military standard 414
DESCRIPTION
Tabla Mil Std 414TRANSCRIPT
MIL-STD-414
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MILITARY STANDARD
SAMbLING PROCEDURES AND
-~MORfkMOO$-10
TABLES
FOR INSPECTION BY VARIABLES
FOR PERCENT DEFECTIVE
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mL-sTD-41411 JEW 1957
OFFICS OF TEE ~ANT SECRETARY OF DE~
Wuhlngkm $5, D. c.
Supply and Logi.ti.. 11 JUIU lb7
Sarnpflng Procedures and Table. for fa.p. ctlo. byVarl.bl.. for Pe=cent DdectlvaMIL-STD-414
1. Thi. .tandard h.. ~en approved by the De Pru’ne.t of Defenseand i. mandatory for . . . by the Departm. rAtoof the Army, the Navy. andthe M. force, ●ffectivm 11 June 1957.
2. h ●ccordance rnth e.tabli.bed proc.dur., the Sfandardi.. ticmDiwl. im k.. d-.ifp.t.d tha Chemical -Carp. Bureau of Ordnance. -dAir For.. , r.. p.ti..ly, . . Amp N.v-Air For.. custodian. .1 thi..tandard.
>. Recommended correction.. sddltlenn, or deletion. .hould be●ddr . . ..d to the Stanbrdi. atior. Divi. iom, Of fic. of the As. imta.t Sec...aary of Def.a.e (Su@y and Logistic.), Wa.hin@an Z5. D. C.
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INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SECTION A GENERAL D&9tiRIPT30N OF tibfPL3t4G PL.#JS . . . . .
Table,:Table A-1 U3LConveraion Table . . . . . . . . . . . . . . .Table A-2 Sample Size Code tiNers . . . . . . . . . . . . . .Table A-3 Operating Char.cteri*tie Curve. 10. Sampfiq
Plmm of S.ctiOa# B, C, and D (Graph- forSan@. Sise tie Letters B though Q) . .
SECTION B VAR3ABIL1TY UN3U40WK-STANDARDDEV~TION METHOD
Par: J SINGLE SPECIFICATION LIMIT . . . . . . . . . . . . . .
Ex8mpl. *:Example B- I
Example B-2
Table.:Treble E.- I
Table B-Z
Example of Cdcafattoiw:, SimglesPeciflcatiOn fAmil-Form 1 . . . . . . . . . . .
Example of Calculations: Sin~leSp*cificatiea Ltmit-l%rm 2 . . . . . . . . . . .
M..ter Tabie for Normal ●nd Tighteoed3nmpecti0n (Form l-Sinnle fAmit) . . . . .
Maater Table for Redueed impection(sOrrnl-singl. LiJnii) . . . . . . . . . . . . . .
Part H DOUBLE SPECIFICATION UhUT . . . . . . . . . . , .
Examplea:Example B-3
Exarn@e B-4
T, blem:Table B- 3
Table B-4
Table B-5
tiample of Cdcrdatiomm: Double Specifi.c8tioa LAnit-Cke AQL vai.4 far Upperand Lawe r Specification Limit Combined
Example of Calculatinna: Double Specifi-cation Umit-DIfferem AC3L values forUpper sud fmwer Specification Umitm .
Mmmter Table for Normal ●nd TightenedImpecti.n (Double Limit and f%rm 2-siIl#le LiInif) . . . . . . . . . . . . . . . . . .
Mssier Table for R=duced faspectiom(Double LImitmnd Form Z-Single Limit)
Table for 3SatimatiaEthe Lot P. rcentDe fective . . . . . . . . . . . . . . . . . . . . .
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Part f3J EST1MATION OF PROCESS AVZSAGE ANDC3UTE- FOR RZDUCEL AND TIGHTENEDINSPECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table, :Table B-6Table B-?
Table L-8
APP=dk B . . . . . .
Value. of T for Tigbtenad k#p8!cti011 . . . . . .~ts of Estimated k; P.rcent
Defective far Roduc=d Inspection . . . . . . . .Value. of F for h4asimum Standard
Deviafioa.[MBD) . . . . . . . . . . . . . . . . . . .
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SECTION C VASliABILfTY ZINKNOWN-~S METHOD
Part 1 sU40LSSPECZF1CATION LZMIT . . . . . . . . . . . . . . . .
kxmlfb:E8urlph c-l Eauanph of Ckicniatidm: Simsle
S~cificatiOa Umit-FOrm i . . . . . . . . . .3hampie C-Z Exuriplm of Cakuiati0a9: StnSle
Specification Limit. Form 2Tsblea :
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Tsbie C-1 Mast-r Tabie for Normal ●nd Tightene4Inspection (Form I_ Siql. Limit) . . . . . . .
Tabi* c-z Msst.r Tabls for Reduced lnapecUorI(FOrml-SiOgl. LImlt) . . . . . . . . . . . . . .
Part u DOUBLE SPEC1IVCATION L3M3T . . . . . . , . . . . . . . .
Exaf+em:Ex.mple C-3 Example of Caleulxtioms: Doubl. Sp.eUi -
catiem LiniIt-Oae AQL value [or Upperand tiwer Spocifieu40m Limit Ckmblaed . , . .
Example C-4 Exunple o{ Caiculaiiom: Double Specif{ -c-ion Limit-D4ifar8st AQL vahm. forUpPer u8d Lower SPRIcZflcacJon LImitm . . .
Table,,Table C-3 A.hmI.r Tabl. for fdmnul .md Ti#hte.ed
~P=c~a (-ble Limit 4 Ferm z _Sias!e Z&nit) . . . . . . . . . . . . . . . . . . . .
Table C-4 Maater Tabl@ #or Reduced lmpectiom(Dauble L&nit - Fown&Simgle IAnIt) . . . .
T.ble C-5 Ttile for Ectinmiinsthe Lot PercentDekctive . . . . . . . . . . . . . . . . . . . . . . .
Part Zu ESTIWTZON OF PROCESS AVIXfAGE ANDcRZT3ZRJA PVR REDUCED AND TZOHTSNEDINSPECTION . . . . . . . . ., . . . . . . . . . . . . . . . . . . . .
Table.:Table c-6 Vaium. of T Ior .Tigbtmmd h,pecticm .“. . . . .Table C-7 z-bits Of Eotiated kt S%rcemt
Defective for R.duced Z.cmp.ectioa. . , . .. . .Tablo C-8 Value. of ~ 10, M&um Awe ra~e
Rsn#e(w) . . . . . . . . . . . . . . . . . . . . .
APWIUUB C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SEC7WN D VARZASZL3TY WWN
P8rt 1 SZNOZ.E SPSCW1GATZON3A3AZT . . . . . . . . . . . . . . . .
Exmpleo :Exumple D-l ZZxampta of Caieubtlms: Siasis
*c4fkati0n Z.imit-rofm 1 . . . . . . . . . .&urnpZm D-3. Example of c+IeuidzioM: Si+e
Smcification ZAtaia_FOsm Z . . . . . . . . . .Ttbim.,
Tabic D-l Msst*r Table fof Normal d Ti#btenedZzmpoeuom {Form 1-Sk+ Umlc) . . . . . .
Tmbb D-Z titer Table [or Reducmd tJ1.p~=tiO_(FOrml-Slr@*LimitJ . . . .. . . . . . . . . . .
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P*T5 u DOUBLE 5PECfF1CAT10N LlhffT . . . . . . . . . . . . .
3hampfe*:3kAmpfe D-3 Esampk af Cdctdationw Double SpecUi-
cation L6mit-Oa* AOL vahm UpPar andfmwer Specification. fAmit Combirmd . . . . .
Exunple D-4 Emmple of .Calculatioms: Double +pecUi -c-tion L6mit-D3ffereut AOL value- forUpVr d kwer Specification Limits . . . .
Tables:Table D-3 Master T*le for Normal and Tightened
fn. pectim (Double Limit and Form Z-Simgleumlt) . . . . . . . . . . . . . . . . . . . . .
T.bla D-4 Master T&ble for Reduced 3nop.ctiom[Ooubk Limit..d Form Z-Single Limit) . . . .
T.ble D-5 T-ble for Estimating the fat PercentageDefective . . . . . . . . . . . . . . . . . . . . . . . .
P*rt Ul SST1MATION OF PROCB AVESAG!C ANDCSJT&R3A FOR REDUCED AND TIGHTENEDINSPECTION . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .
Tsble#:Table D-6 Value. of T for Tightened frt. pection . . . . . .Table D-7 Limit- of Ectinutod IAX Percent
Defective for Reduced hmpecfiom . . . . . . . .
APP*6 D........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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mlL-8’m-414llhfislm?
INTRODUCTION
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Thi. Stamdardwa. prepmred to meet ● growing IIeeo for tbe U. of standard●u’npliq ptmm for Jampection by vari*ble. in ti~rnmatn procurement, DIIpplyand .torage, and maintenance ia.pciion opa ratiozm. Tbe variabf.. sampJ&splane .pply to ● ●in@e quality characteristic which can be rnea.tirmd on ● coattn-tm.. scale, and for which quality i. ●xpressed in term. cd percent de fectiue. Thetheory unclerlying the developrne.t of the wari.bte. .aniplim~ plaua, including theoparatiq charact=rimtic curve.. a.awne. that rnea.urem.mt. of tba quattty char.●cteristic ● re independent, identicslfy di.tribufed normal random varisblea.
1. comparium with atfributa. ..mpfing pfmn., warlah!es umpfiag plammhave tbe ●dvanta~e of ummfly remdtin~ & cmmide rsble .avinem in #ample ●i-for .xmnparabl. a..uruice . . to the correctness. of decision. in judging . .in#lequality characteristic, or for the .arne sample size. greater a.mirance is ob-tained using variable, plan.. Attribute. sampling pfan. have the advantage ofgreater simplicity, of being applicable to either .ingle or rnuttiple quality char-acteristi c., and of requiring no knowledge about the distribution of the contlaueu.rn. a.ur. rmenc. of any d the quality cfur. txeridc..
It 10 imporfsmt to mot. tfut variable. .amptfmp pha. ● rm mot to be um.di.di. crirninat.ly, ,impfy bec.u.e. it i. po..ible to obf.in vaxi.bk. tnea.urarnemt,data. fn conmlderq appfieatlon. where the rmrmatity or irtde~nde.ce ● .smnp-tion. may be que.ticmcd, the user i. ●dvi.ed to cm-..ult hi. technical agency todetci-rh in. the fe.. ibility of appfi calion.
Thi8 Srandard 1. divided into four .ectimm. Section A describe. @n. ratprocttlur. a of the .amplimg plan.. Secfic.m. B utd C de.crib. .Pcifi. procedure.and ●pplic ation. of the .arnpIing plan. when w.=iability i. unknovr., In Section Bthe .stirn.te of lot .%and. rd d.vi.tion i. used .s lh. fn. i. 10. an ●.timat. of theunknc.w. variability, and in Section C the average rams. of the sunpf. 1* used.Section D desc=ibes the plan. when variability is known.
Each of Sectiono B. C, and D i. divided into fbree part.: (l) SAMPJIIW PIUMfor the Single S~cifieuiom Limit Ca.e, 111)Sampfimg Plans for th. mubl. Spc-ific. tion Limit Case, and (3JJ) Procedure. JorEsthnation cd Proce.. Average andCriteria fer Tighmned ●rid Reduced Ja. pection. For tba ●ingle s~cificationlimit ca. e, Lhe ●cceptability trite rio. i. giv=n im two foran.: Form 1 amd Form Z.Either of the fonnc may be u.ed, ●ii-ici they ●rc idettticti a. to .ainple sise -ddeci ion for lot ●cceptability or rejeetabilify. III deciding whether w u.= Form 1or FQrrn Z, the followin~ poiDt . should be bo=n. in mind. Form I provide. the lot●ccept ability cri~. rion without ●.titn.tirtg 10I percent defective. The Form 2 101acceptability criterion require. emtirnates of Jot percent defective. Theme e#li -mate. at.o .r. ~quimd for e stiznatbn of tha proea ●a ●verage.
Operating Characteristic Curve. fn Table A-3 how fhe r=latioa.ftip betweemquality and percent of lot. expected to be ●cce~able for thequality cbaractari.ticinm~et.d. A. stated, the .e Ope rating Characfe ri ‘tic Cur-. are &sed 011tbe..#urnpiari that meam. mment. ● re .ekctedat raadanalrom a ciorsnti distribution.
The corre spending ●unpfin~ plan. in SectiW. S, C. ~d D w. m mstcbed● . closely ., po.. ible ~der ● .y.tem Of fixed .unpfe .Ise with re. pcct to theirOpcraling Characteristic Cu?wes. O~raUng Chsracteristjc Cum. in T.bf. A-3h..= been computed for the .mpling p]an. b... d orj th. ..timate of lof .tudarddeviation ef unknown ..ri.bility, Thy are eqully .pplie.ble ior .arnpllns plan.hoed on th. averaga range of the .awIpI. of unfmown variability and theme bam.don known variabUity.
C.rtaim cln..cmri.:ic. concerning the sunpliag phm. in S..tiom. B amd C-d tbosa la S9ction D dwufd b, moud. Pkn. baa.d on fba ● mtima& ot umk=09mWariablllty require fe~r .M@e wit. for cm~ra~e . ..”ranca -baa tb ●d.Mate of lcM .taadard tiwl.si~ i. “..d than _bg. ib .~..ae rua~. d ffn .-+in u.ed: on fhe ottwr tid, plan. Vsbg the .W~.gG r~ge of the #AM@. r.quira
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mb61v—41411 June 19s7
●imphr compuuttmm. Plarm umlnn bm=variablltty -qutre con*l&rablT f-rsample tmk far comwrabk amUJrMC* tbaI ●ich=r of the plans whw =TIabtuty1s uakam: @we wer, tba roquir=mw.t of k#umII -rkbiUty Is ● ●rtnsent am.The user 1s. dvised to co.milt MS tectalcal~uc~ bdom WPIYLW cunptiajpiano U.tng bDOwa w8rIAbuuy.
Tath B-8 provids ● values of tbe f~ctor F to compute tfia maxfmum standarddewiation hfsD. The hfSD se-s M ● ~uide for the magnitude of tht eatirnate oflot standard de-scion when u-in Plazm for tbm double spcff ication limit c--e,based on the ● intimate of lot .taa~rd deviation of un.bn- .arimtdUty. SimifArlyTable C-8 provides vmlue- of the Iactor f to com~te the maximum average rangeMAR. The MAR ●or.ew m a g de for tbe magnitude of the average ruige of the
“ke do.bfe .pecific.tia. limit . . . . . ba.ed . . the●rnple wk. usin# planm for tave rage range of the cunple of unbam wariddlity. Tba edmate of lot ●tmdarddeviation or ●verage range of the ●mpk, U it is Iem thm the hfSD or MAR.re.●t=ctively. hslps *O immure. but doe. mot guarmt.e, lot accept. bfllty.
AU ●ymbols and their definition. ● re gimn III tha a-ix to Part JU cd theapplicable #*ctim. h Ulumtratim of the com~tiom and proc.durma .~ed IIJthe .unpling plans i. give. i. the ●nmplec uf Part- I and 11of tbe spplkable.ection. The computathmm irwolve simple ●rithmetic operation. such am .dditina,●ubtractio”. multiplicuion, &d dIvimion of mwnbera, or ● most, the taking of ●
.quare root of ● number. The user should become funiliarwith the g.neral pro-cedure. of Sectian A. and refer to she ●pplicable sectioa for detailed iawtructiomregarding ●pccific procedure.. cornpu. ions. md tables for [he Barnpliag plan..
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SECTION A
GENERAL DESCRIPTION OF SAMPLING PLANS
Al. SCOPE
All Pur+’
Thi 8 Sammkrd =stablimhesmmplnng P anm and procedures for inopec -ticm by variable ● for use in GovernmentP*.c. reme.t. s.ppfyuad stora~., and rnAJl-tetts.cc inspection op8rati0rIm. when .ppli -cabfe this Standard #hall. be referenced inthe specification, contrzct, or in8pcctien in-.tructic.r. m, and the provision, set forthherein shall #ovem.
Al. ? III*PC ction. lnmpeclion i. tiw pro . . . .of measur, ns. ●xamining. testing. gaging. 0.othe rwise comparing the “unit of product”(See Al .4) with the appkabfe requirememla.
AI.3 lnspccti- by Variables. Inspection byvariables i. inspection wherein r+specifiedquality characte-ri. tic (See AI.5) on a unitof proeuct i. measured on . continuous.cale. .u. h ● . pound-. iwheo, feet per sec-ond, etc., And ● rneamtreme. t is recurd. d.
A1.4 Unit of Product. The unit of producti. the entity of product in.xcted in orderto dew rrnine it; measurable quality char-●cteristic. Thim may be a single article, apair. a ●et. ● component of an end product,or the end product itself. The unil of prod-uct may or may K.t be the sune ●s the unitof purchame, supply, production, orthipmer.t.
A 1.5 Quality Characteristic. The qualitycharact. riatic for varxablee in. pecti4n isthat characteristic ef i unit of p,oduct thatis actually m.a. uzed, to determim confor-mance with ● given requirement.
A1. b Specificaticm Limit.. The ●peclflca-tion Iimtt(e) is the requi rerncnt that ●
quality characleri. tic .hould meet. Thi*req.~rement may be exprenmd ● n ●. upper●prc~f ication limit; or 6 lower pacificationlimit, called herein ● .in~le specificationlimit; or bolh upper and lower .~cifieatiemlimit., called herein a double ●~cificmionlimit.
A 1.7 Sampli.~ Plans. A sampling pfan 1.a PrOCedUr* *h*ch ●peciiies the rmxnber c.<units of product from ● lot which ● re to hitmpected, arid th. cril. rion Xor aecepfabil -ity of the lot. Sampling pfazm desipated inthi. Standard are ●pplicable to the insPc-tfon of ● chgfs quality cbaracteri-fke of a
unitof product. Tfm se pfwm may be usedwhether pracuremrml inspection i. per.km’rmd at the plant of ● prime coatract?r.wbcontractor or vendor. or ●t destination,-d -S90 may be uaod when AppTOPrU1O in●ppfy and storage. and main fanaace fL18pec-tion ofm rattom.
A3. CLASSIPTCAITO?f OF DEFECTS
AZ. I Mtthodof Cia8sifring~fect@. Asf8m -.ificat, c.n al defect- . . the ●rmine ratio. ofdefect. of the unit of product claasifi. daccording to their irnporfaace. A defect 19● deviation of the unit of product fr-am, re-quirement. of the specifications; drawiags,Purcha.e da~cripfia”., and aay cbu~cthe reto in the contract or order. Defectsnormally belong to one of fhe fOllO*gclasses; however. defects may be plkced kother ciao. cs.
AZ. 1.1 Critical Defeeto. A criticaf defecti. .“. that iudeme. t and axmrience indicatecoule reeult ;.. hazardou. “or unssfe condi-tions for individual. u.ing or m.imainingthe product; or, formajnr end it.rn9 unit~ofproduct, such a. ships, aircraft, or famba. ●
d.f. ct that could prevent fmrforrnaaco oftheir tactic-i fumction.
A2. I.2 Major Defects. A major defect i8 adefect. other than critical, thaf coutd resultin failure, ormateritlly reduce the usabilityof the unit of product for its intended fmrpobe.
A2. I.3 Minor Defects. A minor defect ison. that doc n not materially reduce the usa-bility of the unit of product for itm intem&dPurposa. or i- ● deprfurc from ●stablislmdatandard9 hating .0 signUi CUIt bOa CinI OrIthe effective u.e or operation of th@ unit.
A3. PERCENT DE FECTTVE
A’3.1 =.PT89.88. Of NO. CMtfO_ co. Ttie$fcnt of nonconformance of pro dues 9fnffbe expre-scd i. terms of percent &faetive.
A3.Z Percent f%.feetiwe. Tbe percent d.-fectiv-.~acterimtic of ● Ii%.lox of prodv;t”i. th~ number of unit. of prad-uct de fectiwe for that cfuractc ri.tic dividedby the tataf number of unitm of product Andmultidimd by on. hundred. Expressed ● man.auatiorx Percen: rkfectiv8 -
Number of Aefectivea x 100Numbs r of dtm
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Mk+m+lalx Jlfffe 1957
Ad. ACCEPTABLE QUALITT LEVEL
A4. 1 Acce@abZc Ouaiil bwl. Tba =-● a CBOmlnaf
value ●xpr*s.e.i in farm. of percaat d8f*c -tive .Pcif ied for ● sbigle quUity character-iatic. Grtain numeried vaftws o; AOLr=~img f ram .04 to 1S.00 parce.nt am ●hO-ai. Table A- 1. Whe. . ran- of AOL VUW-i. .pecified. it dull he treated ●s if it woreequal to the WdUC of AQL for which ●mfa2i0cplms ● re lu-whed and which i~ bcludedwithin the AOL range. When the •~c~tedAOL i- a particular value other tb& tivmefor which oamplhg pfanm ● re furniched, theAOL, which i- to be used in ●pP2yihg theyovi.ions of this Standard, .Itafl be ., .ho~m Table A- 1.
A4.2 Specifying AOL1 c. Tin particular AOLvafue le be used for ● ●ingle quality char-●ctarimtic of a given product must be ●pee-ified. fn the CM. of a double ●Pcifi.athmlimit. ●ith. r an AOL value it #PcUied forthe total percent de fecti.. muaida of bathup~r -d lower specification Umita, o. t-eAOL value. are specified. om. for the upperlimit and another for the lower Ifmit.
AS. SUBJbflmAL OF PRODUCT
A5. I lat. The tsrrn ,,1ov hall nmmn ,virt-cpecti~lot, -’ i.e., a collection of unit. ofproduct from which ● sample is dram! adinopec~td to dete rm”me complhrme with fheacceptability criterion.
A5. 1.1 Formation of Lots. Each la; shall,● s far ●mla practicable, con.iwt of unit. cdproduct of ● .ingla type, gssde, ~Ass, size,or cornpo. itkn manufactured under e.. en-ri.Ily the same conditimit.
A5.2 Lot Sise. The lot ●im 1. tha numberof unit. d product in ● lot, and may differf rem the quantity de.i#r.atmd h fbs comtraetor order a, ● lot for prod”ctlar., ●biprnellt.or Ether Purpo..,.
A6. LOT ACCEPTABILITY
A6. I Acce Sabfiity Criferien. The ●cca@-●bility of a lot of material ●iknitid brimapc:kta ddf be detennh.d byum of ~of the .ampling plait. a..oeiaf.d~tb. .pec -ffied value of the AOL{S). Tbi. Standardprovide 8 ●ampliag plaa. baaad ombaowa 4b- variability. fn the Iatfar cantwo affa mativo met+, ● m provitid, -bared on the e ●tfmaia of im ●fattdard dovi.atioa and the die r on lb am rqe range ofthe t-fate. These .r. r. f.rred to . . thestandard dowiatio. method and tbe rinsemethod. For tha case of a single cpeeifiea -tiatl unlit, lb acc.ptabiu~ criterion I-
A6.2 Choice of SarnfAim Plain. SunpUaB~D u!d PIWCEOU-9 a:e pro-dad in d8C-tion B if Variddlity 10 uabnown amd the.taadamf de rf.uion mathd is !mwd, h Soc -ticm C U variability i wunbaewn a?id the rangematbod i c uced. and in Secfioa D if .ariabUityis bnown. Urdesa otkrwi.e ●pcffied, un.b-n variabiUty, ●-d=rd dewiafim method●unF41rtd plans. and the ●ceef=ablfifv crl -terbr. d Farm 2 (for the 9ic@e specificationiimit case) Aaif be used.
A7. SAMPLE SELECTION
A7. I Determination of Sample Sise. The.Unpl. .,- h, tha mm’lfmr of unttmof prod-uct drawn frcan ● lot. Retati~ samph aIws●m Aesimated by cute letters. The 8ampf4sise cod= Iette r“depcitds on the.inq=ticmle.ve: and the lot ●1=4. There ●m fiva h-•f=ctiOale=J~: L U. fU. IV. -d v. ff~e-~othe rwhe ●pecffiod Ia-fmctien Ieval IV shalik used. The ●unple .i.e cod. letter appli-cable to the .pcifi.d izi.pectim l.wel aridfor lots of given sise .hdl be obtained fromTable A-2.
NOTICE-5P. c ial Reservaticm forCritical CharackrnB1ic8. Tbe Go.errm’i.ntre. e.vo. tbe rmhl to insmct emryunit mb-mkkd hy the ;uppfier fos critieti etir.c -te!rimko, uad to reject the remainder of thelot Immedlafelyafter ● defect is fouud. TboGOvemirnent timo rcr:rvee tht right to ●am-pfe fo~ criticmf d. f.ctc evm ry let aubmittadby tk ●uppUer arid to reject any I-* if Asample dr.wm thrnrefr~ is fo-d to containow or more. criticti da fects.
A7.2 Dr.wimB of Samples. A sample 10 om.or mere unit. ol product drawn from . lot.UnItc of ttn munfdo Aa2i be, ,al~ct,d with-O* re#ard to t?bdr q.safity.
Proe.dure ● for ● 8tLmatfmg 22n preeommawrage @ criteria for ticbtaned and re -dweed in. fmcftan bared = th Umpacthnromiito of pmeedinc lots are provided inPart uf of dactiorm B. C. and D.
AS. SPECIAL PVOCEOURE POR APPLI-CATION .F MIXED VARIABLBS-AlTT21BLfTES BA?APLJNG PLANS
8
--
Iii
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● lu prwid=d for tin Miad w8*bl9D-●ttrlbcuaa -Wunpumg phmm bon18 ad thattbOM h ,T=tih A-S a- z-t W#idk.]
Condltlon A. Amptm wwI&mc. oximtaW tbm produ ct cubmittod for iaapctioa IS●mhctod by Ch #Upfli, Z tO meat tfM ,IWXiZIkatlan ltmit(s) by ● ●creemlng proee ●mf rmn ● Iarae r qus.mtity of product which 1.not being produced wltbln tba ,PclficationIlmlt(al.
CodltiaQ B. Other condltiorm adsttbt warrant tb= u , . of a .arlablac-mttributem •ara~i4is *-.
A9.2 Definition..
A9.Z. 1 in.pactlom by Attrlbut8s. fnspectioaby ●ttribute. I* inwpectkoa wbardc. tba unitof product is Chsdfied simply m defectiveor mandcfectiwe with reapact to a given re -qtiire.mom 07 s.t of nqutrnmentm.
A9.Z.Z Mind Variabla ●-Attrib* ● lnmP8c -tion. tinnd varimhle ●-attributes inmp8ction~mgpcction of ● ●arnfie by sttributa ● . in●ddition to inspection by variable. mmlreadymad. of ● previo.a ●unple, before . de-eki,on .ao ~o.,*: ca~qsi!iv.o r .*I- c-bili~ ~● M ctihmtie. ‘. ‘-
A9.3 Selection of Samplirtc Plans. Themiaad *arlable.. att Yi- S -plmg planstall h ●elected in UCOdUICe with thnfcdlovim~
A9.3.1 Select the vsrlableo #vnpliag plmM ●ccorduaca with Section B, C, O, b.
A lotmcdm Ui* ●ccef%abi me ofthe fouo’wln’ Comtitiem. i. .*tL.fic.&.
Camdltkm A. 7bo lot com~i4s withttn apprsprmta variab14 ● ●cca*bllIty crl -terlm of section B, C. or D.
Caa6itLm B. The Ist cmIPU*s +tbtbe ●cceptabif ity crita rkm of pragrapb11.1.2 of bAIL-sTD-!05.
A9.4. 1 U Condition A ia not ●atiefied, pro.coed iri accordance with tk ●tt tibute ● oM’l -plirig plan to meet Condition B.
A9.4.2 lf Condition B ia not cati;lied, thelot doe #not meet the 8ccepabilicy crlte rian.
A9.5 Se=rltY of Iaaopaetion. The proce-dures for .everity ❑f m.pecti.m rel=rred toin ~rarraph A8 are net ●ppficsbl. formixed Vaziable..attribum. inm~ction.
NOTICE- When Gouerrmtemt drawin#..SPedfiCatiOmn, or othc.r data ● re u.e4 tarUIY prmme other than In connection wltb adefinitely relamd Government procurementopa ratloa. thm Lbit.d States Gow rrunenttbe=aby imzur, no re. pm. ibility or my ob-ligation wbtcoevcr; and the fact that theCo.ernnteztt may have form.latd. f.rnimbed.or In uIy way ●pplied the ●aid Lrswiags,●wcificationa, or other data (* II@ t. ‘=rm~arded by implication or otherwime ● inmY m-e r licerming the tilde r or any otha rpcr*On or corporation, or conveying anyrights or p rmis. ion to m-nufbctufe, u**.or ●ell aay patented invention thu may inmn7 =*T h ra~-td tbreto.
a
—
ror spd56d A03. va3u.eIa236q WiIhin mmu r-got
— to 0.049
0.050 to 0.069
0.070 to 0.109
O.lloto 0.164
0.165 to 0.Z19
0.Z80 to 0.439
0.440 to 0.699
0.700 Ie 1.09
1.10 to 1.64
).65 to 2.79
2.80 to 4.39
4.40 to 6.99
7,00 to 10.9
11.00 to 16.4
Use thh AQlVazue
0.04
0,O65
0.10
0.15
0.Z5
0.40
0.65
1.0
1.5
Z.5
4.0
6.5
10.0
15.0
““” mm6610 1JOIB35DF31
111 to 180 Be&c I
181 to 300 Et DFH_j
301 to 500 C32GIK
501 to 800 DFHJL
801 t“ 1.300I EGIKL
1.301 to 3.200 FHJLM
3.ZO1 to 8.000 Gl Lhi N
8.001 to 2z,000 HJMNO
mample .i;e code letter. given in body of
Uble ●re appli. abze when the indicated in-●ptctim levelw are to be “med.
4
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I
VARIABIIJTY
SSCTIW B
uNKNowN-sTANDAmf DEvlAnoN
Parf I
SINGLE SPEUF3CAT10N LUA3T
S1. SAMPIJNG PLAN FOR SINGLESPECIFICATION LXM!’T
Thi. pArl Of the Standard deocribe. theprocedure* for us. whh plani for ● oingleape .ifiution limit when variability y of fhelot with re.pect to the quality charae%eri. -tic i. unknown ●nd the .tandard deviationmethod ia u#ed. The acceptability criterioni. given in two equivalent iorm9. Tbeoe areidentified as Form 1 -d Form.2.
B1.1 Use of SamPtinfl PlaJw. To deter-min. whsther the lot me=t. the ● ccept -ability criterion with respect to ● particu-lar quality cfuracteristic a.ud AQL. -Iue.the applicable campling plan shafJ be ucedin ●ccordance with lb. proviaionm of S.c -uc.n A, Generai Description of SamplmgPlan. .-d th.. e in %hi, part Of th. Standard.
B 1.2 Drawi..qof Samplem. AfI .amplew ●hallbe drawn in accordance -’th paragraph A7. Z.
B1. 3 Determination of Sample Size Code~. Th e .smpla ●zce cod ● letter ●habe selected from Table A-Z in ●ccordancewith parasraph A7. 1.
B2 SELSCTING THE SAMPLING PMWHEN FORhf 1 IS USED
BZ. 1 Maater sampling Tables. Th= muter●anmlmn tables for mlana based or. -ria-bilit~ -MI for ~ ●ingle specificationlimit vben using the ctaadard deviationmethod ● re Tables B-1 .nd B-Z, Table B- Iin .m=d ler norm.] and tighter.ed iriapectionart< Table B - Z for reduced imspeetioit.
B 2. Z Obtaining the Sa?nPlinK PIan. The.mnpl.tig plan cons.st. .1 ● .unple .i.e 8dm ●~nociafed ●Cc.eptability COtI.unt. 1 Thesampling plan i. obtained from MaterTable B-1 -, B-.?.
B2.2.1 Sam Ie Sise. The #ample .ise - Z*~●houm m t e ma.,.. tabl - eo.-.. p-.fing *O
.-.1. ..cnple ●ice cute tetter.
BS. Z.2 Accepu bility brmant. The acc.pc-dility corutaaf k. correewmt .gtotbemun-ple size mentioned ia pnagraph B2.2.1, iaindicmed in the column of the nuster tablecor re~pmxling to tbe applicable A(2L value.Table B-1 i. entered from the fop for nor-mal inopecfion ●nd from the bottom fortightened inspection. Sampling plum for re-duced inspection are providd_ in Table B-2.
B3. LOT-BY-WT ACCEPTABILITY PRO-CEDURES WHEN PURIM 1 LS USEI?
B3. 1 Acceptability Criterion. Tbe degreeof conformance of ● quafit y cb8ractericti cwith respecf lo ● single specification limit.W1 be judg.d by th~, qusntity (u-XJI* orfl-L)/i..
B 3.2. Corn tatien. TtIt following quantity.haff b- (“-X)/’ ., (x-L)/., d,-pendiagon whether the specification limit i,~ qper or lower limit, +ere
U i. tk upper specification limit.L i- tbe lower specification limit,X i. the sample mean. and. i. the ●.tirnate of lot ●sn&rd de.rlatioa.
B3.3 Acc ability Crite rfon. Cumpare the
abifttywmst-nt k. ff (u-x)/m or (x- f.)/a iaequal to .ar gre8ter tlun k, the lot meets the=cc~tiIf.fty criterion: if (U-X)1.** (X-f-)1~ia l.mm Uu8 k or nerative, 3hrm the M &esnot meef the •=e~llity criterion.
M. t31JM3tMRY FOR OPXRATION OF~~MNG PLAN WREN FORM s m
The foLIowfnr ‘soP* •~marise ‘he PrO -=~u... t.. . . mllowed:
(1) Daterrnirw the sxmple .i.ecode lti -ter from Table A-2 by uming the let sise andin.pccfion leeel.
MIL-m-41411 Jt333e1957
(2) Obfai. Pk. from Mamer Tab)= B-1or B-z by .eleeting the sample size n andthe ac..ptabill$y constant k.
(3) Select at random the sampl= of nunit. lrorn the let; inspect ●nd record themea. urernem of she quality characteristicfer each utiit of the sample.
(4) Cmnp.te the s.mpIe mean ~ andestimate of lot sts”dard dcvistic.n . . and● ISO compute the quantity (u-X)1. for anu per specification limit V or the q~ntityA-L)/. for ● k.wer .peciticatio~ lids 3..
15) M the quantity (u-X)/s or (X-W.i. equal co or greater than k, the 10I meetsthe ●c.ept.bilicy criterion: it’ (u-X)/. or(X-L)/. i. [e.. (ha--- k or negative, thes thelot doe’ rwtmeel Iheaccepttii lily criterion.
B5. SELECTING THE SAMPL3NG P2ANWNEN FOfUd Z 5S USED
S35.1 h4asccr Sampling Table.. Th. ma. ter.ampJmg tables for plans based onvariabil -ity unknown for a single specification limitwhen using the m~nd-rd deriatitm methodsre Table. B-3 ●nd B-4 of Part If. TsbleB-3 is used for normal a“dai~htened inmpec -eion and Table B-4 .fc.r reduced.inspection.
B 5.Z Oblainin~ the Sampling Plan. Thesarnpli”~ plan co. ss.ts of . .unpl. ,Ize andsn ●ssociated maximum alk.w=ble percentda$eclive. The samplin~ plm i. obtainedfrom MaDter Table B-3 or B-4.
65.2.1 Sample Size. T)M ●mnple mice n is●hewn m the ma. tcr table cortespendin~ 10each sam>le .iz. code letter.
135..?.Z Maxim. mAllow8ble Percent De fee-t$ve. The rrmxim.tn ● llowable p.=. ent de-=live M for ample ●stimate. correspond.img to the .unple size m=nt ioned inpa:agrmph 95.2.1 is ittdicated in the columnof the nm.ter table .xxre.pondiytg to the●Pplic=ble AOL value. Tabl. B-3 i. =nt=,.dfrom tbe top for normal inspection -d fromthe bottom lo, lsghter.ed in. peetion. Sam --li>g plan. lcIr reduced inspection ● rm pro-
dv-l ea ,. ~a~,e ~-,.
B6.1 Acceptability Criterion. The dc~reeof conformance Of a quallty characteristicwith respect m ● ai.ngle specification limithall b, judged hy the percent of rmnem-,-Iorm,ng product outsidt the upper or low+r
cpecifteation limit. The percentage of Ma-coaforming product is cstimattd by wiieria’T~le B-5 with the quglity index and thesample ●ize.
B6. Z GE-I utatio” of Qtufit~-lity~-X)~rnpE~if the specification limit i. ●a upper limitU, or OL . (X- L)/t if it is a Io-er Jimit L.Th* quaatitie.. X ●md s. ● re the ●arnpl.mean ●nd e.timm e of lot standard deviation.respectively.
W. ~e -ii-t-d P.,. em d.f=~ti- in dlot ●bove the upper specification limit, orby ?z.. th. estimated percent defective belowthe lower .pecifi catian limit. Tbe ●stimatedPc*.=.: defective PU or PL i. obtained byenterina Tabk B-5 with Ou or QL and the●ppropriate ●anple size.
336.4 Acceptability Criterion. Gmpare theestimated lot pereent deIectivepU or pL withthe maximum allowable percent defective M.U PU Or Pl, 1. eqUf to or leas thn U, thelot rneets the acceptability criterion; if Puor p~ is greaier than M or if Qu or Q is,negative, then the 10: does not meet \heacceptability criterion.
B7. SIJ71SMARY FOR OPERATION OFSAMPL3NG PL.AN WHEN PORM 2 3SUSED
The fellc.rnng step. .umrnariz.e the pro-cedure. to be fallc.u.ed,
(1) Determine the ●mple .i=e code let -ter from Table A-2 byu. ing the lot size mdthe inspection level.
(Z) Obtain plan from Master T=ble B-3or B-d by .elecfi.~ the .unple .ixa n attdthe maximum allowable percent defective M.
(3) Select ●t random the #ample of nunit. frmn the Iof; inspect UId record them.asurernemt of the quality charact. rimiccm each .unh of the ●ample.
(4) Cmnpute3h= sample mean X arid theectimale of lot .ta”dard devfatian . .
(5) Compute the quality index Q(U-X)/ * if ●n upp. r .pe.ific.tie,. limit Jfi:
●P.*ified. or OL = (x. L)/. if ● lctwerspec -iiication 1;...;. L <. snecif; ed.
(6) Det~rmb-Ic the estimated lot pereentdefecnive pu er pL from Table B-5.
%. Ex_pie B. z for .a cemplete ●xample of thb. prOc*dure.
:38
Mu.-sm4l411 Juoe 19S7
fi) ff the e.timated lot percerndefective is~reatertl.an U Orif QuOr C3~ is aepti e,
PU Or PL i. ~ud to or 1... than the maxi. rthen the lot doe. ml meet the ●ccepmbi IIYmum .dlowable percent defective M. the lot criterion.meet. the ●cc.pt~bil$ty criteriom if PU Or PL
EXAMPLS B-1
Exmnple of Calcufatio.s
Single Speci!icatlon Limit-Form I
Variability Unknown - Standard Deviation Method
ExAmple The rn.timum temperature of operation for ● cer:aindevic. i. .pecifi.d ● . .?09”F.A lot of 40 item. i. submitted for inspection. Zn. pection Z-evel IV, normal inspec-tion, with AQL = 1-% i. to be u, cd. From Tables A-2 ●nd B-1 i! i. aee : that amarnplc 01 sise 5 i. required. Suppose the measurement. obtained are ● . <c.11ow.:197.. 188-, 184”,205-, and ZOl ‘: and compliance wfth the acceptability criterion i.
Line.—
1
~
3
4
5
6
1
8
9
10
II
lZ
10 be determ%nea.
Information Needed
Sample Si. e: n
Sum of [email protected].: IX
Sum of Squared Me,, ureznentn: XX2
Correction Factor (CF): (I X)z/n
Corrected Sum of Sqmre. (SS): s“X~CF
Variance (V): SS/(n-1)
Estimate of Lat Standard Deviation .: fi
Sample Mean X: ZXln
Specification Limit (upper): u
The quantit~ w-X)/c
Aecept~iIity &natant: k
Acceptiility Criteriozx f2mpare w-X)/O with k
Value Obta{ned
5
975
190,435
190,125
310
77.5
8.S.1
I 95
209
1.5.9
1.53
1.59> 1.s3
Explanation
(975)2/5
190,435 - 190,125
310/4
-s
97515
[209 - 195)/S .81
S.. Table B-1
See Par&. B3.3
The lot rneetm the .cceptabiltty criterion. mince (U. ~)/s is ~remt=r than k.
NOTE: If ● ■ingle lower spcffieat{on limit L is given. fhen compufe the q~ntilY ~-~)f~ inIin. 10 -d com~re il with k, the lot meet. the =ccept8bility *rii=.iQn. if (~-Ll/* isequal to or greafer than k.
!.
M2~-41411 June 1957
Single Specification Limit-Form ,?
Variability Unknown - Standard Detiation Method
ICUmple The maximum temperature of operation for ● certain device is specified ●s 209” F.
A JOI of 40 items is ●ubmilted for inspection. 2nspection Uvel IV, normal inspec-tion, with AOL = 1% in 10 be u.ed. From Table- A-2 and B-1 it i. .een that a
I sample of .ize 5 is required. S.ppome the measurements obtained art ● . follow.:197., 188-, 184.,205-, and 201 ‘; and compliance with the acceptability criterion into be deter rnitied.
Lime—
J
z
3
4
5
6
7
8
9
10
11
1?,
13
Inforrntiion Needed
Sample Size: n
Sum .3[ Mea. urcme.ta: XX
Sum ef Squared Measurement.: 1X2
Correction F=ctor (CFh (IX)zln
Corrected Sum of Squares (SS): lX~CF
.V.4@I<. (v): SS/(n-11.
Estimate of b: Standard Deria:icm .: fl
Sample Mean X: ZXln
Specification Limit (upPer): u
O~lity 2ndmc au . (u-x),,
‘“t” ‘f b’ ‘ercen’ D’*”’ %
Mu. A21mv=ble Percent De:.: M
Acceptability Criterion: Compare Pu vilh M
Vmlue Ob:.ined
5
975
190,435
190,125
310
77.5
8.81
195
Z09
1.59
.Z.19%
3.32%
2.19% < 3.32%
T3U let rmet. the ●cccptablzsty critarion, ●6nce pu is 1.-0 tti M.
tkpl .nati.n
(975)2/5
190.435 - 190,1Z5
310/4
J-7X5
97515
(Z09-195]/8.81
S.. Table B -5
.%. Table B-3
See Para. B6.4
NOTE: U a sin@. lower specification limit L is Siven, then compute the quality index OL =(X-L)/s i“ line 10andobuLn the ●.timate of lot percent defective p . Compar. PL rnth
1-M; the lot meets the acceptability criterion. it pL is equal to 0? C*S lbn M.
! - -- -—--M
... II
TABLE B-1 Standard Deviatiom Methc.d
MIster Table Far Normal &.d Ti~htened fn. pectlo. for PlaIJs Based on Variability Unknown[Single Specification Limit– Form 1)
Sample sizecode letter
B
c
Acceptable (
!
.25 .40
kk
k2.00 1.88
2.11 1.98
2.2o 2.06
2.24 ,?,11
3..26 2.14
-allty.—.65
T
$
.CVCIS (normal inspection)
mGi-
k +
,10 ,15
k k
1.50
k
2.s0 4.00
k k
1.12 .958
1,17 1.01
1.24 I.07
1.33 1,;l 5
1.41 1.23
1.47 1.30
1,51 1.3)
1.53 1.35
1.55 1.36
1.57 1.39
1.58 1.39.1.61 1.42
1.65 1.46
1.67 1.48
1,70 1.51
1,70 1.51
4.00 6.50
m
T10.00 15.00
k k
.566 .341. .
.617 .393
.67S .4s5
.7s5 .516
.82n .611
k
7
1.45—
1.53
1,62
1.72
t.79
1.8.?
1.85
1.86
1..99
1.89—1.93
1.98
2.00
2.03
2.04
1.50—,fVela
k
.765
.814
.874
.955
1.03t—2.64
2.69
2.72—
2.73
1.17
2.77—
2.83
2.90
2.92
i—
2.53
2.58
2.61
l-k.?.24
v1.34
D
E
F
G
34
,1
5
7
10
1.65
).15
1.04
1.91
1.96
1.98—
2.00
2.03
2.03
1.40
1.50
1.58—
1,65
1.69
1.72
1
15
20
25-
30
35
I2.42 2.3?. 1.09
1.12
1.14
+
.886 .664
.917 .69s
.936 .71,?
.946 .723
.969 .145
.971 .746
I2.47 2.36
g2.50 11.40
J
K
2,61
.?.65
?.,66—
2.71
2.77
2.80
2.51 2.41
12.2.9 2,15
2.31 2.18
2.31’ 2.18—2.35 2.22
2.41 2.27
2.43 2.29
2.47 a.33
2.47 2.33
.4o i .65
1.73
1.76
1:76
1.1s
1.18
1.18I2,54 2.45
LL
5.4
N
o
P
Q
40
50
75
100
+
2.5s .3.44
2.6o 2.5o 2,08
2.12
2.14
7,1!
2,1[
1.80
1.84
1.86—
1.89
1.89
I.ZI
1.Z4
i.26
1.29
1.29
i
1.00 .774
1.03 .ao4
1.05 .819
I.07 .841
1.07 .845
I 5.00
2.66 2.55
--t-
2.69 2.58
2.13 2.61L150
zoo
2.96
2.97—.065
Z.84
2.85
-t
2.73 2.6.?
.15 .25.10 I ,0(—alit,
Z.50 ,0.00
A21AOL wdue8 ye knpercent de-a.
AcceptableC lightened inspectio!
1:::,,V.V ,tern hth. lot must be inspected.[Irst tunpllq plan belcw ●rrow, that is, both sample OIZ.Sas well ao k va2ue. When nample sise equdt er e=ceedo lot ~~
TABLE 23-2 “Standard Deviallm Method ~E
Maater Table for Reduced lnmc.ectimfor Plana Breed On Varlabilitv Unkmwm(Single Sp’c.ifi..tl.n Litnit-F. rm I )
I I uality Levelo
EEE“Ac
x.—k
—ISampIe size
I
SunpleCode latter size
.04 I .06S I .10 Z.50
k.—
.958
.958
.958
.95.9
1.01
1.07
1.15
1.23
4,00 6.50
k k
.165 .566
.765 .566
,76$ .564
,165 ,566
..914 ,617
.874 ,675
.955 .755
1:01 .828
1.03 .828
1.09 ..986
I.lz .91?
I.lz .917
1.14 .936
1.15 .946—I.zl 1.00
1.24 1.01
i65i.15
k
iZoo
Z.11
.40—.
k—.
I
—
.—1,65
i.75
1.84
-L kmI1.$8
1.9a—1.9a
J+~~l.lz
1.12
1.12
I,lz
.141
.141_—
.141
.341
.393—
,455
.536
.611
II
.664
.695
—
—
z-i-
D 3
E 3
T 4
G 5
H 7
1,45
t
1.34—. —1.51 1.40
1.17
1.Z4
1.62 1.50 1.33
1.41
*
1 10
J 10
K 15
1.7Z
k
1,58.1.72 1.50IZ.Z4 Z.11
Lzo
Z.Z4—
.LZ4
2.Z6
2.Z8—Z.Y5
Z.41
!.84
1.91
:.96
1.41 1.23
1.30
1.11
1.33
1.35
1,36.—1.4Z
1.46
-1--1.79 1.6S
1.8Z 1.69
1.8z 1.69
2.06 1.47Z.53
t-t
Z.4Z Z.)z
Z.58 Z.47 z.16—
2.58 Z.47 Z.36
z.61 Z.50 2.40TL Zo
u Zo
N 25
0 10
P 50
Q 75
Z.11—
Z.11
1.51
1.51
—
1.96
1.90
2.00—
Z.08
2.IZ—
.695
.712
.72J
2.14
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1.85 I I,7Z 1.51
* d1.86 1.73
—1.91 1.80
1.98 (.84——
1.55—-
1.61 ,114
.80$.—
2.27I
1.65
All AQLvm3ues ●re in percent defective.
~~;;, e,:,, ,,,m i“ the ,0, lll”,t t., ,mpetted.f2rotdunplln,g plmbelowtrrow. that it, both mm-qde nize no well •~ kvalue. Whertaemple oize equal, or exceed. lot
Part n
DOUBLE SPEC337CATZ034 3XM3’I
I
S8. SAbfPLLNG PLAN FOR DOUBLESPECIFICATION ~
This part of the Stan-dard describe. theprocedures for use with plain for ● doublespecification limit when variability of thelot with re.p. ct to the quality cluracteristici. unknown and the standard deviation methodis used.
Bfl.1 use of Sampling Phm.. TCIdeterminewhether the lot meets the ●cceptability cri-terion with respect to a particular qualitycharacteristic a“d AQL value(.) the appli-cable campli”g plan ●ha31be used in accord-anc. with the provisions of Section A, Gen-eral Description of Sampling Plans, andthose in this part of the Stamdard.
B9. SEIJ2CTI?JG THE SAMPLING PLAN
A sampling pJa. for each AOZ. value.hall. be ●elected from Table B-3 or B-4 m[C.;J”WS:
B9. 1 Determination of Sample .Stze Codektter. The .arnple i.. cone letter .hal;be selected imm Table A-Z in ●ccordancewith paragraph A7.1.
B9. Z Maater Sampling Table.. The mastersatnplmg table. for plum based on variabil-ity .“kt-mwn for a double specification limitwhen using the standard deviation mctbodare Tables B-3 and B-4. Table B-3 i. u.ed10. normal and tighlened ir.spection amdT=ble B-4 for reduced impectiom
B9. 3 Obtaining Sampling Plan. A samplingda” consists of a .arrml. ..ze and the as-.—soeiated maximum allowable perceni defec-tive(s). The sampling plan to be ●pplied i.inspection shtil be ob-iaed from WSterTable B-3 or B-4.
B9.3.1 Sample Size. The .unple #ize o isshow” in the mater tablas correape=dingtO each sunple size cod. letter.
B9.3.2 M-.imum Allowable Percent Defec.*. T h. maximum allowable percemdefective for #ample estinuLe. of pert.mtde fe. civ. for the Icxmr. upper, or both .pec.ificatiori limit. combined, corresponding tothe sample .ize mentioned ia paragraphf39.3.10 in shown in the COhmm of the mas-ter table corresponding to the applicableAQL value(s). U different AOL, S ● re a.-sign=d to each .pe cification limit, de.ignmfe
the maxfzmIM tiowable percent de fecfivc byML for the lower limit, mad by M for fhe
3upper limft. If one AOL is asci~e to bothIiAt. contbi.ed. designate the timumUlowable percerd d-f% by ht. Table B -3i. ●ntered from 3be 30p for marnul flupec-tion and from the bottom for tisbtaaed fLl-Wpecffon. Samp3fng pfuu for reduced fn-spect.ien ● re provided io Table B -4.
B 10. DRAwU?G OF SAMPLES
Sample# shall be elected in accord-ance with paragraph A7.2.
B11. ;:&-.o;&O T ACCEPTABILITY.
B 11.1 Acceptability Criterion. The degree01 Conformaa Ce or a WlA3ity elaaractcria3fcwith re. pect to m doubje mpacification limit.hafl be judged by the percent of r.onconform-% P.tiuct. The percentage of manconforrn -img product i. e.timated by entering TableB-5 with the quality index and fhe’.ample.ize.
U is the upper specification limit,L ia the lower sp.cificacion limit,X is the sample mea., ands is tkm estimate of lot standard deviation.
B 11.3 Pere=nt Defective i. the Lat. Theaualitv of a lot shall be cx~r.a~terms. .of the lot perc=nt deiecti~c. Ita estimate+33 be de.i~ted by p~. PUO Or P. me
iadicsten cmifornunce with:::;52ptL upper .Pe.tllctiorl limit, PFw.ilh .e. pee: to fbe lowez .pecifiutio. lima .-d P for both .Pecifiati.n limit- eom-bimed. The emtimstea p mid p
+ Y ‘w’ bedetermined by wIterins ● ble B- . r=.pec -tively +f.h QL and f)” md the sample ●isc.The eotinute p Zhmfzbe determined by ●ddingthe corresponding ectinuted percent defec-tive- pL and p“ found in the tible.
B12. ACCEPTABILITY CRITERION ANDSUMMARY FOR OPERATION O FSAMPLING PLANS
B 12.1 be AOL value for both Upper andLower s’ ecxlncatson Lwm umd.
MI L-STD-41411 JurIe 1957
B 12.1. I Acceptability Criterion. 4 Caraparethe ●stimated lot pe.rcatt delective P = PW +PL with the maximum ●llowable p=rcentd. fective M. 11p in ●qual to or less tfun M,the lot meets the accepmb{lity criterion: ifp is grcatertban Mor ii eifher Qu or QLorboth ●re n.@ive ,then the lot does not meetthe ●cceptability criterion.
B 12.1.2 Summary lor Operation of Samplin#Plan. In cases where a ●m.glc ACfl. value is~lished for the .tmer and lower .pccifi -cation limit combined for ● .in81e qualitycharacteristic, the following mtep. ■umma -rize the procedures to be used
(1 ) Delerminc the ample size codeletter [rem Table A-2 by “sing the let .i%e●nd the iriap. ction level.
(2) Select plan from Master TableB-3 or 8-4. Oblain the ample size “ ●ndthe maximum allowable percent defective M.
(3) Select ●t random the sample .af“ unit. Imrn the lot: i.sp. ct and r-cord themea. ur. merit of the quality characteristicon each unit O( the amp]=.
(4) Compute the ●mple rnesn Xand c.timltc Of lc.t .tand=rd dcviatic.n s.
(5) Compute the quality indicesQU = (u-X)/. and QL= (X. L)/,.
(6) Determine the estimated lotp.,r.n: d. fecfiv. P = PU + PL from TableB-5.
(7) lf the e.tirnated lot percent de-fective p i. equal tc. or 1,.. than the maxim-um ●llowable ptzcen% defective M, the )otmeet, the ●cceptability criterion; if p isur.~t=, th=n M Or if either W or QL -bolhar. ne~.tive, then the 101doe. not metthe ●cceptability criterion.
B] 2.2 Different AOL Valueo for Upper andLower specification Limit.
B 12.2.1 Accernability Crit’eria.5 Gmpareth. e.tirnated 101 fJC,C.llt dd ectives pL andPU with the cm? c.pn.ding rntimum allow.able p.rcem defective. Mcompare p = F.L + Pu wfth tke%~#~fa?Land Mu. If pf, i. ●qual to or Iesn than htL,PO i. =qu*: to or le.. than MII. and P im.@al to or 1.*s than the larger ‘of ML “and
tdu, the lot meets the ●ccepubi.fityc riteria;otberwimm, the lot doe. not nwet the ace~.abf3ity criteria. U .mither QL or Qv or botbare me~tiive, then the 101does not meet theacceptability criteria.
BIZ.Z.2 SurnmaryfOr Opertiianal Sampffrt&Plan. 3n ca. eg where ● t erenf AOl. walue~stablished le. the upper and lawer .pec -ification limit for ● single quality cfuract=r -istic, the following steps sunururi’e theprocedures to be US=CL
(1) Deterrninethe ample .izecod=letter from Table A-2 by twin, the lot sizeand fnspectimt level.
‘(.?) Select the sampling plan fromMaster Table B-3 arB-4. Obtain the.ampfe.ize . and the maximum allowable percentdefective Mu and M’. corr=apondi.g to theAOf. va2ues for the upper and lower speci-fication limft., respectively.
(3) Select .1 random the ..ntple ofn unite fr.rn tie lot; ia. pe.t and =ecord themeas”remerd of the quality cfur. cterimticon each unit in the .mrIple.
(4) Compute the sample mean Xand estimate . 10I .tamlard deviation s’. ,,
(5) Compute the quality ittdice.Qff = (u-X)1. and OL = (x- L)/a.
(6) Deterrniae tbe estimsted lotpercent defective ~ and p~, correspand-iag \othe percent defective* shove fhe upperand below the lower .peciIscaticm limit-.A2eodetermi”e the combin.d percent delec -tive p = pu 4 p~.
(7) 11all tbre=of the f.dlowin~ corl-dition.:
(a) ~ i. equal t. 0? 1... thll
% ●
~] PL !9 =LNJ81tO 0, h.. t3UII‘L.
(c) p is equal to orlemmthanfbelarger of ML ●nd btU,
are sati. fied, fh= lot meet. the ●cceptabifhycriteria; ofhe=wi. e the lot does mat meet theacceptability criteria. ff either OL or Gffor both ●re negatiwe, then the lot does nottne=t tbe acceptability e=iter ia.
+S.. Etimple B. 3 {or . cmnplete ●xample of ibis proc.dure.*W Example B.4 lot a cmmpl=te exatnple of thfs procedmre.
42
Z41L-STD-414Ii June 1$S7
I
iII
1’
1’
E-de
Line—
1
2
3
4
5
6
7
s
9
10
II
12
13
14
15
16
17
3SXAZ4PLC E-+
Example of Cdcu3ati0nm
Double spa Mlutino Ltmtt
VariabiNty ?.bbnamn . Stutdard Zkuiaticm M.thod
0.. AQ L Value far both Upper and Lower Specification. Limit Cmmbined
Tbc minimum temperature of operation for a c=rtAtn device 48 speetfied 8.180- F.The masimwnt.mprst.re h 209” F. A lot of 40 item. i- submitted for imopection.3nmpection Level 3V. normal in.pect(on, wtth AOL. s 1% im to be ..d. From TablamA-2 and B-3 it is neen that s sample of ●i=e 5 is zequird Suppo*e the rne...re.mcntm obtained ●re 8. fof30w.: 197”, 188”, 1M., 205”, md 201-; ●nd cmnpliuw.with the acceptability criterion i. w b. determined.
Znforrnatian Needed Value Obtained Explanation
Sample Sise: n
Sum 01 Measu.. mant.: SX
Sum of Squared Measurement: XX2
Correction Factor ICF): (2x)z/n
Corrected Sum of Squarca (SS): XX~C~
Variance (V): SS/(n- 1\
Estimate of Lot St&rd Deviation s: &
Sample Mean ~: ~1.
Upper Specification Limit: U
Lowe r Specification LitnAt: L
QtuIity Index: Qu - (U-X)/s
C3udity tid=: OL = & L)I.
Eat. of L9t Percen5 hf. Ab0V8 U: %
Est. of Lot Percent Z)ef. below L PL
Tataf E81. Pe.rcm13 hf. & La& p = pu + pL
Max. Nlowable Percent Da f.: 3.4
Acceptability Criterion: Compare P . Pu +p~ with M
s
975
190,435
190,125
310
77.5
8.81
195
209
180
1.59
1.?0
2.1 9%
.64%
2.85%
3.32%
2.85% < 3.3.2%
(975)2/5
190,435-190.125
310/4
m
9?5)5
(zo9-1951/a.nl
(195-180)/8.81
.%- Table B-5
See Tablm B-5
2.19% + .66%
See Table B-3
See Para.812.1.2 (7)
‘3& lot meet. the ●cceptability criterion. Ante P s Pu + PL i. 1=. s t~ M.
I ,..43
—
m&6w1411 Jone 1957
EXAMPLE B-4
Exampl* of cazcU2Mf0m
DOnbla Spcffiuti.=n Z.imtt
Vari&i3fty Uakm - 5tsadard Deviation Method
Different AQ3. Value. ior Upper and Luwer Specification l.imitc
Example The minimum temparamre of optra3foa for ● certiin dewice i. .pecified ●- 180- F.The rnu5mumtempQ=a3ure ii 209” F. A lot of 40 items in subrnkted for inmpm=3ion.f.mp=ctic.n L=v=l Iv, normal imW=CCICQI.--I* ACZL = 1% foI *= upper -d ~~ =2.5% for tha 10uer specification limit is to be used. From Tables A-Z and 23-3 itis ●.en that . sample of sise 5 ia required. Suppcme the measurements obtainedare aa follows: 197. , 188. , 184”. 205”, and ZOI. ; and compliuce with the acccpt -ability criteria i. 10 be determined.
~
1
z
3
4
5
b
7
k
9
10
11
lZ
13
14
is
lb
17
la
Information Needed
Sample Size: n
Sum of Mesmmements: Z X
Sum of Squared Meaour.m.mta: XXZ
Correction Factor (CF): (ZX)2/n
Corrected Sum of Squares (SSh lX~CF
Variance (V): SS/(n-1)
Estimate of Z.ot Stam&rd Deviation s: fi
Sample Me= X XXln
Upp=r Specification Limit: w
Lower Specification Limit: L
CluaIity 3ndex: Q“ . (u-X)/o
OAity index: (ZL = (X. fJ/.
Est. of z.&4Percenf DA ●hove U: ~
Eat. of f..of Percent Def. belsw k. PL
Total E.;. P. rcent &f. in Lot,: p . PU ● pL
Mu. Allowfahlc Pereent Def. •bov~ U: MU
Mu. Allowable Percent Def. below & ML
Acceptability Criteria: (s) Comp-rc PU
@) ;;;p;f pL
(c) Compare pWifh ML
Vat.. Obtain. d
5
975
190.435
190.125
310
71.5
8.61
195
Z09
,1s0”
1.s9
1.70
2..19%
.64%
2.85S
9.00%
2.19%. 3.3.?%
.bf+ < 9.80%
Z.esn c 9.80%
Explanation
W75)215
190.435-190,125
31OI4
m
97515
[209 -195) /6.s1
(195 -180) /n.81
See Table B-5
see Table B-S
2.19% + .6W
See Table B-3
See T*1. B-3
See Para.Blz. z.z(7 )(a)see Psra.BIZ. Z.2(7)(bjS.. Para.BIZ..2.Z(7)IC)
~e lot meet. tbE ●cceptability criteria. ●be 18(s), (b); ad (c)are •ati~fied; i.-.. PU ~pL<MLsndp<LtL.
44
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Pmrt m
C5TZMATZON Or PBOC= AV~E AND ~TER3AREDUCED A35D TIONTU4CD =PECTION
FOR
B13. ESITbfATfON OF PR~ AVBR-AGE
The ●verage percent defectiwa. b-cdup. = group of let- submitted for origfndinspection. i. cafled the proceo- ●voragc.Originaf imspectimi i. the firm im*pecfiOn Of~ -~cb? ety of p~ ●bmtttedfor ●cceptability a. dfotiaguf.kd from f3Mimmpec;ie. of product wbfch ti. been remtb-mifted after prior re&cftcm. 3%. pro-..average .fuU be ..timated from flm r..uft.of in. peetic.. of samples dr.wmfmrn a .pee-ified number of precedfq lot. for the pur-~.= Of d=~=rdaiag ●.v9rity of iacp.cfiand.rin~ the c..r.e of . cmdr.cf in accordancewith ~rag,.ph B14.3. AD, 1- sM1 b- iu-cIuded only once in ●stinuffag lb pxocem..verqe. The ..ti_t. ef Uw prw.. ●wr-=K= i. d=. i~t=d by PU -be. eompufed wifhre. pect to an upper ●pee fficatier. lisnit, byPL w.h=. c,.mpyte,d w+fh rc.pecf to ● lower.P=c,f,.~t*- I.mtt. md by p when computedwith re. peet to a double .pecfficatio. fimit.
.-.
B 1~.1 Ahn.rmA R.muft.. l%. r.. ult. ofinspection ef product _ufaetured under. ..”diti... mot” typfcd of ..IuI p.odmeficm.3u15 be exeluded frmn the ●.tinnted pre-ce.. avera~e.
and the ~rremmondtnsedmtid 1c4 +rcud&fOcfiw ~ & p=,-respectively. iw madfrom tfm fable. Tbe ectinuted proceco ●v-crage ~ i* * ~ifhnwfic meaaef fbe fad3-vtdual e.ttrnmted tot perce.t defective- pu’ c.6tmitarly. the etiimated procem ● ●=rage$L it tbe arithmetic mean of the individual●ctfaut9d 30t pareemt &facUwa pL’8.
B 13.L2 Uoubl. SpecW. UtImI Limtc. The. ●timated Iof percent defecfive ● c &-.termIned from Table B-5 for the pfaim ba.edon the standard deviation method. The qtuf -It,imdf... Qu d 0= sti ba e-vu-f.Tabfe B-5 i- enzered ●epar.tely wlfh ~ andQL d the -unP5e ●iae, d the eor--mpmd-fag ~ and PL us read fmm the t8ble. Th.eatitrmt.d lot percent defecfive t. p = p .+PL. The eatimuted proc. ●S a=rage p is se●rifbm.fic mea. of the individtuf c..tinutedlot ~rcenf defective- p’..
D 13.Z.3 S cfal Cam. It the qtulity indexOIJ or C3L< a negative ‘numb=.. the. TableB-5 i. entered bvdimrenardins the negative.ip. f-i---- , ‘i. tbi.- a., ‘h. c.. fi&atedlc.t percent de fecfive above ftm uppa r limitor below fbe lo=. Zimit i. obtafned br mzb-tractiq the PCrcenuge found i m the” tablefrom 100%.7
B 13.2 (hnputmtion of the Est5nuted %0. .BIL. NORMAL TIGHTENED, AND m-
‘~ ‘h. estimated procem- ●=r- DUCED IkBP33CTfON
atm t. t e ●r thmetic mean of fhe .atfmafedl~t percent defective. computed from b.amptia~ iit.p. ction *..uft. d the pxecedtmsten (10) lcIt. .M a. may be othetwf. e decig.nated. b order to e.tirnate tbe lot percentdal.etive, tba quality Ucea QU tiler QLshaff be cmn~ted for ●ub lot. Tbom ~e:C3U = (u-X)/c md QL= (X. L)/a. @em pus.Sr*pb 3511.2.)
Thts S-*rd esti5fah*d campfiagpfam for normal, tightened, and reducediMpactiOn.
B 14.2 -as 31WWetfon D9rtm, tba c0ur9*Of hmcuon. Mrnuz tirncttan ●haff be
fisbtmnd er ‘r.duc8d LrJsp.cficm 1. ~ mr-quir9d b •ccor~ wttb pr.sr.~ B 14.3d n14.4.
B14.3 Tishtaa8d 311spectioa. TI~btarnd h.●poetfon ●balf b- fmtitmad whn tha c cti -matid pro- ●a .nragm wmpidmd from tfm
When Form I -Sfngl. Spectff~tfon ~ 1. rm.d for tba acmptabfflty criterion. tbe “octl -mafe of 101percextl &feetfve pu.or pL 10 mot obta.lmed;fmordertoewtimate the proc.am ●v8r -~s=. it i* n=c=a~=rr to complete paragrapba B6.2 uuf B6.3 of Form L
7FOraXUnP18. U ~ . -.50-0 = 1.60. us~ ●SMPZO SCM SO,PU = 100% - 30.93% = 69.071b,P1. 9 ~-n -P* 69.07s + S.sk . 74*.
52
. ..-
I
II
XIL-STD41411 June 19S7
I
preceding ten (101 108. (Ot ..& 04h*r rlwn -bar of lat. de. i~ted) 1. =crnrduue withKr=zr&pb BIXZ i- srestcr than the AQL,-d when more than A c=rta~ number T ofthem lots have e.timafes of flx percent de-fective sxceediq the AQL. The T vdttbs●re given in Table B-6 far the procea. .v-erage computed from 5. 10. Or 15 Iots.eNormmI inspection shall he reinstated if the..tinut.d preces. ●ver-ge of lots und=rtightened i..prction is cqud to or 1..8 tkmnthe AQL.
B 14.4 Reduced Im.pectiom. Reduced ilI-.pection may be inmitumd prc.vid. d that ●llof the following condition- are ●atiofied:
Condition A. The preceding ten [10)lot. (or .uch other mmnber cd lm. de. igruted)have been under nornul ia.peclio. and nomhas been rejected.
Condition B. The e ctimated percentdefective for each of theme preceding lot. io1=.. U- the appUcable lower limit shownin Table B-7; or km =ertak .arnplirIg plan. ,
b estimated lot percent defective is eqtntto =ero for a ●pedfied number of conmeeu-tiwe tot, (gee Table B-?).
Cad6tfon c. PrOdnctiM is ●t a●teady rata.
Normal impaction ●hall he r.in.tated if anyoaac of the following condition. occ. ra undcrreduced inspection.
Condition D. A lot i. rejected.
Condition E. TM emtimated prc.cem●
●.eragc is greater tham tbe AQL.
Condition F. Production become.irreguI~r or delayed.
Condition G. Qther condition. .. .~? ~brrmt that normal inspection .houldbe reinstated.
B 14.5 Sampling P18m. 1.. Tightened Or Re-duced lmpecthm. Sunplu-ig plan. ior tight-ene d and reduced in.pecticm .re provibd inSection B, Part. 1 and U.
I:
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MIfA3TD-41411 Jwm 1SS7
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11 11 11 15
4 4 5: a a 10
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4 4 4 58 8 10
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4 4 4 5a e 8 10
11 11 11 15
4 4 58 : 8 10
11 11 11 15
4 4 4 58 io
11 1: 1: 15
4 4 4 58 8 a 10
11 11 11 15
4 4 4 5s 8 8 1011 11 11 15
4- — 4-- -4 5“8 a a 1011 11 11 15
mm ●re m 9mp31a# pluu prwuad la thio Staa&rd far Unse code lctirs dAO1.wshm9.
M
..-. —-
unmlTP51411 Jrmd 19s7
TAB= B-6<0nfif=d sUmdard D8dmnua U8fbd
vdtms of T [or TiKhtaud Impaction
Th. top figure ia ..ch ilock refers t. fbe preced~g 5 10C~. the ~ddfe fi-re ~ ‘epreceding 10 let. and the boftom fipre to the preceding 15 let-.
Ti@encd ia.pection i. required whom tbe numb. r of lnta wltb e~tfmates of percentdefective ●bove tbmAQL from the precediq 5. 10. Or 15 Lets is srester tbmn th= xiveri wdueof T in lhe table. ad tbe pro.en~ average from them. 10t@ .=.=.da tba AQf-.
N1 estirnatew of the tot percent defective are c.btained f rem T8ble B-5.
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Q ●ub L
p sub U
p s“b L
M sub U
M sub L
p bar
p bar sub U
p b-r ●ub L
Mx~1411 Juno 10S7
APP@Du B
~efinitkons
Definition
Sample ●ix. for ● .i=~le lot.
~P1. M==. Arithmetic mean Of .mup3m me.surememm i~~m● .Ixl.qlc lot.
E.tinute cd lot ctandmrd deviation- Standard deviation of ●un -ple measurement [mm a ●insle lot. (See &xmpIe* iaSect40n33.)
Upp=r ●pecffic~tiOm limit.
Lower ●pecificalfiOn limit.
The ●cceptability eon. tant @ven i~ Table. B- 1 and B-2.
Quality index for u.. with Table B-5.
Ouality index for u.. with Treble B-5.
Sample ●.tirnale of the lot percent defece . . above U fromTable B- 1..
Sampl. estimate of the 101 percent defective below L fromTable B-S.
Total .ampl. e.timate of the lot percent defective P = PU + P~
Maximum ●llowable percent defective for .-pie eatinutea~iven in Table. B-3 and B-4.
Mtimum allowmblc Pcrceat defective ●bove U given i. Table.B-3 and B-4. (For uoe when differeot AOL valuea for U andL are specified. ]
Maximum Alowable percexaf dcfecfive below L given in Table-B-3 and B-4. (For we when differenl AQL vtiuea for U &L ●re #pacified. )
Bamp3e ●intimate of the proceem percemf defectivw i.e., theestinuted procea ● ●ve rage.
Tbe estimated proce. m8varage far u upper specification limit.
The eslimatad procenm sv.rqe for ● 10W* r ●pacification Mmft.
The maximum number of eattnnted prece. s sveragam wbkbmay ●xceed tb#AQL BlverI in Table B-6. (For u.e in deter-mining ●pplication O! ti~hteaed inspection. )
A lactez ua.d in d.te rmim.i~ the ~um Standard Deviation(hLSD). The F valu=s are given In Table B-8.
Greater than
ham than
sum of
Ml
MZL-STD-41411 JufM2 19s9
I
I
I
SEC’ITON c
VARIABILITY UNSNOW7J-3LMJGE METBOD
Part 1
sZNG LE SPECIFICATION UT
Cl. SASIPLUJG PLAN FOR SINGLESPECIP3CATZON LDdIT
‘This part d the SUmZ. rd describes theprO.y@ur=~ fOr. u*e wilh PlaM for s Si=ulerep..c1ficati0n knit whcri variability O{ cbelot with rempecl 10 the qtmlily cbarseteri. -tic M u.knowm and the ZWC nmtlmd i. used.The -cceptability criteric.ti i# give= in lwoequivalent form.. Th. mc arc identified asFo,rm 1 d Form Z.
the .“pplic~ble ●amplih~ PI- ●hall be treedin .ccordance with the provisions of Sec-tion A, General Demcripciou of Samplingpl.m.. b the... in thi. part of the Sc.ndard.
CZ.2.2 Accep-ility Comstit. The accept-ability COa.t-t k. correspo~w tithe sun-ple mi. e mentioned in paragraph CZ. Z. 1. isindicated in the column of the master t.blecorre. poading m the applicable AQL value.Table C-1 i. enmred lrom the 10P lo. nc.r -rn.1 impection ●md from th. bottom fortightened inspection. Sampling plans for re-duced inspection a*e provided in Treble C-Z.
C3. WT-BY-L&fT ACCEPTA=ITY PROZCEDURES WffEN FORM 1 IS USED
C1.1 use of SUnpliag Plan.. To deter-mine whether the. 10C meet, tbe ACCCpt- C3. 1 AccepUbiZity Criterion. The degreeability criterion wJth respect to a particu. of coaormance of a quazmy characteristiclar quality characteristic •~d AQL vaZue. with re8pect to ● #ingle specification :imit
●haZl be judged by the quantity (u-X)/R or{X- f.)lsi.
Cl.2 Drawing of Sarnp3e.. AN .armples sbdlbe draw. m accordance wltb [email protected].
Cl.3 Determination of Sample Size CodeLetter. T he sample sme cod e letter •hd~=ected from Table A-2 in ●ccordancewith par~raph A7. 1.
CZ SELECT3NG THE SAMPLINO PLANwHEN FORM 1 ls USED
CZ.1 Master Samplin~ Tmblec. The matter●mplmfi tal C* cor DlaM b- ed on varia -blIity u---n for ~ single ●peef.fieationlimit wbenuakg & raag. unfkodaro TablesC-1 ●nd C-Z. Tabia C-1 b .u..d for nor-mal ●nd ti~htened inspecfi.m uuf Table C-2for reduced izupoction.
CZ.Z Obtining the SunptinS P3an. The.unp3im~ plain ccmsastmO{ . .unple ●X ● -d●m ●sociated accepIAbUiv C- taut. f The.unplimg plain ia obtain.d from MaaterTable C-1 or C-Z.
CZ. Z.1 Sam le Si=e. Tbe sample size a it~.homa ,n 1 e nla’ter table CC4rrm#p0~ tO
each ●mple .1== e-de Iater.
:/::1 -i: ‘iw%”%(ilwzdepending on whether the specification Iimi!is = upper or ● lower lirnis. where
U im the upper specification limit.L is fhe lower specification IimIt.X is the sample mean, and~ i. the ●verage range of the #ample.
3n this Standaqd. K ia the average range of,.bKrmip ranges. 32ach d die subSro.p.consists of 5 mea*u*emenl.. except for tbOa*plans with ●unple ●ke 3, 4, or 7 in whichu** fbe ●kgroup ●im 19 fh sum as i.hsanw3e sise. Zm wanpufiq K 338= Ord=r OfIhc sample meam=rem=iits u .-de c=u*t b=rer.-iimd. Smkgrwpa af cnumcrmive nn.. -urements must ba formed d the range of.xh .ubgroup obtalwd. X is the ●weraae oftbe individnaZ ●bgroup nngea.
C3. 3 AeceptsbIlltY Crite Finn. compare theq.mtity (u - m (X- L1
‘Kwithtbe “C’%%●bilitv cor.8cant LOrZf (u-XI/X or (X- L)equal “to or Creater than k. the lot meats tbe●.ccptab13icy c rito rloix u (u-X)/R or(X- 2.)1X ia less tbm k or m.’afiva. tbea thelot deem not met the .c..ptability e ritoricm.
1Se. Appendix C for definitions of afl cymbolo us id b tbe ●ampllng pl~o bac.d on varIabllttyuak90wm- raaga mmbod.
%we f+ample C-1 f.r ● cmIIp3eto ●xunple of tbi. procedure.
al
._ . ..-
I
3A1L-m-41411 June 1957
CL f3uMM~YSNAP LANGUSED
FOR OP3IRATION OFPLAN WHEN FORM 1 LS
Th$ following 8tepm umun.riz. the pro-cedure. fn be followed:
(1) Determine the ●ample .i, c cede let-ter from Table A-Z byu. iq the 101.ize andthe in. pecti.an level.
(2) Obtain plan from Mater Table C-1or C-Z by .elecfin~ the sample ●ize n andthe acceptability ccm.taat k.
(3) select *1 random the .;rnpl. of m“nit. from the lot: in. pect .nd record themeamurernenx of the quality charactari. ticfor ●=ch uait of the sample.
(4) Compute the .;rnple mean X and the●vera~e range of the .arnple ~, .md ●l.ocompute the quantity (u- X)IR for am upper●pe. ificatiomlirnit V or thequamtity (X- L)/Rfor . lower specification limit L.
(5) ff th= quantity (u-X)/R c.r (X. L)/Ri. equal to or greater thas k, the lot meet.the ●cceptability criteriow if (u. X)/11 or(X- L)llf i. I.*9 than k or negative, then thelot doe. not meet the ●cceptability criterion.
C5. SELECTING THE SAMPLING PLANWHEN FOR64 2 3S USED
C5.1 Ma#ler Samplinj? Table.. The ma. ter●amplmx table. for plana ba. ed o= varisbil -ity unka&n for a single specification lititwhen u.iq the rang. method ar= Taidec C- 3●nd C-4 of Part IL Table C-3 is used fornc.n’nal and tightened inspection ●nd TableC-4 for reduced inmpectimi.
C5. Z Obtaininz the Sampltng Pllrl. Th ●
sampling ptan con. i.t~ of m .UIWI]e .ize andan aooo~ik.d maximum a310w&le percentdef ●ctive . The ●amplfq ptam ic obtdncdfrom Ma.t=r Table C-3 or c-4.
C5. Z.Z Maxd8mtmAIIc.wable Pereent Defec-tive. The madrnwn allowable percemt de-=ive M for s-pie eotim.tes corres~nd-ing 10 tbe sample ●iz= me~tie tied inparagraph C5.Z.1 i. indicated tn tbe COIUMIIOf the rnmms.r tabte correa pending to theapplicable AfZL value. Table C-3 ii enteredfrom lb. top f-r ~orrnal iaapectian mad fromthe botfom for ti~htened in. pecticm. Sun-P~ Plaru for reduced inspecticm are pr.a -vided in Table C-4.
CO. f.CfT-BY-LOT ACCEPTABI w P%CEDU3432S WNEN FOR3A 2 3S USED
c6. 1 AcceptabUity Criteric.n. The degreeof conformance of ● qutilty characteristicwith respeet CC.● ●imgle .pecificstimi limit.hafl be judged by tbc p.r. mit of notlccm-fomnirt~ p.od. ct out. ide the upper er lowerspecific aticm limit. The percentage of rmn-conforming product i. estimated by emteringTable C-5 with the quality iadex and the#ample ●i*e.
c6. ?. Computation c.f Quality Index. Thequality izidex Or, . (U- ZC)CIR hall be com -puted “if the sp%cificaticm limit i. an IIppcrlimit U, O= QL = (X- L)c/K if it is a lowerlimit L. Tbe q“amitie., X ●nd R, ●re thesample mean and ●verage ran~e of tbe samp-le, respectively. The compmatioa of K i.●xplairted in paragraph C3.2. The facbar cis provided in Master Tabl=s C- 3 an& C-4corresponding to the .unple size code letter.
C6.3 fhtimate of Percent Defective in bt.The quditv of a 1.s1 hall be expre.. ed byPU. the =.timated percent de fe~tive in thelot ●bov= the upper specification limit, orby PL. the ●.ti-@d p.r. =ntd=fectiv= belo-thc lower ●pccificatiort lirnii. The ●.tima~edPercent de f=cti~. PU O, PL i. mbt~im=d by.mteri+j Table C-5 with Qu or QL .nd the●pp. Opri~t= ●AMPlt ●i*e.
C6.4 Acceptability Criterion. Compare thee.timated 1m percent defective PU or pL withthe m~imutn aZlew.hle perceM defectiveM. U .pU or pL is equml to or le.. Uun M.the lot meet. the’ ●cceptmbitity criterion, ifpu or pL is grekter than M or U QU Or QLi~ negative. then the lot does not meet theacceptability criterion.
Cl. SUMMARY OF OPERATTON OF SAM-PLING PLAN WHEN FOR3d 2 IS USED
Tha fellowinK ,tep~ ●un’unar 3s9 theptwedures to be fallowed:
(1) Demwime ihe -ample .ise code lel -ter from Table A-S ~u~inn the lot dae andthe iriapecttosi Iov@l.
(Z) Obtmi. plan from t.mater Iable C-3or C-4 by .electirg the -ample sk= n. thefactor c, and tbe maximum ●llowable pw. -ceat defective M.
(3) Select ●t random the sample of nunit. {ram the 10C inopect and record themeamm.mem al the quazity characteristicon each nut; of the 8sMple.
3See 3cxAmple c-z tar a complete example of thim pru..dur..
62
.
MI L-sin-41411 June 1057 I
(4) timpute the ●unple me-m X 4 the (7) Uthe ●.timaled lot pcrcentdelectiveav.ra~c raaSe of the ●ample K. PU or PL i. eqtml to or Ie*. thaa the md-
(5) Comp@= the q.=lity “ index QU =mum azlowable percent defective M. 3he lot
(U-X)c/K M the upper speckfieation limit Umeets the acceptability criterion; it PU or
iripecified, or QL = (X- L)CIK i3 the lowerpL img.eater than M or U Ou or O’i.%=_~
.pccificatirm limit L ia .pecif ied.-i”.. them the lot doe. W1 meet the ●ccept-●biliw criterion.
161Decermirie the ●.limaled 10s m.rc.r...-, ———defective PU or pi. from Table C- 5.-
~PLJl c-1
Example of Ca3culati0n*
Single Specification Limit-Form 1
Variability Unknown - Range Method
EXarnple The lower .pecifie.tion limit for electrical r.miataace of ● certtim ●lectricti com-ponent is 620 ohm.. A lot of 100 item. is submitted for inspection. InspectionLevel IV, normal inspection, tith AOL = .4% i. to be used. From Tablet A-2 udC- 1 it i. ..en that a sample of size 10 i. required. Suppose that value. of the’sample resistances in the order reading from left to right ●re . . follow-:
643. 651, 619, 627. 650, (R, = 658 - 619 = 39)67o, 673, 641, 538, 650, (Rz = 673 - 638 = 15)
and compliance with the ●ccept ability criterion i. to be determined.
Line—
1
.?
3
4
5
6
7
8
3nf. rrn.ti.. Needed
Sample Site: n
Sum 01 Measurements: I X
Sample Mean X: XXI.
Speckfieatio. Limit (LOwer~ L
The qu~tl~ (X- L)/It
Accep3AZZity Camsmt: k
Acceptability Criterion Compmm (X- L)/l!with k
Value Obtained EXP1anatiom
10
647o
647 6470/10
37 (39+35)/2
620
.7s0 (647-620)/37
.811 &- Tabla’ C-1
.710< .811 ●&e ParaLc3.3
The lot doe. not meet tbe ●cceptability criterion. .irIce (X- k.)f~ is 1c99 than k.
= U ● .imK1e .PP=r .Pecificati.. limit U im give., then compute tb. quantity (u-Xl/X knline 6 ●ad cmmpar= it with k the lot meet. the acceptabUitY criteriom, if (U- rnf~ i-equal 10 Or greater [ham k.
.-—
MIL-ST13-41411 June 1957
EXAMPLS c-2
12xample 01 Calculation.
Single Specification Limit-Form Z
Variability U.knowmi - Rang. Method
Ex. mple A lo.ver specification limit for electrical re. i.tan.e of ● certain electrical com-ponent i. 620 duns. A 10I of 100 item. i. submitl.d for inspection. ZaspectionLevel lV. normal in. Dection. wish AQL - .4% i. m be used. From Table. A-2 madC- 1 is is seen thal ; sunple of ●izc 10 i. required. Suppo. e lh. v*Iu=. Of thesample reaiatance. in the order readimg from left m. right are as follows:
643. 651, 619. 627. 6S8. (R, = 658 - 619 = 39)670. 673. 641. 638, 650. (R2 = 673 - 638 = 35)
●nd compliance with the acceptability criterioo i. 10 be determined.
Line—
I
z
3
4
5
6
7
8
9
10
Inlorrnati.n Needed
Sample Size: m
Sum of Measurememtm: IX
sample M,.. x: ZXJ.
Average Range ~: XRlne. of subgroup.
Factor c
Sp=. ific*tiO. Limit (~we. ): L
Q.a2ity Zndex C3L = IX- L)CIX
‘ct. ‘f bt ‘ercent “f.’ PL
Max. Allowable PerceIIt De f.: M
Acceptability Criterion: Compare pL with M
Value Obtained
10
6470
647
37
2.405
620
1.76
2.54S
1.14%
2.54%> 1.14%
6470110
(39.3S)12
See Table C-?
(647-620)2.405/37
See Table C-5
See Table C-3
See Para. C6.4
The jot doe. mat meet the acceptability criterion. ■ince pL is gr=ate. than M.
-E: U . .ingl. upper specification limit u i. Rive., th=. compute the quaii3y frufax QU ~fU-X)c/3! in line 7 d obtain the eotimate of lot percent defe.tive PU. -mpr= PUwith M: the let meet. the ●cceptability criterion, U p“ ia ●qu~ io or i’z*. ~hn M.
M
...
——
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.!325
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.336
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.17
8
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6
D E F G H 1
.18
4
.189
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.
.68
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3
.73
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6
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.78
0
.79
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9— 2
.90
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58
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.111
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.441
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Parf 1I
DOUBLE SPECIFKATION
xf~1411 Jfffw 19s?
Lf3d3T
C8. SAAfPLDfG PLAN POR DOUBLESPECIFICATION LtMIT
This part Of the Sf-rd describes theprocedures for tue with plain [or ● doublecpecificafioa Iimft when variabttify Of thelet with respect to tbe quality characteristicia u.knc. wm ●nd the range method is umed.
cA. 1 u.. a{ S-.11.. Plan.. Tc, determine------- -. ——..- .. —”. .—— .—-—~hethe r the 8.x meet. tbc .C eept.bility c ri-te rion *ith rcapeet to a partiastar qualitychar.eteristic .~d AQL. vtiue(. ), the .ppli -cabl. ●ampliag F.lao ●U be used in accord-atxe with the pre. i.imm of Section A, Gen-eral De.eription d SunplinS PIMa, ●wJthe. e in thi. part of the Staadard.
C9. SE LECITNG THE SAMPLING PLAN
A ●unplhg plaa for ● ach AQI. .tiue.N1 be .clectcd from Table C- 3 or C-4 ●m10UOU.. , . . ...- . . . . . . .
C9. 1 Determination of Sunple Size Code~. Th ● .unple .s. code letter =hfib. ●elected from Table A-Z in accord-eewith paragra~ A7.1.
C9. Z hta-tor SamIIlimX Tabla-. The mastermunnlinn tablem [or mlam hmed Onvariabil -ity ~fca~wu for a d~ble specification limitwbeo uming the range rn.tbod ●re Tablea C-3●nd C-4. Tsble C-3 is used for norrnaf andtightened im.pectiom and Table C-4 for ra -duced Lrup.ccfion.
C9. 3 Obtaintng Sampling Plan. A ●sM@in4plm Comai,ts of ● ●ampfe sise - the sl -●octatad maximum attowablo percent dafac -tiw-e(. ). The cunplin3 plan to be ●pplied inkn#pect&a stmfl be ~btied from MaaterTable c-3 or c-4.
C9.3. I Sun 10 Si=e. The ●antple sise m Is.bownbiitdl,.. .Orr..pmdiag toeach ●unple ●ice code letfer.
C9. 3.2 Maximum Allowable Percent DeIe c -five. The maximum-t allowable PCrcrnnt de-~tive for cunple e.tirnatec of percentdef ●etiv. for the lower, qpsr, or botb ●p.c -
-..
67
mmtimum ●llowable ~rcemt defectively MLfor the lower Iindt. ad by MU for the upperlimit. If ~ AOL i8 88sinmd to bofh limitsc.mbiaed. designate tbc -urn aflo.ablepercemtdelecfiveby M. Table C-3 is enteredtram fhe cop for aornul inspection and fromtbe bottma for tAIhtamd inspection. Sam-plim8 P1W9 Sor roduce!ttmpaction ●re pr. -— . .vialed iii Table G-4.
C1O. DRAW7NG OF SAMPLES
sample. .fmfl be ●lected in ●ccord -aace with ~raarapb A7. Z.
C1l. ;~~OT-~;~O T ACCEPTAB1_
Cl 1.1 Acceptability Criterion. The degreeof c.nfo~aracteristi.with re. peel to . doub_fe .~cific. tion limithall be Judg.d by tbc percent ei wnco. -ICr.rni.g producL The per.enta~e of no.-Cwderming product is estimated by enteringTable C-5 with the quafity imd=x ●nd the‘ample :Ue.
Cf 1.2 timputatioa of Ouality bdicei. Thequalify inchcea Q {u xl.C [R and QL=(X- L)c/R cbdl be !o&uted. -here
uLc
xu
im the upper specification limit,ia the lower .peeificalion limit,is ● iacfor provided in Tables C-3 andC-4,
i. fbe ●mple mean, andi- the ●verage range of the sample.
b tbh Standard. R is the >verage rmge oftba ●bsroup rauKc& ~cb of tie sti#*0Up9consimt. of 5 meuurement$. ex’c=pt for thosepduu dtb ●rnple ●is. 3, 4, or 7 in whichcase flu ●ubaro.p ●is. h th= ●ame ●e thes-pfa ●~e. 3a computing R, the Order Offbe .unple meamtrernemm ●s nude mat beratahad. subgroup of co-ecutive meu -urementi mnot be formed and tbe range ofetch ●ubgreup obtahed. K ia the ●-eraseof the individud ●ubgroup ranges.
Cf 1.3 Percent Defective In the Lint. Thequalify of ● lot ●hall be exprew~ed SrImrm-of the lot ~rc.nt dof=cfi.=. Its •c~~** W~be dosipawed bY P L, PUO 0? P. The ●gtiwtaPU iadic*eD contmrmca ~tb respect to tbeUPPGr spockfieatien Mnait. p with resp.ef tothe lower .peckfi.atim lAU. - P fOrb o t h spaekfieation limlta combined. TIM
.
—
=.cirnatc. p.Laad pU ●baJl be determined byentering Table C-5. r.mpacti..l~ ‘iJb Qt.●nd Qu ●nd the ●ampl* ●i=.. The =~tim~tep shall he dew rmined by ●ddin~ the co rres -pcmdimg estimated percent defective. PLamd PU found iii the table.
C12. ACCEPTAB1~ CRZTER20N ANDSUMMARY FOR 0PE2tAlTUN OFSAMPLING PLANS
Cl 2.1 O!ie AQt- value for both Upper ●ndb-e r + Cit,catmm Limit Cmnbmed.
Cl 2.1.1 Acceptability Criterion. 4 Compareche eetimamd lot percent delectlve P . p“ +PL -ilh the maximum ●l10-abl* Prc=ntdcfcc:ive M. U p is equal to or less than M.$h. lot meets the ●cceptability criterion, ifP i. e,e*t=, th*n MOr if either QU ‘r ‘Lorboth .re negative, Ihenthe Jotdoes not meetthe ●cceptability criterion.
C12.1.2 Summary for Operation of SampliagPlain In came. where ● .ingle AQL value 1.=blished forth. um~er and lower s~ecifi -C~t;ori limit cornbin;~ for a ●i=gle quality.haracleristic. the following steps summa-=i.. lh. procedure. to be used:
.ll)”Dctcrminc the sample si. ecode
letter from T.ble A-2 by using ‘the Jot sicand the in, pe. tie. level.
(2} Select plan from Maater TableC-3 or C-4. Obtain the sample ttie n. th=factor c, and the maximum mfloumble per-cent defective M.
13) Select m random, the ●ample ofn unit. from the lot; respect and record tbemea. urem.. t of the quality characteristicor. ● .ch unit of the sample.
(4) Compute the sample mean X ●ndaverage rmge of tbe ●ample R.
IS) -mpt tbe quality indite. OUF. IU. X)c/K arid QL, = (X. L)C/R.
(6) Determim the emtimtiad loty-fi=nt d= f=ctiv= P * PU + pL frOm T~bl=
(7) 2f the eotinuted lot percent de-fective pi. equal to erlem. thui the maximumd20wable percent defective M. fbe 10Jmeetsthe acceptability criterion, if p ia graatarlIIM M or U either Ou or QL Or both amnegative, then the lot doe. awt meet tbe ac-ceptability trite rion.
CIZ. Z.1 A.c=ptabitity Critdria. 5 timp8rethe estimated lot Per.cenc de fcctive~ Pt. ~P with the corresponding maximum aTiow-e8 Ie percent defective M
k●nd Mu ●lso
compar. p . pL + Pu with t e larcer Of ML●nd Mu. 2f pL ia equal to or 1=6s ~h~ MbPU is equal to or lees than b4u. d P isequal to or 1=0s than the larger of btL ~Mu. Ihc lot meet8 the *cceplability critcri=,otheruase.7be lot does not meet the scce Pl -ability criteria. 33●ither QL or OU or both● re negative, then the lot does not meet theaeceptabitity c riteri&
Cl 2.2.2 “Summary far O~~atic.n -f ~mPliWfPJan. & ~.ses m.h.re ● cliffere.t AQL value~tmblished (or the upper ●nd k.wcr .Pec -ificatio” limit fc.r a sim~ie quality character-istic, the fol Jmnimg steps ●m-.mari=e theprocedures to be used:
(1 I Dcternai~e the sample ai.e &d.letter from Table A-2 by using the lot ●i=cand inspection Jewel.
(2) Select the sampJitig plan fromMaster Table C-3 or C-4. Oblain the amp-le size K.. the factor c. -d the m~mum● llowabJe percent defective. MU and ML.corre. pondi=g to AOL VaIUeS fo, the uPP=r●nd lower Specific atiec. limit., respectively.
(3) Select ●t random lhe ●ample ofa utit. from the 10C inspect and record themeasurement or the quality characteristicon each unil in the .UTIPIC.
{4) Ckmpute the ●ample mea. X ●.d●.er.~e rams-kof tbe ●unpJe R.
(5) Compute the qualiJy imdicec QfJ. (u- X)c/R. and OL =(X-L)CfU.
(6) Determine the ● .timm~ed lotpercent defective. pU amdpL. correspondingto the p.r. em defective. above the upperand below the lower specificticw limitt.AJSO determine lbe combined percent detec-tiV= p - ~ + pL.
(7) 32atl three of the lollowlris cos-dbt~ons:
(a) PU is =q-~ tO Or lEM tbu~u.
(b) P,. ia aqtml co or I=*w th*m
ML-{c) p is equal toor Jesmtin the
l.rger of ML and Mu.
●re ●aticfied. fh lot m.mtmtbe accepfAbi21tycriteria; otherdse the lot hew not meet thescc=ptability criteria. If either Oz.,or QU orboth ● re =gative. fba. *h. lot dw* tit UI**Cthe acceptability criteria.
C#w.~r Different AOL va.luet for Upper a~dp8cuLcmU0m LamIL.
4tie ~pk C-3 for . campl,ete ●xample d tbi. proc.dure.SW *PI= c.4 for . =om**t* exunpZe of Ma PrO=~ur*.
-. -—.. . .
MIL-STD4MllJunelDS7
I
*.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
EXAUPIX C-3
Example of Calculations
Double Specification Ltrnit
Variability Unknown - Aver age Rsnge Method
One AQL Value for Both Upper and Lower Specification. Limit Combined
The ●peclficstioni [or elec:riea2 recisfaace -f a certaiu electrical cOrnponeu5 *65o.o ● 30 ohm.. A lot of 100 item. is ●ibmitt.d for In*petiiar& fmspecfi.. Uwe2IV, normal intpectiea, wftb AOL . .4% ii to be used. From Tuble. A-2 and C-3 itis ●eer. that ● samfle of size 10 1. required. Suppose the vafuea of the ●mnp2eresistance in the order reading frm-n left to ri~ht are ●s follows:
643, 651, 619, 627, 65B. (Rl . 658 - 619. = 39)67o. 673. 64). 630, 65o. (R2 s 673 - 638 c 35)
and compliance with the acceptability criterion i. m be determined.
Znf.armatiom Ne.ded V.lu. Obtti~md Zcxpla.atien
Sunpl. Sise: . 10
sum of Mea. u,. m.clt.: xx
.%mpl. U... X: XXI.
fawer Specification Ltmit: L
Ctudity Index Cfu . (U-X) c/R
Ouality Zndex: C3L = IX- L)e/11
~-t. of Lut p--t D=f. ●b- u: w
Est. of 3A Percent Def. baleu L pL
Tota2 Est. Parcant Def. h fak P = Pu + PL
Max. A210wable Percent Def.: M
Acceptab12ify Crtterloa: Carnpare p -Pff + PL titb 64
6470
647
37
.?.405
680
620
2.15
1.76
.35s
..2.54%
: 2.89%
1.14%
2.e98 >1.14s
6470/10
(39 + 35)/2
See Table C-3
(680 -64Y)z.405/37
(647-620)2.405/37
See Table C-5
see Tsble C-5
.s5s + 2.54s
SOe Table C-S
See P*ra.CIZ.1.Z(7)
Tbe lot dtm. nut meet tbe ●cceptabifify crilerlOn. since p = p“ + pL 1~ greater ~ M.
de
—
xm.-sTD-4l411 Jute 1957
I EXAMPLE c+
I ~ph of Cakuhuom
Doub3e Specfficatlom LimI1
I V.riab33ity Unknown - ~we ra~e Range Method
Different AQL Values for Upper and Lwer Specification Limit-
I ZZ.unple The ●pecifi.aticm. f.r electrical reaiscance of ● certain electrical cmnpone~t i-650.0 ● 30 darns. A J*1 of 100 items im ●ubmitted for inspection Zn.pectimi 3AV.1IV, rmrmmz impecziou, vifb AQ3. . 2.5$ far the upper and AQL E 1% far tbc lowerspecification limit i. Ie be used. From Tablet A-z and C-3 it i. ●ce= that ● .am -P1. of size 10 is reauired. SuPrmse the values of the sample resistances in theirder reading fmm left to right “a-re a. follows:
643. 651. 619, 627, 658. (R, = 6S8 - 619 = 39)670, 673, 641, 638. 650, (Rz = 673 - 638 = 35)
and compliance with the ●cceptability c*iteria i. co be determined.
3
4
5
6
7
I 8
9
10
11
I lZ
13
14
I 15
Intc.rrnation Needed
Sample Six.: n
Sum of Me.. urcment.: 1X
.%rnplc Mean X: IXf.
Average Z4.nge ~: X3tlno. of .ubgroups
Factor c
Wp=r specificatio~ Limit: U
kwer Specification Limit: L
0ua2ity index Qu = (u-X) c/R
OuaIity fndex: QL = fX-L). /R
~s~. Of ~t Perce=: Dcf. =bOv= u: FU
~.t. ‘=f kt p=c.mt D=f. belOw fA PL
Tad Ems. Per.emt Del. in tit: p = PU + PL
MAX. A130wab1= Percent Def. ●bove U: Mu
- A330wabla Percent Def. below 3A M’
Acceptability Criteria: (a) CDmpmre PUwith Mu
(b) Compare PLwith ML
(c) ~t~p~ue p
Value Obtained
10
647o
647
37
2.405
680
620
Z.15
1.76
.35%
2.s4%
2.89%
1.42s
3.23%
.3s% <7.42%
2.54s . 3.Z3U
2.898 <7.42s
6470/10
(39 + 351/2
See Table C-3
(680-647)2.405137
(647-620)2.405137
See Table C-5
See Table C-5
.3s% + 2.54%
S.. Table C- 3
See Table C-3
See Pars.clz.z.z(7)(dSee Para.C12.Z. Z(7)lb)See Pars.CIZ.Z.Z(7)(C)
The 10t rtmetm ttm ●cceptability criter&, slats 15(-). (b) and (cJ ● re satisfied; i.e.. PU <MfJ. pL<M~uldp <Mu.
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ESTIMATION OF PROCUS AV~GfZ AND CRfTERfA f=ORR=UCED AN(3 T1Gf4TENE0 3NSPECTION
C 13. fig~MATION OF PROCESS AVER-
Tbe .verag. percent defective, based~POa ● group of lot. .ubmttted for c.ri~iii.lIn. pectmn. i. called [be prc.ce. a ●verase.OrigiM1 im.pectiert imthe fir.t inspection of. particular quantity Of product .ubmittedle. ●cceptability . . diati~uiah.d from theia. pe. tion of praducl which hambeen re. ub -rnisted after prior rejection. The pr.acc..●vera~e shall be e.timated from the remdtmof im. peetion of ●mple. drawn from . .pec -Uied numb. t of pr. ceditq lot. for the pur -PO.. of delerminiag .everity of imapectiondurimg the .our. e cd ● co=t?.ct in aecordaacewith paragraph C14.3. Ay lot .bdl be in-citided md, ante (m rt.dnutfri~ chmproc...avera~c. The e.timate of thepmcc.. aver-age i. de. igriated by p“ wbem cwnpuc.d withrempect tc. ●n upper .pecific.tion limit, by(JL -b.. ..mP.ted rnth respect to a lower.p. cifi..tic.n limit, and by p when computedwith respect to ● double .pecifi..t ion Ilmft.
.
C13.1 Abnormal R.. uft.. Th. ra.ult. ofic!. pectitin of product rnamuf. cmred underccanditions aot typica3 of u.tmf productionhall b. excluded from the emtimaled pro-ctm. ●verage.
Cl 3.2 Compufatio. of tbe EsUnmted Pro-Ce.. Average. Th e estmuted pracemm ●vmr -.;. 18 the a%hrnetic mean of 4(I. e-hatedlot percent d. fecti.=m computed from tbe●ampliag i.. pectioa re. ufto of the precedlmgten ( 10) lot. er ● . may be otberwi. e de. ig -matad. & order to eatim.t. the lot p.rcemdefective, the qua3ity hdie.. Q“ andlcw OL
r9ball be Coin ●d for aach lot. Tb... ua:Ou = (u-X)C X and Ot, = (X- L)c/IL (Seeparwraph Cl 1.2. )
C13.7..1 6S&l* Specific& 3An& Tbeemilmuea lot percent d●1eetlva ●bQ b. d.-Iarmin.d from Tabl. C-S forth #_ ti.don the r~c tuetbod. T& qdity M-x Ou●bd k uood for tbae~e ti u-r •~.Ific.tlmiMrnft er Q~ ler tb8 cu. d . tir●p.cuictiom ulmlL T&l* c-s b tirtidfb C)uor QL ●nd (h* ●rnfla ●ti=. d ~*
corresponding e.limated lot prcent dcf. c-Uve p or p . rempecfivel~, is red fromthe ta~)e. Tk ..tirnated proce.. .ver.~e
% i~ the -it f-=*ic M-= Of the individu~-.titn.ted lot percent d. fectiva. pu’s. Sim -itarly. tbe estimti.d proces8 ●.=r8ge PLi. fbe srifhmetic mean of the individual esti-mated lot perceot defective. pL’..
C13..?.2 Dc.uble Spccificatioa Umit. Thee.timateii lot pe,=.nl de fcct, ve shall be de-termi~ed {mm Table C-5 fc.r the Plan. baaedcm the rmt~. method. The quality iridice.OU and OL shall be computed. Table C-5is cmter.d #.parately with Cfu ad QL ●ndthe .ampfe .izc, and the c.rrespohdi:g Pu-d PL ● re read from the table. The ●sti-m.ted lot percem defective i. P . PU + P .
t+Tb. e.lirnated proce.. ●verage p i. c ●
● rithmetic mea. of the i.divid.af ..tinuted10I percemt defective. p,..
C13. Z.3 Special C.. e. If the quality iade.Ou or 01. i. . aegativ. amber, lhen TableC-5 i. entered bydi. regarding the negative.iar.. Howcwer , ii. thi. c-.. the ..timat=dlot perce.m defective above the uppar limitor below the lower limit i. obthic.ed by .ub -Cr.cting fh~ percentage lc.und in the tablefrom 100%.
C14. NORMAL TIGHTENED, AND RE-“DUCED IkSPECTION
Tbia Standard esmblisbed ●u’nplfngP(U far normal, tightened. and reducedIEmpectk.n.
C14. 1 At Start of fa. pectiom. Normal in-spection .hd3 be used ● t the start of ias Pee-U& uateoc otb.rwise dacignated.
C14. Z ZturirIg 3aspection. Qurimgfhe courmof iwrnctiim, normal &xctio. sbdl beUDd vba. imspoctian Coaiitimms are ●uch(&85 tibteaed or reduced iMmcc?ion io notr.4dTd Lm ● ccordume -itb” paragrmpfuC14.3 d C14.4.
Cl 4.3 Tisbtened fxukmcfion. Tishw..d ia-9D0ct10m 91M31be ttmtituted wbem tbe estj J&t&f procemi ●verage computed from td
1.
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prec.di.# t.. ( 10) lots (or ●uch other aem-ber of lot. de.i~nat.dl in ●ccmrdaoee .ithpara~raph Cl 3-Z is greater than th= AQL,sod when mere than ● cc.rlaln ~r T oftheme hats have emtimatea O! the percemdelecctve .xecedisg the AQL. Tba T-values●r.give. ln Table c-6 for tbeprocem ●wer,rage compted from 5, 10 or 15 101*.8 r40r-mal in. p.ctioa hall be reiiut.ted i[ thee.tinuted proces. ●verane of Iota herCightea.d im.pecxic.n is ●qtd to or le.. tknthe AQ t..
Cl 4.4 Reduced ln9PccUon. Iled=ced in-●pecti.a rrmy b. uutitutad providd that allof the following conditions ● rc catiafied:
Conditioa A. The preceding ten {10)lot8 (or .uch other number of Iota deaigrmted)have bee. under norm81 inspection and non.ha. be.m rejected.
thmdicioa B. The ecttnu:ed pereemtdefective for each d theme preceding Ietm i-le.. than tbe applicable lower limit #bow.in Table C-7; or for certain ●ampiius plar.a.
the ●stimat.d lot percent defective i- ~to sero for b ●vclfied ~r of towau-tiv. 10CC(see Table C-?).
COmdItkl c. Production i- ●t ●
●teady rata.
Normal Iaspectlen ●hall be reinstated M ‘myone of the following cooditiea. eccvra ti.rreduced ia.~ctiOU.
Cmditbm D. A M k rejected.
condition E. Tbe ●ettmatad procema●va age 1. greater tbao tite ML
tkmditi.. F. Prehcttom become,irregular or delayed.
Camdittc.aG. Dtber condition. wmay warrant Umt normal impaetio. . bauldb. r.ltwtated.
Cl 4.5 S- Pling PIUIO for Tfuhta.d or Re -dimed LompeCroon. Sam #w P~ ior tight-ened -d reduced in@p@ctioa ● re provided inSectio. C, Partm 1 aad U.
... ,... .. .. .. .. .. .
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TABLE C-6
VA.e. of T for Ti~ht.ned k.spcction
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The S-D fiiwm in each block refers to the precedim 5 lot., the middle li~rc to the.-preceding 10 lots and lhc bottom figure to the pre&ding I S-lot..
Tightened inspection i. required when the number of lots with ● .timatem of percentdefective above th= AOL from the precedin~ 5, 10. or 15 lots i. ~rester fhan the given vtiueof T in the table, and the pr-.e=m averaae from these lat. exceeds the AQL.
Aff estimates of the lot percem defective are obtained from Table C-5.
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he
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ant
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able
C.
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f.For
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T-b
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f
mL-SlW414.11 June 19s7
APPENDIX C
mMlmitfO.s
Definition.
sample ●ike far ● single lot.
Read
X bar
SY@.?!m
x %rnple mean. Arithmetic meam of ●mple mea.. r.m.rmfrom . .ingle lat.
R Range. The difference betweer. the Iarge. t and ●rnalle.tmea.ur. mests in . .. bgroup. & this Smitdard, the #ubg.o.psite <s 5 except for them= plan. in which m . 3. 4: er 7. inwhich ea.. the ●ubgroup i. the same a. ths .ampl. size.
Range e: the fir. t subgroup.
Range d the ●econd subgroup.
R bar Aver.~e ruag.. The arifhn-.etic mean of the rug. values ofthe subgroups ef tbc sample measurcm.nta [ram ● single lat.
u
L
k
Upper spec Uication limit.
faumx apecificstien limit.
The acc.pcability conctanr given in Tables C- 1 nc.d C-ZIA factor u.ed in determinizi~the quality index when using therange method. The c values ● re given is Table.. C-3 and C-4.
Ouafiry fmdex for “.= wijh Table C-5.
c
Qu
QL
Pu
O ●ub U
Q ●.b L
p .ub U
Ouafiry fndex for use with Table C-5.
I
I
I
Sample estimate of the let percent defective above U fromTable C-5.
p ●ub f. Sample ●.tixnale cd the lot percent defective below L fromTable C-5.‘L
P
M
Totti SUTIple estimate of the 101percenl defective p = Pu + PL.
M&imum ● llowable percent defective for sample ●mtimam.given in Tablmm C-3 and C-4.
M,ub. U Mtitun allowable percent d. fecfive above U gi.em in TablesC-> scuf C-4. (For use wbem differenf AOL valuca for U andL ● re specified.)
~uxn mflowmble pert..t de f.cti.. blew f. Siv.m in Tabfe.C-3 and C-4. fF~r u.e -ha. different AQL value. for U adf. ● re cp=dfied.)
%
ML
P p bar
p bar #ub V
p bar suh L
S-pi. ..tinut. @f the p.ece.. p.rc.m defective. i.e.. Cbeestinmt=d prc.ee.. average.
$U
FL
T
The estimumd proce.. ..era~e for UI upper ●pecUication lf-mit.
The ●stimated pro . . . . ●verage for a lower .pecific.tion limit.
The m- um number of emtin’tated proces. a.er4ea w~cbmay exceed the AOL given in Table C-6. (For use in deffr-_ WW+fiCafiL= U fi~ht=aod Ampeefloa)
8s
.—.
MIL-STD-41411 Jffffa 10s?
SECTfON D
vARIABIIJ’I-s KNOWN
I
Part 1
SINGLE SPEC1fICATION LIMIT
01. SAMPLfNG PLAN FOR SINGLEsPEC1 nCATfON LfhffT
This part of the Stand~rd de.tribes tbeprOc=<u, =* fer u*= with plan- fOr ● ●in81=.peciftcac ion limit whe. variability of thelot with rcapecl to the quality chbracteri. tici. known. Tbc acceptability criterion i.givcm in two equivalent form.. The.. areidentified am Form 1 ●nd Form 2.
D1. 1 U.c of Samplinu Plan.. To determinewhether the lot meets the ●cceptabilitycriterion with respect to ● particular qtmtitychsracteristi. and ACIL value, the applicable.ampling plan shall be umed in accordancewith the prcwi. iom of Sectic. n A. GeneralDescription of S.mpling Plan.. ●nd lhose inthi. psrt of the Standard.
D1.2 Drawing of Sag. “All -ample. ●hailbe dramt i. ●ccarrJa.ce with para#rmph A7.2.
D1.3 Determination of Sample Size Cod.Letter. T he m-pie 91ZC code,letter .hdf~.cted from Table A-2 tn 8ce.rdmcewith paragraph A7.1.
D2. SELECTING THE SAMPLING PLANwHEN FORM 1 IS USED
DZ.1 Master Sampliq Table-. The rzm. t.r●amplms fabJe. Ior planm ba. =d on v8ria -bttlcy ~ k? ● ●imsle qeetfkattc$m ltmlt● re Tables D-1 and D-z. Tablo D-1 i- omd(m -rmsl Ind tightened tnapectiom andT&l. D-z for rod.ced icupectioa.
DZ. Z Obtdmimr 8ampffnR PtM. Tbo Qu81-pli8* ph. C.nmmtm 01 ● ,unpl* ●i.a,wd Ms~moclated ●cceptability conmtant. Tbesamplimg plan ia ebtahed from k.te rTable D-I ●nd D-Z.
DLL, ~pfe Sise. The ..niph she m i.●howa in t e mamter table correspoadhs foeach ●ampl. ●he code leffer & AOL.
Dz.2.2 Acceptability Com.tant. Th= ●=c=Pt-●bility comstaut k. corrcapOd@f to the SUTI-ple is. mentioned in paracraph DV..2. I, imi-dicated in the column of the maater tabl*corre. p.amdingto the ●pplicable AOf.. vafue.Table D-1 i- .ntered from the t.pf. r normali.. peetion ●nd from tbe bottom for tightenedim.pection. Sampling plan. for reduced ic.-apectioo ●re provided in Table D-Z.
D3. WT-BY-~T ACCEPTAEfl-~ PRO-CEDURES WNEN FORM 1 IS fJSEf#
D3. 1 Acceptability Criterion. The dear-of conformance of a quality characseri. ticwith re. pect to a •in~le specification limithall be judged by lb. quantity {u-X)/_ or(x- L.)/..
D3.2 timputation. The folio witas qu~tifY●ball be compute& (u-X)1. or (X- I.)l. . de-pendins on whether the .p..fficatiom limiti. u upper Or ● 10wer limit, where
U i- the upper specification Mntlt,.L is the low-r ●pecKicatioa llmit.X i. the sample mean. ●nde is the bnown variability.
btlltv Criterion. timpar. theqmantity - L)I. with tba ●ccept-●bifity coaatant L M (U-X)1. or (X- L)le i..quf ’te ox sroater tb- b. tfmbg=-e~ ~●cc*pfabfflfy crtsertcud If (U-w. or ~- L)/.Is 18** tbn k or Decative. tin tbe lot dOa*mt mat tbo 8cc*pfAbtltty c rlterioa.
D4. SUMMARY PUR OPERATION’ OF8mAuNGm..Az4wmz N?onu 12s
[1) Determine [be sample sise coda let-ter from Table A-Z by u-lr.I Ibc lot ●iM adtba tipecftoa lee:.
lS.a Appcadis D for d= finicia=u al all ●pnbals used in tba sunptiQz PIUU bned oavar~U~
Z~-~PIe D. I fo, ● COmpfete .sunpf’e Of tti prO=eda.e.
67
mL-snb41411 June 1957
(21 Obtain PI*. from Master Table 33-Ior D-Z by sel=ctitag the ●ample .i%e rI ●ndthe .Cceptabitity Coti.ta-t k.
(3) Seleti at random ~ha .unple ef ❑
units from the lot: inspect ●nd record thetn. amur. merit of the quality characteristicIor each unit of the ●ample.
[4) Cornput. the .unpl. me.. X, ●nd●lso compute the quantity (u-X)/e for anu per specification limit U or the quamtity
{f- L)/. for ● lower .peciiicatiaa limit L
(5) lf the quatitity (U-X)/. O. (x- L)/ai. equal to or greater lhas k, the lC.I meet.the acceptability criterion; U (u-X)1. or(X- L)/W is Icaa :han k c.r eesative, them the101do=. not meal the acc.ptabillty criserbn.
D5. SELECTING THE SAMPL3NG PLANWHEN FORM 2 3S USED
D5. I Master Samplirm T. bles. The ma.t.rm.rnpling tables for plans ba. ed on vari. -bilily knc.un (~r ● .ingle specification Iirnil●rc Table. D-3 ●nd D-4 of Part IL TableD-3 is used {or normal .ad tightened in-spection and Table D-4 for reduced inspec-tion.
D5. Z Obtainin~ the Samplinff Plan. Thesampl.ug plan .onsi. ts c.{ ● ample .iz. ●ndan ●ssociated maximum ●llowable perccnldefective. The .amplimg plan is obtainedfrom Master Table O-3 or D-4.
D5. Z.1 Sample Sise. The .ampl. .i=e ~ i..hown in the rnasler table .x. rreaportdine toeach s~mple .i=e code letter,
D5.2. Z Maximum Allnr.. able P.rcecIt De-fe<tive. The rnaxirnum ●llowable ~ereenti~ve M for 9UTIP1. ●.timalc. corr.. -poadkmg b tbe sample ●i.e meatlomed i.r-wr~pb D5.z. 1 I* irtdicated in the Colwn.of the mseter table corrempoadiag to the~PP1ic~hle AOL value. Tabl. D. 1 is acte, edfrom tbe t.pfar .armaf inopecfioh and frc.mtbc bottom let tight.md tip.cuon. Sun-plirig plans for reduced Iamfmctima.are pro-vided io Table D-4.
DE. ~T-BY-WT ACCEPTABILITY PRO-CEDURES WNEN FORM Z IS USED 3
Db. 1 Acceptability Criterion. The de~reeof con>ormae.ce c.f ● quality eha~aeterimticwith respect m ● .iagi. .pecifi. atio~ limit.hdl be judpd by the prc=a of ~~con-formimg producl nutside tbe upper Or lm.er
●Pecificalion limit. The p.rc.mtag. ef nom-c.nferming product i’ ● .;imamd b~ ●nfcr-Tablt D-5 with the quality index.
D6. Z Computation of Oualilv lade-. Thequality ic.de= QtI . [U-X) VI. .h.lf be corn.puted if the 8pe; ification limit im u. upperlimit U, or C3L = fX-L) v/. if il is s lowerlimit L. The quzc.litie.. ~ and . . ●re the..mplc mean and known variability. respec-tively. The laclor v i. provided in TablesD-3 and D-4 corre. pc.ading to the .unpfesize.
D6.3 Estimnte of Pert.nt Defective in Lot.The quality of ● lot ●hall be exprem. ed byPu. the estimated percent delective in thelot ●bove the upper .pecificstmn limit, orby P
l-”the ●stimated percetit defective below
ih. owcr specific alior. limit. The citimatedpercent de~ective PU or pL i. obtaiztedbycmte. img Table D-5 with OU or Cfti
D6.4 Acceptability Criterion. Compare the”estimated 101 p=rcent defective p~ or pLwith th. maximum ●llowable percent de fcc -ti. e M. lf pu or pL i’ equal to or le.. thanM, the lot meet. the acceptability criteriotxif PU or PL is ~reater than M or U QU or
‘L ~S negative. ~h=n th= 10t do= C@ IIWCtcn. acceptability crxterior..
.137. SUMMARY FOR OPERATION OFSAMPLZNG PLAN WNEN FOffhf 2 ISUSED
The following steps summarice the Pro-cedures tO be followed:
(1) Dele. rninethe .m’nple size code 141-cer from TabIe A-Z by ..ing the lot .ise andthe in. pecliem level.
(2) Obtaia plmr. from Mater Table D-3or D-4 by ●electing lhe ●unple ●i=e U. fbefbctor ., ●nd the mulmum df.wable per-cent defeefiwe M.
(3) S4ect st ramdom tbe .unple of numits from the 10G irs. pect and record thenma.ur.nmnt 01 the qualhty charutari9ticon each umit of tbe ●empl..
(4) Compute tbe sample me- X.
[5) Compute the quality index f2u .( U- X}v/- U ● . upper t cificatimn limit U
= (FL)v/. If ● ,-*;F%%%$; %ai% i, .peeified.,
16) Determine the ●mtimsted lot prcasddefective PU or pL fram Table D-5.
‘S=. EXamPI. D-2 far . complete exunple of thl. precedure.
88
I -——
MUA7D-41411 Juoa 1SS7
I
I
I
I ..
I
I
I
I
I
(7) U the emthrmtcd lot percent de f.c -UW* pU or pL im eqtml W or Ie*a ttmo tbe u ‘u ‘r “ “ ““”=’ ‘- M “ ‘f ‘4ZQL h nesattve, thea the let deem admaximum atlowable percent defective M, the =ccopMbUitY criterion.the lot meata thm ●ccaptabiii.~ cricerla~
EXAMPLE D-1
&Ample of Ca3ctiiiam
SiaCle Spec51ictii0a L%iit- Form 1
VariabiIlfy t(cw-n
Example The ●pecif ied minimum yield point for certain ●t4el c~-ttags is 50,000 psi. A lotof 500 item. im wubmicted for inspection. lo bpection Level IV. normal Ia.poction.with AOL . 1.5S i. to be u..d. The variability . i. knowm te be 3000 p-i. FromTable. A-Z and D-1 it i- seen that ● mample of ●kc iO io re.autred. SUPW9C fhe
Lint—
1
2
3
4
5
b
7
8
yield point. of the ●unple specimen, ● re:
6Z,500; 60,500; 68,00(h 59.000; 65.500;6z.000; 61,000; 69.000; S6.000; 64.500;
and rompliame with the acce?tabilitv criterion i- to be determined.
Information Ne.ded Value Obtained Expluulion
Sample Sise: n io
Known V.riabitity: . 3.000
Sum af Mes..rcmcnt.: IX 630,000
Sample Mm. X: ZXln 63.000 6J,000110
Speeificatioo Llmlc (Luwer): L 58,000
The Quantity: (X- L)le 1.67 (63,000-5.5.000)/3000
Acceptability CoLI. taat: k 1.70 See T-ble D- I
Acceptability Criter- Compare (X- L)/. 1.67 c 1.70 see Para. D>.3with k
The lot does mot meet the =eceptabi3ity critmriom, dnce (X-L)!. is le.. th= ~
NOTE: If ● ●ksie upper specUiCatiOn ltrrdt u i. SWen. tbeh compute tbe quaatlfy (U-X)1. tm— lb- b d compu~ it with k the 10C meet. the .cceptabiiify crit=rio. if ( u-X)k i.
equal to or greater tbui k.
89
54flL-sl’13-41411 Jumd 1957
E~LE D-2
fkampfe of Cafcuhtfonm
Single Specification L4mit - Form 2
VariabUity Known
Example The specified mimimum yield poiuf f-r certain .teel casting. in S8.000 psi. A lot. . .
Line—
I
2
3
4
5
b
7
8
9
10
or 500 item. is submitted ror inspection. inspection Level Iv, normal lnspectlon,with AQL = 1.5% is to be u.ed. The variability e is known to be 3000 psi. FromTable, A-2 and D-1 it is . ..cI that ● sample of ●ize 10 i. required. .SuPpa. e theyield points of the sample mpecimen. are:
62.500; 60.500: 68,000; 59.000; 65,500:62,000; 61,000; 69,000; 58.000; 64,500;
and compliance with the ●cceptability criterion is m be determined.
biforr?mtirm Needed Value Obtaimed Explanation
sample size: n 10
Know. Variability: c 3.000
sun-l of Mr.a.urerncIll’: xx 6>0.000
sample Me- X: TXln 63.000 630,000/10
Factor, v 1.054
sp=cific aliOn ~mi, ltiwe r): f- S8.000
Ouality fnder: OL : (X- L)v/o !.76 (63.000-58.000)1 .0543,000
‘m’” ‘f “ ‘Crcent ‘“1 ‘L 3.927. Se. Table D-5
Max. A1l.awabl, Percem Def.: M 3.63% See Table D-3
Acceptability Critcrian: Compare pL 3.92% a 3.63% S=. Par.. D6.4with M
The lot d~es not rn. e$ the ●ccepf.abifity criterion, since PL is great=r than M.
~E ff . sin 1. upper .pecific.tion Iii-nit ff i. given. the. compute the qu~lity index Qu =F-(U. XIV . m lme 7 and ebtain the sstimale -f $he perceml defective PU. compare PUwith W. the 1.s rn. et. the ●cceptability criterion if pu i. ●qual 10.0. 1.*S than M-
90
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kUL-sm-414llJums 106?
Psrt n
DOUBLE SP3ZC3SXATZON Lfb4ZT
DE. sAM’PU?JG PLAN FOR DO CfBCEsPECIF3CAT10N _
This part Of the Standard describma theprocedures f.r use with pftis for ● doubleSpecific-tiom limit when variabttlty of thelot =ith reopact to the qtmfky c~rscteristici. known.
DE. 1 U.* Of SUnplimc Plan,. TO determinew%the r the lot meets the ●cceptability cri -le.-ion with ?=*PCCX co ● XrtiCtIISr qu~i~characleri~ tic and AOL v’azuels). the appli-cable ●ampliag plan shall bc u.ed in accord-ance with the prwimic.nm cd .$ection A, Gea -eral DeacriptiOm of SkrqdiW Plmns, mdthose in this part of the Standard.
D9. SELECTWG THE fMkfPLfNG PLAN
A sampling plan for esch AQI. .ake.h.11 be selected from Tab)e D-3 or D-4 ●
[0110-s:
D9. i Determination Of S=mple Sise CodeLetter. T he ●ample ●ma cade letter .bfib~.cte.d [ram Treble A-Z in mecordamcewith paragraph A7. 1.
D9. Z Master SamPlinE Table.. The maaterSUnpl-es ier w bs. ed on wuiabi3-ity known for ● double cpecific-tti Itit ●r=T=ble- D-3 and D-4. Table D-3 11 u~ed for.O rmal amd tightened izupection ud Tmblc
. D-4 for reduced inspect.ion.
D9. > Obtaining .sunpli.g P1_ A ●unpliagplaa Celia, mt, 01 ● ●mple ●2*, d M ● s80-.dated maximum aflowsble ~rc=m defec-tively). The ●uf@ins PI- ti be ●pp3Aed Joinspection shall be ebtahed from 3dmcterTable D-3 or D-4.
D9.3. 1 Sun 1. Si.e. The ●unple ●i.e m i-~#how. = t e master ZAb3e. eorrecpondlag to
each ●unple ●txe code letter -d AOL.
~Iv* for .unpte .8Unut.* .of percentdafeectwe for th4 Imr. nppe?. 0rb04b cp*c-tfication limits co~ta.d. eerr*mpOndbs fatb. sample ●ize memfiomed in parasrmpbD9.3. 1. i. #ho_ in the cdunm of the W18mtertable eorreaponding co tba applicable AQ3.wdte(s]. K dKferemtAQLos m aa~isad w●xb speckficatlon Umlt. demtsuua th8 --tmmm tile-able percent defective by ULIOZ
the lover Itrnlt. M4 by MU for tb= UPWrlimit. u one AOZ. i- ●ssigned to bath l~ltccombined. demipte tbe maximum A31.wablep-rcerd defective by M. Table D. 3 is enteredfrom the zop for uornuz tipeczton and fromtbe bosom for ttghtened imopectdon. Sam-pli.s plans for redoced imcpeczion sre prO-vided in Table D-4.
D1O. DRAWING OF SWLES
Samples #ball be selected In accord-●nce with parasraph A7. Z.
D1l. #.&-T-Y~O T ACC~PTABIIXl%’
D! 1.1 Accepi.bility criterion. Tbe degreeet conformance al ● qutiltY c r.cleri~ ticwith respect to a do~le sF&c Ification limit.ihll be judged .by tbe perce~ al ~con-farmiog product. The ~TCeIIUSS Of Wa-.IJaforzniq product La estimated by enterkgTable D-5 wAzh Z& quality M-x.
D 11.2 Computation of Quality lndice ■. Thequa3ity iadices Q . (U-xwi e and OL=
(X- L)v/c. ●ball be ~omputed, where
U is the upper specification limit,L i- the 10wer ●peeificmion limit,“ is a facsor providsd in Table* D- 3~d D-4.X is tk .unple mean. and. ia zbe ksowm wariabifizy.
es
nlL-s’nk41411 JuIIe 1957
..
Pi +b *= s-Am .Uew*Ie ‘P~z~tidelceuve M. 25p u equaf to or lea- 3baa Uthe Id meeb the ●ccep3abUIty crUeri~ ffp ic ‘re=ter tbm M or if Of) or Of. or both.,* Itapfive. Umn the lot &es ml meet theacceptabffity criteriam
D12.1. Z Suna~ryef OP erati.n of SunpliaPlan. la caoe. where a .ingle AOLvtiue ~~bliohed for tbe upper and lower ●pacifi-cation limit cornbim.d (or a ●fwle qualitycharacterimtlc. the tolZowinS steps 8umma.ri. e th.. procedtwe. to be u.ed:
(1) Determine the sunple ●ise codeletter from Table A-2 by u.ing the lot .izeand the in. pectioa level.
(Z) Select plan fr.am Mater TableD-3 or D-4. Obtti tbe .unpla si.e n. thefactor ., and the rruximurn allowable per-ced defective M.
(3) .%], ct ●l ra=dem the .am~le ofn unit. from the lot; in. pect and record them... ttmeatat of tbe quality characcerimticon ●.cb unit of the sample.
(4) COmpute the .unple mean X.
(s) compute the quality indicem Qu= (U-x)vl. ad QL . (X. L)v/..
(6) Determine the ●.tinmxed lotpercent defective p . pu + pL from TabIeD-5.
(7) M tbe e. f.inuted lot percent de-fective p i. ●qual to er le.. than the maxi.mum allowable p.rceas defective M. tbe lotme. t. tbe acceptability criterion: if p issreater than M or if Qu or OL o, both ●xe=S~~V~. tfI*n *- let doa - not meet ~emccapc-bility criterion.
DIz. z Dlff8remt AOL Values for Upper and&w.r .Sp.eUi.aUOO LiInlL
D1 2-2; 1 Aceap4abflUy Crit9ria. 5 COirtfu*ethe ●stdnuted 1ot pmrc~t defeetivem m.. hPU dth the cerro@omd4ng ~ -a..-=bI= Perta=t de f==ttvew M d Mfj alao=Omi=r. P . Pfi + PU wittt k larger d MLmmdMu. lf pL sequmt taarle*attmm ML. Pic 9qtmf to or Ie*m tbul Mu. ad p i. q Ato or lam than the larger of ML aad Mu,the lot meat. tbe ●ecepbility criterk
athrwi. t, tbe 10I doe. rat meet tb. ●ce.pl -ability .rit. ria. Zf either OL O* O“ or bothar. ae*.U.e, UMrI the 10; &e. 03%rpe.t the●ccep3abUtty criteria.
: D12.Z. Z summaryc.f operation ef s-Plan. Za em=. wtmre ● diflereot AOL~ctabliched f., the “p-r -d lower t~c.Aficatiom limit for a •in~le qtmii17 character -imtic, tbe ;dfow- .tcp. . urnnmrime tbeprmcedurem fn be u.ed:
(1) Determlae the ●unple ●k. codeletter from Table A-Z by uefa, the 105.&ed in.peetio. level.
{Z] Select tbe san-tpliag plan frontMate. Table D-3 or D-4. Obtaio tb. amp-le .ise tI .ad the I.cter ., eorre.podirqto the lar~erof lb. two AQLva3ue.. dal. othe maximum .U.Ywable percerit delecgive.
●nd M‘Y #
corresponding to the AOLva ue. for 1 e apper and lower specificatiealimit., respectively.
13) Select at random the ●mple ofn unit. from tbe 10C irIap. ct ●md record themcaauremcm of the quality characteristicon each unit in the .arrtple.
(4) compute tie .8mpIe mean x.
(5) Compute the q~ty indiee. QU= (U- fov/. and CZL = (X- L)v/&,.
(6) Determine the ●.tImued @tp.rceat de fectl.es p“ mud pL, correspond -ins to tha pa rc.af d. f.ctivec tie tb. upperand b.lmw the lower .pecific.tkm limit..Afmo d.te rmine th. combined percent de f.c -tive p = p“ + p~ .
(7) u all three of tbe fallowing cc,n-diuolta :
l.) ~u i’ equaf to or 1... tbma
%.
(b) pL i. mquaf 1. or lR.8 ffun
Mu
(CJ p b equaf ts Or Ie*#fzlamthelarger of ML and Mu,
u. satiaficd, th. lot umato the ~C~tdiii~criterk other+se. the lot does MC meet the
“’=~ “’’”’A’* ‘*’ %::%or both am aesativ~ tbeo * lotm..t tbe acc.ptiifiiy criterb
—--- . .
.
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E.mtple
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1
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3
4
5
6
7
8
9
10
11
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13
14
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EXAMP= D-S
fsxanlpze of Cdcufat,ioms
DOEbh sp4c3d&az10a ZAm2t
varhbmfy XmOwm
Dm. AC3L Vahie for Seth Upper @ &w.r SpeeUiea320a 2AMA1 Combined
The ●peclfie.d maximum ad mitdmnun yield 3,0311u[m cemd. steel rutimzN are67.000 p. i and 58,000 psi, rucpceUvel y. A lot of 500 items is ●tbmitted for impec -tloa. 3nop.ct30n &val ZV. aornd insPct3aa, W3UI AQL = 1.5% 1- to be ..4. T&variability c is &o-n to be 3,000 psi. Frati ?abka A-2 ●nd D-> it i. seem fzut a.unpl. of ●i.e 10 i. required. SuPpu. e the yi.ld point. of the ●ample specimens● re:
6z, SOO; 60,500; 68.000; s9,000; 65.500;6z.000; 61,000; 69.000: 58.000; 64.500;
●nd compliance with the ●cceptability criteriom is to b, determined.
lnIornutio. Needed
Sample Size: n
Know. Variability: o
Sum of Meaaurem6ats: ZX
Sample Mean X: sXln
Factor, v
Upper Specification Untie: U
Zmwer Specific=cion Limiti L
QuaIity Index: Qu = fU-X)V/.
Quality Lufex: Z3L . (~- Z.).1.
Est. of Lot Percen: Def. Above U: pu
12tc. of &t PerccnI D*I. Below IA P&
TelaJ ~*t. P=r=e=t D-f- ~ ~~ P -Pu + P~
Max. A310w~ble Percent D.[.: M
AcceotablI1tv C.ite rioa: cmn~r= n .. .pu + “pL with M
V. I.e Obtaim.d
10
3,000
630,000
63, o0O
1.054
67,000
56,OOO
1.41
l.?b
7.93%
1.92%
11.85%
3.63S
11.85% > 3.63%
Explanation,
630,000/10
See Table D-3
(67,000-61,000)1.054/3,000
(63,000-58.000)1.054/3.000
See Table D-5
See Table D-5
7.93% + 3.92%
Seo T*1c D-3
See Para. D13.4
The 3ot doe ● not met the ●ccepzcbiflty criterion. da.. p = pu + PL io sreater than ~
97
------ . . . -—
um=slv-41411 Jnne 19S7
Lime—
I
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3
4
5,
6
7
8
9
10
11
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11
14
15
EXAMPLK D-4
Exampte of Cafcutatimu
ml= sp0dfka3A9n ZAmtt
V.rkatduty KaOwt!
Difiere.t AQL. Vti.ss for Upp.r & lmwer SpeeUicDtinm ZAmlt.
The .pecified maximum and minintum yield p0&39 for cer3mim oteel ca.tl~o ●re67.000 psi -d 58,000 psi. reapectivdy. A lot d S00 item, is submitted for inspee-UO.. znspctko. *CI IV, uarnuf knspctinn with ML = 1%.for the uPP8r aadAOZ. . 2.5% for the lower tipecificuiom lkmit im m. be u..d. The vari.bilicy . iskcuaw. m be 3.000 pi. Frern Table. A-Z ●d D.> it i. .... that ● .unple cd ais.11 c~rre. poridir..g to the s.rnple .ise code letter, 1, ●nd the AQL value Of 2.S% i.required. S.ppc.. e the yield Pc.itis d the ●mple specimen- ●re:
6Z.500; 60.500: 64.000; 59,000; 65.500:6Z.000; 61.000; 60.631; 68.000; 62.000; 63,000
and cmnplisnce with the ●cceptability criteria 1. to be determined.
Information Needed
Sample Size-: n
Kn~wn Variability: o
Sum .f Me... rernen:.:
.%rnple Mean X: XXIC.
Factc. r: v
Ix
UPPe r Specific atiort Lirnic u
faw. r Speci[ieatiea Limit: L
Quslity Index au = (u-X)v/.
Ou-lity htdex: QL = (X- L)*/a
=.~ ‘f ‘t ‘“’cent Def” -’e u: Pu
E.1. of bt Percent Def. Selow b pL
T.atal Cat. Percent Del. h bt: p = pu +Pz.
Value Obtained Expl-ation
11
3,000
67.9,131
61,64.9
1.049
67,000
58,000
1.07
1.28
3.07%
10.01%
13.10%
Mu. Allowabi. Pe r..mt Del. Abo.e U: % 2.59%
- A31.wable Pe rcest De[. B=lmu k ‘L s.60%
Acceptabilit~ Criteriw (al Compare PLI 3.07s ~ 2.59swith Mu -
(b] Compare PI. 10.05% > 5.60%with ML
(c) Cemoare 0 13.10% >5.609with “ML
678.131/11
See Table D-3
(67,000-61,648)1.049/3,000
(61.648 -SB.000)l.0491J. oOO
See Table D-5
See T-ble D-5
3.07% + 10.03%
Se. Tabl. D-3
See Table D-3
see Par*.DIZ..Z. Z(7)(a)see Para.1312.Z, Z(7)lb)s.. P.**.D12. Z. Z17)(C)
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Part Ill
ESTIMATION OF PROCESS AVDLAOE A34D CRfTER3A ~31REDuCED AND TIGNTENW 1NSPECTION
D 13. ~:S#fATfON OF PROCESS AVER-
Th. ●ve rage percent defecti*e. baoedUPOn A 8r0.P 0[ 10U ●tbmitmd for or~imalin. pecticm, i. called Sbc proceaa average.OrlgirIal inspection is the fir-t Inope.tion Of● prticular quantity 01 product .ubmitted[or .eceptahslity ● . di.tfngui.hed from thein. pectian of product which ba. b=cm re. ub-rnirted after prior rajectimm. Th. procea.●.eragc shall be ..tinuted frc. rn tbe re. ult.of i.. pe. tion of wampl. mdrawn from . ●pee-ifi.d murnber of preceding lot. for the pur-pose of decermis.img severity cd inspectionduring lhe tour. e of ● contract in accordancewith paragraph D14. J. Any Iot. .htil be in-cluded OUZYonce io e.timatitig tbe proce. aaverage. The estimate of theprec... ●ver -●t?. is designated by $u what computed withr.. pect to ●n upper ●pecific.tion limit, byPL wb=n cOmp~t=d rnth r=~p=ct tO ● 10w=rspecification Iirnit, and by p when cmnput=dwith re. pect W. a dc.uble .pecificaciOm Iimit.
D13.1 Abtmrrr,a) Remult,. Th. re. ult. 0[irmpectior. of product manufactured umdcrconditions not typical cd tmual production.shall be excluded from the estitrmted pre -cemm’ average.
D1 3.2 Ccmputatiem d the Esf.inuted prc-ce. a Avers e. Th ● e.tmuted proce.. aver-●ge M the ●r~thrnetic mean of tbe estimated10t pe rcem def ●ctive computed from the.unpling itt*pecti.ma re.. tit. of the precedingtea (10) low or S* may be .alhenvi. e d.miS -❑ated. In order to estimate the lot perceratdsf.cti.e, the quality kdicem Ou &\.ar QL●lmfl be computed for each lot. Theme ●re:(3u . (U-X)WI. and QL = (X- LWIO. (S8.paragraph D] I. Z.)
!. with Q or QL 4 the corr. spondin~ .mti-Ymuted et perce,att defective Pu 0. P L. ?*-
spectively, is read from #he ~bIe. Thee.tinuted proces. ●verage pu i. the arith-metic m-u. of the Itidi.idual e.timated lotpercent defective. Pu’ ●. Sinaihrly. the e.ti -nuted procems average p is the arithmeticme- of tbeiadividdemt~atcd lot percemtdefect%ve. PL’..
D13. Z.Z Double Specification lAmit. Tbee.cim.ced lot percent dciectzve ●hall be .de-termim.d from Table D-5 for the pluI. bm. edon variability b.swa. The quality Indic.s0 and QL shall b. computed. Table D-5 i-
Yen ered separately with QU and OL ad- thecarre.pomding pu snd pLare read frOm thefable. The e.timtied ict percemt defectiveis p = pU + pL. The e.tirnat.d pro . . . . a.er -●ge p i. th= ●rithmetic rn.a.mof the individual=atimsced lot percent defective. p’..
D13. Z.3 Special Case. U the quazity index0,, or Q, ,s a nt~atm.e number. them TableDY5 i..~~ter=d by-di. regarding the negativesi~n. However. io thi. case the e.timated iotP. TC.nt defective ●bove the upper limit orbelow the Jow.r limit i* obtained by ●ubtract -~~~~ Per==at=ge found in the table from
‘“ %%%dWPECITC)NAL TXGZiTENED, AND RE-
This S$azidard e.tabli. ha. wamplingpl*rsh for normal, tightened, and reducedi-peetioa.D14. 1 At Start of Inspection. Normal in-.pectiom SW b. wed ●t the ●tart of inapec.UOa IU13C.*Secberwim de#$gm4ted.
D14.Z OuriaS fn.xctiou During the co.r ●eof In9puctia, -rmal uumction shall beused when taapeecio. cmaditioo. ●re muchtbt t6sht.nod O. redncad iaapection is notrqufred fn accordance with prmS.aphsD14.3 and D14.4.
D13.?.. I SiI@. Sp.cifieatlon Z.lml% 6 Theestimated 1ot percent dof ecu-e ●bal-1 b de-Cennined frarn Table D. 5 ter the plum hawedO. bnowa varbbi3ity. Tbe q-am3ityiadex Q“hall be us.d far tbe ea.. of aocJppr .pec -iiic.tiom limit c,r QLlor the c.. e of a 10X.●pecifi..ticm limit. Table D-5 ii entered
6Wbem Form ~_~l. s~di=utia d.tmit ti a-cd (0? Czu ue*ptabi3~ty crltariO=, ~h= a~ti-
rnste Of lot percent defective pzz or pL i. ❑m ebtaiaed, 10 order to emtinmte the procems●veraga, it ia aecea.~y to eornpiete paragraphs D6. Z d D6. S af hrm 2.‘ra, .m~e. ifQ . -.50and O = 1.60,thenpu = 100IL -
~ P “ 69.146% + &S . 74.6z6&.30.854% = 69. J46%. pL = %4g%
D1 4.3 Tight=imd 31Wpecttoa. Tiuhtermd tn-Spectltl. .W1 be in. ututed wb. n the emti -naat.d proce. m ●verage computed from’<he
..-— ----
!’
I
prece4iag [e. (1OJ Iot# (.r much other smm-ber of lma demig=atedl in ●ccordmce withparagraph D1 3.2 i. greaur thaa the AQL.and when more thao ● certAn number T Ofthese 10ta ‘have ●stimmen of the percentdeiective exceeding ctaeADL. Tb* T-value.are SiWeaI in Table D-b when tbe pr.acuaaverage is computed from 5, 10. or 15 lots. 8Normal inspection still be reimtmted if the.stinnted pro . . . . ..erage of Iota undertightemed iiwpectio. i, equaf tc.c.,lem. thanthe AQ L.
D14.4 Reduced fnsp=ctior.. Reduce4 b-cpectien may be instituted provided that allof the following cOndiliOn. ● re ■atisf ied:
Condition A. The preceding tea (10)lc.ts (or such other mmnberoflots designated)have be.- under r.c.rrnsl i.. pecti.m -d no.ehas been rejected.
Condition B. The e.linuted percentdefective for ●ach of these preceding lots is
MUAID-41411 Jftfld 10s7
Iesm than the ●pplicable loumr limit cbowni- Table D-7.
Caufitiom c. Pr0dmct50n is ●t ●
●tcD4y rak.
Nonnsf impecthm *baff be retostate4 U myone of tbe foIlowing eondftiom occurm tiad~rredueed tic wctlon:
Condition D. A Iot-ic rejected.
fkradiiinm E. The estiunkd plwJce~-. ..erage i. ~re.ter tbn the AQL.
Comditiom F. P.oductiom be=om.airregular or delay=d.
COtisti.n G. Dthe r ccmditiom umay wtarrwt that normti inspection shouldbe reinstated.
D1 4.5 Sarnplin~ Plans for Tightened or Re-duced k,C.~=CtLOIl. S~PIIDS Pl~S fOr *lghl -e~ed and reduced inspection ●re provided inSection D, Parts I and 11
. .
10s
I
TABLE D-U
v.iu. mof T for Ti+t.oed k+spsctbon
Sample size Acceptable OustIty tavels (in percent deft!,
code letter .J-t .065 .10 .15 .25 .40 .65 1.0 1.5 2.5 ●-o
B . . . ● ● . . ● ● ● ●
3 3 3c ● . ● ● . . ● 5 5 5 :
6 6 7 7
3 3 3 4 4D ● ● ● . . ● 4 6 b
b : : a 9
2 3 3 3 4 4E . ● . ● 4 4 5 6 : 6 7
5 6 7 7 8 9 9
3 3 3 4 4 4 4 4F . . . 6 6 6 7
: : : 8 8 8 ; 9
3 3 3 3 4 4 4 4 4 4G 4 4 5 5 : 6 6 ‘1 7 7 7
b 6 7 7 7 8 8 ,9 9 10 la
3 3 3 3 4 4 4 4 4 4H 5 5 b 6 6 2 7 7 7 7 7
b 7 7 8 a 9 9 9 10 10 10
4 4 4 4 4 4 4 46 6 7 7 7 7 7 7
3 4 4 41 5 6 b b
7 a 8 8 9 99 ! 9 I.101 10110
4 4 4J : b b b :
8 a
44444477
181819119101 :1:1:
4K : b
8 8 9 9 9 9 10 10 10 10 II
4 4 4 4 4 4 4 4 44L b 6 6 7 7 7 7 7 ; 88
a q 9I I I
44d
9 9 9 10 10 10 10 11 11
t 4 4 4 4 4 4 4 47
1: 9 1: 1: 1: 1: 1: 1! l.:
—i.e—,.5—
●
479
—479
47
10
47
10—
48
11—
48
11
48
11—
4a
11—
48
11—
48
11—
4a
II
4811
—
7FNu13160r
10.0 15.0 of bm
● *
w
-++-
44588 10
11 11 15
44588 10
II 11 15
44588 10
11 11 15
u445en 10
11 11 1s
-l-J--44588 10
11 11 15
44=a
+E44588 10
11 11 Is
44’58 8 10’
.11 11 15
.There are no .antplimg plMM provided in this Standard fer these code letters 8nd AOL.a3nOS.
I&
—
I
TABLE D4-CmtJmd
VAM., of T for Tl@umd f519~Cti00
Sample ●L. Accepmkle Ouatlty Lavelo (in PC rcemt ttefe
code letter .04 .065 .10 .15 .25 .40 .b5 I .0 1.5 2.5 4.0
4 4 .4 4 4 4 4 4 4 4 4P 7 7 1 7
10 10 10 10 If< 1: i! 17 1: J: 1:
4 4 4“ 4 4 4 4 .4 4 .4 4Q 1 7 8 s 8 s 8
10 10 lJ 11 11 11 11 1: 1: 1; 1:
hfnATD-41411 June 1951
v ●riab.bMc7 ~
4445888 10
11 11 11 15
The top rigure in cacb block refer. to tbe precedi~ 5 lot., the rniddlc figure m thepreceding 10 lot. ●nd the bottom figure to the precedi~~ 15 lots.
Tightemed i.. pectiom i. rquir.d wbem the aurnber af lotm with .stirn.tea of percentdefective ●bove the AQL from the preceding 5, 10, or 15 Iotm i. greater thaa the Eiven valueOf T iu tbe t.ble, and the proceos ●verage from th.. e lat. e=c=ed. th= AOL.
N] estinutea of the lot p.rcemt de fectiws ● re Obtaimed from Table D-5.
I
107
TA
BL
ED
.7V
.fI
ab
lllI
~K
now
n~
~
Llm
lto
o{
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ima
ted
Lo
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vrio
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ed
uc
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ecti
on
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mp
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ze
co
de
lett
er.0
4.0
65
35●
*
c●
*
D●
*
E●
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J-●
4
.001
.001
G.0
04.0
08:
.010
.01.
9
.002
.004
53”
.009
.017
.018
.033
.004
.011
I.0
14.0
11.0
25.0
51
.006
.011
J.0
16.0
11.0
30.0
51—
.008
.014
2(.0
21.0
36.0
33.0
56
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ren
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ble
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evel
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.197
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.384
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. J .021
.2,
?2
.558
!
.027
.222
.558
,16b
.62Z
1.12
4
.311
.874
1.19
4
*
1.71
414
.z91
I5.0
0
510
Is
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I,Z48
2.14
5
.769
1.64
54.
386
Z.3
544.
496
8.04
93.
850
6.50
10.0
0I5
.00
1$
II
.086
.)57
.669
%
.631
1.22
5z.
q37
5.15
41.
64J
2.9z
45.
69?
9.33
02.
504.
006.
50I0
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1.56
01.
3Z5
6.11
41.
880
3.25
05.
958
9.80
62.
504.
006.
5010
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1.1)
6t.
166
4.o
451.
093
Z.1
413.
698
6.34
210
.00
2.50
4.00
6.50
J
1.32
6Z
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A
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8.8
67
10.436
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b
510
1$
l-l
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.0Z
602
7.0
49.0
9305
5.0
90.1
67.-
1-.0
78
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85.3
47.6
OZ
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18.0
0
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I,IJ
91
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11.4
705
15.0
010
AIS
01
3.0
2.?
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304
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.252
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071
.114
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.382
.65
.375
,773
,.00
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1.Z
70
1.s
0
-L12.0
545
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275
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0
TF
Z,6
43
4.7
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1,7
86
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2.75
84.
909
8.05
s3.
987
b.5
010
.00
4.00
Aa
+018
.030
0s1
.081
082
.129
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J.0
380s
8.0
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.10’
9,0
9b.1
S
.070
,164
.244
— .08Z
,177
.2s
,09
I.1
8B.2
5
.142
.298
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— .15.9
.J13
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— .171
.JZ6
.40
.252
.508
.65
.298
.549
,.b
5
1.46
1Z
.J59
2.50
.451
.847
,.00
. .316
.892
1.0
0
.718
1.34
61.
50 .85J
1.J9
41.
50 .910
1.4z
71.
50
1.56
22.
412
2.50
12,6
9315
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510
’15
.3!7
.564
.b5
.540
.908
1.00
1.64
12.
89!
5.00
98.
205
2.44
9,4
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6.50
10.0
02.
50A
AA
12.8
485
15.0
010
A1$
11
1
_——
.
5
,. 1
TA
BL
ED
-7-C
on
lln
ue
dV
~rI
ab
Illt
yK
now
s
Llm
lto
of
thti
mit
ed
La
tP
erc
en
tD
efe
cti
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rR
ed
uc
ed
fnn
pe
cti
m
.017.030.049.080
N.03Z,054,086.134
.04
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.10
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*
?“X.4
0
.107
.191
,203
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.Z5
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.Z14
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.Z51
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.191
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.,.-
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.
.348
.586
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— .383
.608
.65
we
u“a
lftv
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---1
-.5
01.9
34.9
341.
440
I,00
1.50
.6zl
I,o1O
I.9
591.
415
I.00
1.5
0
C19 T2.
54.
06.
S
1.73
2z.
96Q
5.13
1Z
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4.00
b.io
2.50
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1.82
13.
093
5.31
02.
504.
006.
50h
a,
T10.0
—
8.3
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ko.
oo h
8.51
610
.00 A
.435
.705
1.11
31,
959
3.Z
7Z5.
546
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2.6
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941.
502.
504,
006,
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.00
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m+
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mb
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1.0
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13,0
175
I5.0
310
1115 -1_
13-2
385
IS.0
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-1-
13.5
88s
15.0
0-
3u-
115 —
13
.80
15
I5.0
01
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15
14
.03
45
IS,o
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14
14
.17
35
15
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5
All
A(3
L●n
dts
ble
vduec
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Inp
erc
en
td
efe
cti
ve.
bU
met
he
flro
tfl
#u
reIn
dlr
ec
tlo
no
fa
rro
wa
nd
co
rre
ep
on
din
~n
um
be
ro
f10M
.In
ea
ch
blo
ck
the
top
(Ig
ura
refo
rmto
the
pre
ce
dlm
[5
lott
.th
em
idd
lefi
gu
reto
the
pre
ce
din
gIO
lots
.a
nd
Ihe
bo
tto
mfi
gu
re1
0th
ep
rec
ed
ing
15
lots
.
Rw
!uc8
13im
pec
tkon
may
b-
tna
litu
led
when
eve
rye
mtl
ma
led
lot
pe
rce
ntd
efe
cti
vefr
om
the
pre
ce
din
g5
,1
0,
or
15
lot-
inbdow
the
flsu
reglv
on
Inth
eta
ble
.fn
ad
dit
ion
,II
Ic
.th
er
co
nd
itio
mfo
rre
du
ce
dim
pe
cti
on
,In
Pa
rt3
23o
fS
ec
tlo
aD
,m
ust
bc
dti
ltfl
ed
.
AN
en
tkn
mte
oof
the
lot
pe
rce
nt
de
fec
tive
●re
Ob
tain
ed
lro
m‘T
ab
leD
-5.
=H
II
baL-sTD-41411 June 1957
Sz@!s!!n
x
.
u
1.
k
v
Q“
QL
m
PL
P
M“
Mu
‘L
P
P“
‘L
T
<
>
I
Read
X bar
Sigma
Q ,ub U
O .ub L
p sub U
p ●ub 1.
M ●.b u
M ●ub L
p bar
p bar ●ub U
p bo ●ub L
Less than
Greater tbM
SLunof
APPENDIX D
Defhiflmu
Def intt.io.s
Sunple site for + ●ingle lot.
S-pie rnemn. Arithmetic mean of ●unple rneawaremento from8 tingle lot.
fbowa variability. The predetermined variability of the quaf -ify cbaract.ristic which vill be u.ed rntb the .ariabifify bow.●cceptabfltfy plus.
Upper specification Iimtit.
Lawmr ■pectficatian limit.
The .ceeptabi3ity constant givem in Table. D. 1 and D-z.
A factor tw.d in determining the quality indices when ua ingthe bnowLI variability acceptability plan, The v vafues., ●regiv== in T~b10. D-3 -d D-4.
Quality Index for use with Table D-5.
C3uality Index for use with Table D-5.
Sample estinute 0[ the Iot percent defective ●bove U front.Table D-5.
Sample escinute of the lot percent @ef.ctive below L fr.amTable D-5.
Total ●unple emfirnsfe .af tbe 101percent defective p = p“ + PL.
Maxdmum dfowable percent defective lor sample eatimateagiven in T@bles D-3 and D-4.
Maxfmum allowable percent defective ●bove U ~ivem h Table.D-3 and D-4. IForuce when different AQf- v81uec for W andL ●re spactfjed. )
Maximum ●llow.blcpercent defective below 1. @em ia Table.D-3 and D-4. (For usawhen different Mf- value. for U =dL ●re ●~edfted. )
Sunpfe ewtdnnte Of the procemw merceut defective, i. e., theamfimated procema average.
Tbe ●mfimuod pw..s. .Verq. [*. -n upper Spectficstlom unlit.
The estimated process average for a lower ●pecf3icatlon Umit.
Tbe maximum number of emttnuted pr.xeoa ●verage- whichmay exceed tbe AQL given in Table D-6. {For u.e indetnr -=1- applic~t~a Of ti8bt=n=d i=~p=ctiOa. )
L.eom than.
Greater than.
110
.—.—— . - ---- ----
I I
-.,FOM d.m# thb lhn,
lFOM k-, Ih” It”. )
DEPARTMENT OF THE NAVY
111111OFFKIAL ●krJNE5●ENALTV FOm ●RIv ATC USC E.100 BUSINE:SNOR~,P;~M,M,fi[&,
rlnsl CLAWPOSfAGE WILL BE PAID BY THE DEPARTMENT OF THE NAVY
nNo PGE?AOewscE!EEAmv1S UAILEO
1947MCUNITED STATU
Co@xuanding OfficerNaval Ordcmce StationStandardizationlDocumen tatiop Divieion (Code 524
Indian had , KO 20660
I
,.
DDa??”1426. . .. --?r