a large collection of items,observations, test results, or quantities of material that serves toprovide informa
22、tion that may be used as a basis for making adecision concerning the larger collection. E22343.2 Definitions of Terms Specific to This Standard:3.2.1 acceptance number, nthe maximum number offailed items allowed in the sample for the lot to be acceptedusing a single or multiple sampling plan.3.2.2 h
23、azard rate, ndifferential fraction of items failing attime t among those surviving up to time t, symbolized by h(t).3.2.2.1 Discussionh(t) is also referred to as the instanta-neous failure rate at time t. It is related to the probabilitydensity and cumulative distribution functions by h(t) = f(t)/(l
24、 F(t).3.2.3 mean life, naverage time that items in the lot orpopulation are expected to operate before failure.3.2.3.1 DiscussionThis metric is often referred to as meantime to failure (MTTF) or mean time before failure (MTBF).3.2.4 rejection number, nthe minimum number of faileditems in the sample
25、that will cause the lot to be rejected undera given sampling plan.3.2.5 reliable life (r), nlife beyond which some specifiedproportion, r, of the items in the lot or population will survive.3.2.6 test truncation time (t), namount of time sampleditems are allowed to be tested.3.2.7 Weibull distributi
26、on, nprobability distribution hav-ing cumulative distribution:function Ft! 5 1 2 expS2St 2 DD, t. and probability densityfunction ft! 5St 2 D21expS2St 2 DD3.2.7.1 DiscussionThe Weibull distribution is widely usedfor modeling product life. It can take a wide variety of shapesand also the characterist
27、ics of other types of distributions basedon the value of its parameters. is called the location,minimum life, or threshold parameter and defines the lowerlimit of the distribution (Fig. 1). is called the scale orFIG. 1 Effect of the Parameter on the Weibull Probability Den-sity Function, f(t)E2555 0
28、7 (2018)2characteristic life parameter and is equal to the 63.2 percentileof the distribution, minus (Fig. 2). is the shape parameter(Fig. 3). The exponential distribution is the special case where = 0 and =l.4. Significance and Use4.1 The procedure and tables presented in this practice arebased on
29、the use of the Weibull distribution in acceptancesampling inspection. Details of this work, together with tablesof sampling plans of other forms, have been published previ-ously. See Refs (1-3).4Since the basic computations requiredhave already been made, it has been quite easy to provide thesenew f
30、actors. No changes in method or details of applicationhave been made over those described in the publicationsreferenced above. For this reason, the text portion of this reporthas been briefly written. Readers interested in further detailsare referred to these previous publications. Other sources ofm
31、aterial on the underlying theory and approach are alsoavailable (4-7).4.2 The procedure to be used is essentially the same as theone normally used for attribute sampling inspection. The onlydifference is that sample items are tested for life or survivalinstead of for some other property. For single
32、sampling, thefollowing are the required steps:4.2.1 Using the tables of factors provided in Annex A1,select a suitable sampling inspection plan from those tabulatedin Practice E2234.4.2.2 Draw at random a sample of items of the size specifiedby the selected Practice E2234 plan.4.2.3 Place the sample
33、 of items on life test for the specifiedperiod of time, t.4.2.4 Determine the number of sample items that failedduring the test period.4.2.5 Compare the number of items that failed with thenumber allowed under the selected Practice E2234 plan.4.2.6 If the number that failed is equal to or less than
34、theacceptable number, accept the lot; if the number failingexceeds the acceptable number, reject the lot.4.3 Both the sample sizes and the acceptance numbers usedare those specified by Practice E2234 plans. It will be assumedin the section on examples that single sampling plans will beused. However,
35、 the matching double sampling and multiplesampling plans provided in MIL-STD-105 can be used ifdesired. The corresponding sample sizes and acceptance andrejection numbers are used in the usual way. The specified testtruncation time, t, must be used for all samples.4.4 The probability of acceptance f
36、or a lot under thisprocedure depends only on the probability of a sample itemfailing before the end of the test truncation time, t. For thisreason, the actual life at failure need not be determined; onlythe number of items failing is of interest. Life requirements andtest time specifications need no
37、t necessarily be measured inchronological terms such as minutes or hours. For example, thelife measure may be cycles of operation, revolutions, or milesof travel.4.5 The underlying life distribution assumed in this standardis the Weibull distribution (note that the exponential distribu-tion is a spe
38、cial case of the Weibull). The Weibull model hasthree parameters. One parameter is a scale or characteristic lifeparameter. For these plans and procedures, the value for thisparameter need not be known; the techniques used are inde-pendent of its magnitude. A second parameter is a location or“guaran
39、teed life” parameter. In these plans and procedures, it isassumed that this parameter has a value of zero and that thereis some risk of item failure right from the start of life. If this isnot the case for some applications, a simple modification inprocedure is available. The third parameter, and th
40、e one of4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 2 Effect of the Parameter on the Weibull Probability Den-sity Function, f(t)E2555 07 (2018)3importance, is the shape parameter, .5The magnitude of theconversion factors used in the procedures
41、 described in thisreport depends directly on the value for this parameter. For thisreason, the magnitude of the parameter shall be known throughexperience with the product or shall be estimated from pastresearch, engineering, or inspection data. Estimation proce-dures are available and are outlined
42、in Ref (1).4.6 For the common case of random chance failures with thefailure rate constant over time, rather than failures as a result of“infant mortality” or wearout, a value of 1 for the shapeparameter shall be assumed. With this parameter value, theWeibull distribution reduces to the exponential.
43、 Tables ofconversion factors are provided in Annex A1 for 15 selectedshape parameter values ranging from12 to 10, the rangecommonly encountered in industrial and technical practice.The value 1, used for the exponential case, is included. Factorsfor other required shape parameter values within this r
44、angemay be obtained approximately by interpolation. A morecomplete discussion of the relationship between failure pat-terns and the Weibull parameters can be found in Refs (1-3).4.7 One possible acceptance criterion is the mean life foritems making up the lot (). Mean life conversion factors orvalue
45、s for the dimensionless ratio 100t/ have been determinedto correspond to or replace all the p or percent defective valuesassociated with Practice E2234 plans. In this factor, t repre-sents the specified test truncation time and the mean item lifefor the lot. For reliability or life-length applicatio
46、ns, thesefactors are used in place of the corresponding p valuesnormally used in the use of Practice E2234 plans for attributeinspection of other item qualities. The use of these factors willbe demonstrated by several examples (see Sections 5, 7, and 9).4.8 Annex Table 1A lists, for each selected sh
47、ape parametervalue, 100t/ ratios for each of the Practice E2234 AQLp(%) values. With acceptance inspection plans selected interms of these ratios, the probability of acceptance will be highfor lots whose mean life meets the specified requirement. Theactual probability of acceptance will vary from pl
48、an to plan andmay be read from the associated operating characteristic curvessupplied in MIL-STD-105. The curves are entered by using thecorresponding p(%) value. Annex Table 1B lists 100t/ ratiosat the LQL for the quality level at which the consumers risk is0.10. Annex Table 1C lists corresponding
49、100t/ ratios for aconsumers risk of 0.05.4.8.1 These ratios are to be used directly for the usual casefor which the value for the Weibull location or thresholdparameter () can be assumed as zero. If is not zero but hassome other known value, all that shall be done is to subtract thevalue for from t to get t0and from m to get m0. Thesetransformed values, t0and m0, are then employed in the use ofthe tables and for all other computations.Asolution in terms ofm0and t0can then be converted back to actual or
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