SAMbLING PROCEDURES AND TABLES - Barringer1.com

1 MIL-STD-41411blvs7 IMILITARYSTANDARDSAMbLINGPROCEDURESAND-~ MORfkMOO$ I.:I,. -_. -. mL-sTD-41411 JEW1957 OFFICSOFTEE~ANTSECRETARYOFDE~Wuhlngkm$5, ~enapprovedbytheDePru iiiEsu ii1:535373839404143444546475?. ,1 ,. comzNls-cOfmffwdP* *:3kAmpfeD-3 EsampkafCdctdationwDoubleSpecUi-cationL6 mit-Oa* :Double+ :TableD-3 MasterT* (DoubleLimitandFormZ-Simgleumlt).. [ ).. *rtUlSST1 MATIONOFPROCBAVESAG!CANDCSJT& # * m-414llhfislm? ~i. mb61v # , * , #* ~ ~ ,lubtractio .multiplicuion,&ddIvimionofmwnbera,orlmo st, [ ~1411 Jmfe14s71,1 1 1 + Thi8 Sammkrd=stablimhesmmplnngPanmandprocedur esforinopec-ticmbyvariablelforuseinGover nmentP*. ~., # ,contrzct, ,andtheprovision,setforthhereinshall# * , unitofproduct ( ) + ( ) ,feetpersec-ond,etc., ; , , ,supply,production, , , (e) *req.~ ~ficationlimit;or6lowerpacificationlimit , ~lespecificationlimit;orbolhupperandlowe r.~cifieatiemlimit.,calledhereinadoublel ~ ~ **h*chlpeciiiesthermxnberc.<unitsofprodu ctfromllotwhichlretohitmpected.]]

2 ,andaaycbu~ *gclasses; . ;..hazardou. $ ~acterimticoflIi%.loxofprodv;t ~ :rkfectiv8-NumberofAefectiveax100 Numbsrofdtm1.. ~c~tedAOLi-aparticularvalueothertb&tivme forwhichoamplhgpfanmlrefurniched,theAOL, ,.Itaflbe.,.ho~ # ~r-dlowerspecificationUmita, ,,1ovhallnmmn,virt-cpecti~lot,- , !adinopec~tdtodeterm ;shall,lsfarlmlapracticable, ,gssde,~Ass,size, , # ,llotforprod ~ :andthelotl1= f=ctiOale=J~ ~e-~ ara~i4is* * * ~ , , ~o.,*:ca~qsi! *I-c-bili~~lMctihmtie.. * ~ #vnpliagplmMlccorduacawithSectionB,C,O, *lccef%abimeofthefouo wln * ~i4swithttnapprsprmtavariab14llcca*bllIt ycrl-terlmofsectionB, *s+ ! , =rm~ardedbyimplicationorotherwimelinmYm- erlicermingthetilderoranyotharpcr*Onorco rporation, ,u**.orlellaaypatentedinventionthumayinm n7=*Thra~ ). , , mm66101 JOIB35DF31111to180Be&cI181to300 EtDFH_j301to500C32 GIK501to800 DFHJL801t , ; 4!.. * )!!aI .. m00w100U%RATINOCW#fWTERISTICCURVESFORSAM PUNOPLANSBASEOONSTANOAROOEVIATIONMETHOOi i~.

3 -----..__ ._ 0wbo# ,*t9#wqpm,bedmmm,.dtil*9k ,m . l*+.do t1-010IQ3040ww!ma40looM,I.,rq!lmom-UtIs# .ul44,1,1 1,I.,-I tpn, ,,t! ~RISTICCURVESFORSAMPLINGPL;NSBASEOSWR_ES IZEcowLETTERF:,,,[cormf S*,, ,b,,,dm., ,.9A,49.#t -? , ONSTANOAROOWIATIONMETHOO* , (++,,uk,td)1hl-, # ,o.!-94dIuo9k,-m,t b.+ ,OUAU1 V0?W3Mt?lC0 LOTSI1.,. ,! )* +7 SAMPLINGPIANSQASEDwuSIZECOW$ , !DLRDDEVIIITIONMETHODiiSiMFLES1 ZECOOELETTERG:~*IC.*. ,p! <a ..IM .~ ..lld+~. )_ ;OPERATINGCHARACTERISTICCURVESFORSAMPUNQ PL+W8 ASE0 SAMFLESIZECODELETTERG(Con!lnwd)ONSTANOAR OOWIATIONMETMODwOUUllYOrSWMlllfO10U(hpod tihdb,I%.----k.+. ,1 ,m ,Il___1 ,,44W4know,. i,blll!, ,,,,,d,+wI.,IA).. + ~. *WI, ).-ame.,TABLEA-3 OPERATINOCHARACTERISTICCURVESFORSAMPLIN1 3 PLANSBASEDSAMPLESIZECOOELETTEfiI(Contllw l)ONSTANOARDOEVIATIONMETHOD?sTAMEA-3yOPE RATINOCNAIIACTERISTICCURVESFORSAMPUNOPLA NSBASEDONSTANOAROOEVIATII?NMETMODE!jSAMW SIZECOOELETTER?&J*fCnnsfor u#l., ,,dmm,, *k-l. lMI, , Al+b+ . ITASKA.,3O~RATINOCHARACTERISTICCURVESFOR SAMPLINIJPL~NS8 ASErIONSTANDARDDEVIATIONMETNODSAMRESIZEC ODELETTERJ( ) ,kM@ ,, ,b.]

4 T-Is.,.AM## , *Um ,-II*Iqwdmf) ,,. +@LESIZECODELETTER!!g ,bdll,w,,,,, 1;4$ 1j!3., :1 STANDARDDEVIATIONMETHOOSAMFLESIZECOOELET TERK( ~){-tb*Ip-th-imlul\s- ~.9l**W++! .1-1 Iht.,~,,m- bm+ ,1 ,!,1--d, @ELETTEII~yCm$!4 ,:aIh,,,1 ,,q,!h,,hnsb,,,dm,,.9,,A,b,,*hnwmvwl,blh l,w,,,nwdl,ll,,,u(v,M}1,Tli+n*dmmaItofbl ,npwl,*$.h-W!*9!-*h *--s4419!? [h,, ,.)?&I,%f,~,,,m,-, ,8.,,,!,,,,O@,,c .,,f-w,,,, ,,,,,,..m+dall?--dtiwr-ehiletiti rti-1, mb9mddb-* { ! !1.,Im,,~.,* +.0 .l,t,L . *Ih+., OPERATINGCHARACTERISTICCURVESFORSAMPLING PLANSBASEOONSTANDARDDEVIATIONMETHOOSAMPL ESIZECODELETTERM( ) ,, ,0604 , . ,b,,.dm,, ,, ,l, .,,, MI.,aummorwoumoLOUII.,,,, ,nw,-- ..!1!,1 ,1,t. - ,M*,*,*). ,1 a+,,Im,$,,,4m,,.,.44W, ,.bdlt, - - - .- *d)ICnrmfw !, ..,,,.lhl~qll., ~15 OPERATINGCHARACTERISTICCURVESFORSAhiPLIN QPLANSBASEDONSTANOAROoEVIATIONMETHOOgiSA MFtES!2 ECOOELETTER:P!/d:tC4WW8t-,qll.,,Im,b.,. ,,&. +,,,,,,,. 1,+,,.,..1 1)W+.,dlb,WcmldIt,*ml*41, -w.**ti.,-,,.*4dMk,-4M MI*9 UALIT7Of9u9Ul~DLOTSI1.]}

5 ,,,w,TId,f,,l),,IMA)f,~,,,0!unu ,. (e--m1--I)IulWmIre,,d-4i -. kbllllj , oatId+ !)lbdat?l-wddbf,-?-abb---** O--*, .k~,.,,.0,.1!,,L .1, ,,,,,,.. ,.$,TASKA-3 CURVES,FORSAMPLINGPLYRA5E0ON5T, ,01, ,},,.4mf. ,,..* i,blmy ,,,,m,,d,,_ ,.,!M!)mmkuilm~tibl,~,, *ubal-,,.1-04dak*d41,+. $uBMITrCoLOTS(h,.,,, 9,.1,,1,.,)W., ~ ,l,, ,1I,TV,,I,W.,., ~lCCURVESFORSAMPLINGPIANSBASEDONSTANDARO DEVIATIONMETHODSAMPLES1 ZECOOELETTERQ (Cmfln.,d)Ih,f-,+*,, ,b.,d01,,.,.dtimm, ,.whb,hly * # , , ~. ~-MIfor~ , ] < ~ , # *~lhoummtema.,.. * ,iaindicmedinthecolumnofthenustertableco rre~pmxlingtotbeapplicableA( ~,qusntity(u-XJI*orfl-L) ( -X)/ .,(x-L)/.,d,-pendiagonwhetherthespecific ationlimiti,~qperorlowerlimit,+ , (u-x)/mor(x-f.) ,thelotmeetsthe=cc~ :if(U-X)1.**(X-f-)1~ ,3hrmtheM&esnotmeefthe =e~ ~~MNGPLANWRENFORMsmThefoLIowfnr soP* ~marise hePrO-=~ :(1) (2) )= $yconstantk.(3)Selectatrandomthesampl= ; (4) ~andestimateoflotsts (u-X) ~ntityA-L)/. ~ )Mthequantity(u-X)/sor( , :it (u-X)/.

6 Or(X-L)/.i.[ (ha---kornegative,thesthelotdoe ~ dai~ ~ ~ , $ ~ ) ~10eachsam> $ ,.dfromtbetopfornormalinspection-dfromth ebottomlo, > ,.~a~,e~-,. ~ ,judgedhythepercentofrmnem-,-Iorm,ngprod uctoutsidttheupperorlow+ T~ ofQtufit~-lity~-X)~rnpE~ ,orOL.(X-L) * ~e-ii-t-dP.,. ~ti-indlotlbovetheupperspecificationlimi t,orby? *.=. , ,thelotrneetstheacceptabilitycriterion;i fPuorp~isgreaierthanMorifQuorQis,negativ e,thenthe10:doesnotmeet\ ,(1) (Z)ObtainplanfromMasterT= ~ (3)Selectltrandomthe# ; (4)Cmnpute3h= (5)ComputethequalityindexQ(U-X)/* ,.limitJfi:lP.* ( )/.ifllctwerspec-iiication1;..;.L<.snecif;ed.(6)Det~ *dure. ) ~ ~isaeptie,PUOrPLi.~ ~bil$ ! ,normalinspec-tion,withAQL=1-% , ! < ,184 ,205-,andZOl X~CFVariance(V):SS/(n-1)EstimateofLatStandardDeviation.:fiSampleMeanX:ZXlnSpecificationLimit(upper):uThequantit~w-X)/cAecept~iIity&natant:kAcceptiilityCriteriozxf2mparew-X)/OwithkValueObta{ned5975190,435190, > (975)2/5190,435-190,125310/4-s97515[209- 195) (U.]]}

7 ~)/sis~remt= :Iflninglelowerspcffieat{ ~ntilY~-~)f~ ~reilwithk, *rii=. (~-Ll/*isequaltoorgreaferthank.!.M2~-414 11 June1957 SingleSpecificationLimit-Form,?Variabili tyUnknown-StandardDetiationMethodICUmple Themaximumtemperatureofoperationforlcert aindeviceisspecifiedls209 ,normalinspec-tion,withAOL=1% :197.,188-,184.,205-,and201 ; t fb ercen D * ; *SlbnM.!---- ~ [SingleSpecificationLimit Form1)SamplesizecodeletterBcAcceptable(! . ,?, .65T$.CVCIS(normalinspection)mGi-k+,10, , ,; , ) , , , , , ). 1, +. ,?. , ,66 , , + , ,1!2,1[ . ,0( alit, , !1:::,, , [Irsttunpllqplanbelcwlrrow,thatis, ~~TABLE23-2 StandardDeviallmMethod~ (SingleSp )IIualityLeveloEEE Acx. k . , ,76$.564,165, , , .k .I . 1, $ +~~ , . , z-i-D3E3T4G5H71, . * , . !. :. ,36. ) . !5 , * (.84 , $. ~~;;,e,:,,,,,mi the,0,lll ,tt.,, , ,bothmm-qdenizenowell ~ , ~ dAQLvalue(.)theappli-cablecampli ,Gen-eralDescriptionofSamplingPlans, [C.]]]]}

8 ;J ; soeiatedmaximumallowablepercenidefec-tiv e(s). #izeoisshow inthematertablascorreape= *. # , , (s).UdifferentAOL, , , ~ # ;: & . , ,Xisthesamplemea., ~ ~ ~ + ~tedbyp~. :::; , +Y w + ) (2) lndthemaximumallowablepercentdefectiveM. (3) (theamp]=.(4) (5)ComputethequalityindicesQU=(u-X)/.and QL=( )/,.(6)Determinetheestimatedlotp., +PLfromTableB-5.(7) ,..thanthemaxim-umlllowableptzcen%defect iveM,the)otmeet,thelcceptabilitycriterio n;ifpisur.~t=,th= ~.tive, ] ofML andtdu, ;otberwimm, ~. ~tiive, ~ ,thefollowingstepssunururi etheprocedurestobeUS=CL(1) ,thelotsizeandfnspectimtlevel. (.?) .corr= ,respectively.(3) ; (4) .,,(5) (u-X) (x-L)/a.(6)Deterrniaetbeestimstedlotperc entdefective~andp~,correspand-iag\othepe rcentdefective* ~.(7)11alltbre= ~corl-dition.:(a)~ ~]PL!9=LNJ81tO0, L.(c)pisequaltoorlemmthanfbelargerofMLln dbtU, ,fh= ;ofhe= ,thenthelotdoesnottne=ttbeacceptabilitye =iteria.+ { * $S7 IiII1 1 E-deLine 1234567s910II1213141516173 SXAZ4 PLCE-+ExampleofCdcu3ati0nmDoublespaMluti noLtmttVariabiNty?}

9 (on, * :197 ,188 ,1M.,205 ,md201-; :SXSumofSquaredMeasurement:XX2 CorrectionFactorICF):(2x)z/nCorrectedSum ofSquarca(SS):XX~C~Variance(V):SS/(n-1\E stimateofLotSt&rdDeviations:&SampleMean~ :~ :ULowerSpecificationLitnAt:LQtuIityIndex :Qu-(U-X)/sC3uditytid=:OL=&L) :% ) + +p~withMs975190,435190, < (975)2/5190, )5(zo9-1951 (195-180) +.66% (7) 3& + ~ ,..43 m&6w1411 Jone1957 EXAMPLEB-4 Exampl* ,normalimW= *ACZL=1%foI*=upper-d~~= :197.,188.,184 .205 ,andZOI.; ~1z345b7k91011lZ1314islb17laInformationN eededSampleSize: :XXZC orrectionFactor(CF):(ZX)2/nCorrectedSumo fSquares(SShlX~CFVariance(V):SS/(n-1) :fiSampleMe=XXXlnUpp=rSpecificationLimit :wLowerSpecificationLimit:LCluaIity3ndex :Q .(u-X)/oOAityindex:(ZL=( :~ ;. , +< ) ,12531OI4m97515[209-195) (195-180) +.6 WSeeTableB-3 SeeT* (7)(a) (7)( (7)IC)~ (s),(b);ad(c)are ati~fied; ~pL<MLsndp< *rdDevittlonMethodMinterTsbleforNorm81an dTightenedtnapcctionforPlmsBlsedonVariab ilityUnknown( )Acceptable~. ;-i+ , , , }50.]

10 !lctimSamplecitecodeletterBcDErGHIJKLMNo PQi~~ . ,07z.# ; , , , ZzoI l4 0$ ,03Z, 47I 2 61 024I s [ , [ (AllAQLandtablcvsluetlreinpercentdefecti ve., TABLE23 AMuterTablefarReducedfnvpecclm[ (DoubleSpecU{ !clficatimLimit)Acceptabamplecitesample- j:xI*Iettsr81; }.( ,. B3Ic3D3E3F4v , ,17J10, ~ ,zv,?. , ~= ! (7 , , ] < ,330-=l=t+ ,20 { :a, ~ #pecled,firstounpllngPIUbdowlrrow,thatis ,both# Whencunplosiseequa2@orexceedslotI . _ ._____TABLEB-5 TSWOforEotkmtlqth~&tPe,CCIIID efectiveU# # ! *(ectlveU#lngS;mdardDevlaiionMQ~hodk! .. a TABLEB-5-CadimedTatdoforEattnutlqthoktPo reantDef*ctlweUOlagStandardDerlatien,Mot hodE- .ML-rm-41411J5fffa1957 PmrtmC5 TZMATZONOrPBOC=AV~EAND~TER3 AREDUCEDA35 DTIONTU4CD= ~ *pecfiOnOf~-~cb?etyofp~ ; ~.=Ofd=~= ~ ~rag,. , ~t= , ,.mpyte,dw+ ,f,.~t* ~. ~ ~rremmondtnsedmtid1c4+rcud&fOcfiw~&p=, ~i**~ $Littbearithmeticmeanoftheindividuallctf aut9d30tpareemt&facUwapL , ~andQLdthe-unP5eliae,dtheeor--mpmd-fag~ + ~rcenfdefective-p.))))]]}