1、Designation: E2555 07 (Reapproved 2012)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 t
2、he 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 ta
3、bles 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. Ins
4、pection 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 Thi
5、s 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 Document
6、s2.1 ASTM Standards:2E456 Terminology Relating to Quality and StatisticsE2234 Practice for Sampling a Stream of Product byAttributes Indexed by AQL2.2 Other Documents:MIL-STD-105E Sampling Procedures and Tables for In-spection by Attributes33. Terminology3.1 Definitions:3.1.1 The terminology defined
7、 in Terminology E456 appliesto this practice unless modified herein.3.1.2 acceptance quality level (AQL), nquality limit thatis the worst tolerable process average when a continuing seriesof lots is submitted for acceptance sampling. E22343.1.2.1 DiscussionThis term is often referred to as the“accep
8、tance quality limit.”3.1.2.2 DiscussionThis definition supersedes that given inMIL-STD-105E.3.1.2.3 DiscussionA sampling plan and an AQL arechosen in accordance with the risk assumed. Use of a value ofAQL for a certain defect or group of defects indicates that thesampling plan will accept the great
9、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 defects per hundredunits) for which lots will be a
10、ccepted 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 small ones, for agiven AQL. The AQL alone does
11、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 determine therelative risks.3.1.3 consumers
12、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), nquality leve
13、l having aspecified consumers risk for a given sampling plan.1This practice is under the jurisdiction of ASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.30 on StatisticalQuality Control.Current edition approved May 1, 2012. Published May 2012. Origina
14、llyapproved in 2007. Last previous version approved in 2007 as E2555 07. DOI:10.1520/E2555-07R12.2For 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 Docum
15、ent Summary page onthe ASTM website.3MIL-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.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,
16、United States.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 for other purposes, forexample, production, shipment,
17、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 thecombined samples.3.1.7.1 DiscussionWhen the quali
18、ty 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 are required andthe total sample size will be larger
19、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 information that may be used as a basis for making adecision
20、 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 hazard rate, ndifferential fraction of items failing a
21、ttime 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 F(t).3.2.3 mean life, naverage time that items in th
22、e 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 that will cause the lot to be rejected undera given s
23、ampling plan.3.2.5 reliable life (rr), 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 distribution, nprobability distribution hav-ing cumulative dis
24、tribution:function Ft! 5 1 expSSt ghDbD, t .gand probability densityfunction ft! 5bhSt ghDb21expSSt ghDbD3.2.7.1 DiscussionThe Weibull distribution is widely usedfor modeling product life. It can take a wide variety of shapesand also the characteristics of other types of distributions basedon the va
25、lue of its parameters. g is called the location,minimum life, or threshold parameter and defines the lowerlimit of the distribution (Fig. 1). h is called the scale orcharacteristic life parameter and is equal to the 63.2 percentileof the distribution, minus g (Fig. 2). b is the shape parameter(Fig.
26、3). The exponential distribution is the special case whereg = 0 and b =l.4. Significance and Use4.1 The procedure and tables presented in this practice arebased on the use of the Weibull distribution in acceptancesampling inspection. Details of this work, together with tablesFIG. 1 Effect of the Par
27、ameter g on the Weibull ProbabilityDensity Function, f(t)E2555 07 (2012)2of 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 factors. No changes in method or details
28、 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 ofmaterial on the underlying theory and ap
29、proach 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 sampling, thefollowing are the required
30、 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 of items on life test for the specifie
31、dperiod of time, t.4.2.4 Determine the number of sample items that failedduring the test period.4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.FIG. 2 Effect of the Parameter h on the Weibull ProbabilityDensity Function, f(t)FIG. 3 Effect of the Parame
32、ter b on the Weibull ProbabilityDensity Function, f(t)E2555 07 (2012)34.2.5 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 theacceptable number, accept the lot; if the number failingexceed
33、s 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, the matching double sampling and multiplesampling plans provided
34、 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 for a lot under thisprocedure depends only on the probability of a
35、 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 not necessarily be measured inchronological terms such as minutes o
36、r 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 special case of the Weibull). The Weibull model hasthree parameters.
37、 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“guaranteed life” parameter. In these plans and procedures, it isassumed
38、 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 the one ofimportance, is the shape parameter, b.5The magnitude of t
39、heconversion factors used in the procedures 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
40、proce-dures are available and are outlined 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, theWeibu
41、ll distribution reduces to the exponential. 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 re
42、quired shape parameter values within this rangemay 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 l
43、ot (). Mean life conversion factors orvalues 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
44、. For reliability or life-length applications, 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
45、 Annex Table 1A lists, for each selected shape 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
46、probability of acceptance will vary from plan 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
47、is0.10. Annex Table 1C lists corresponding 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 (g) can be assumed as zero. If g is not zero but hassome other known value, all that sha
48、ll be done is to subtract thevalue for g 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 absolutevalues by adding the value for g to
49、each.5. Examples, Mean Life Ratio5.1 A Practice E2234 acceptance sampling inspection planis to be applied to incoming lots of product for which the meanitem life is the property of interest. An acceptable mean life of2000 h has been specified, and under the plan, used lots with amean life of this value or greater shall have a high probabilityof acceptance. A testing truncation time of t = 250 h has beenspecified. From past experience it has been determined that theWeibull distribution can be used as a life-length model and ash
