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MIL-STD-414
11 blvs7
MILITARY STANDARD
SAMbLING PROCEDURES AND
-
~M
ORfkMOO$-10
TABLES
FOR INSPECTION BY VARIABLES
FOR PERCENT DEFECTIVE
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—- _
.— .—
mL-sTD-414
11 J EW 1957
OFFICS
OF TEE ~ANT SECRETARY OF DE~
Wuhlngkm $5, D. c.
S up ply a nd Lo gi. t i..
1 1
JUIU lb7
Sa rn p fln g Procedu r e s an d Table . fo r fa .p . c t lo . by
Va r l.bl.. fo r Pe=c en t
Ddectlva
MIL-STD-414
1 . Th i. .t an d a rd h .. ~en app roved by t h e De P ru ’n e .t o f De fen se
an d i. m an da t o ry fo r . . . by t h e Depa r t m . rAt o of t h e Arm y, t h e Navy . an d
t h e M. for ce , fe c t ivm 1 1 J un e 1 9 5 7 .
2 . h
ccord an c e rn t h e . t a bli.be d p roc .du r ., t h e Sfa n da rd i. . t icm
Diwl. im k .. d -.ifp . t .d t h a Ch em ica l
-Carp.
Bu re au of Ordn an c e . -d
Air For .. , r .. p . t i .. ly , . . Am p N.v-Air For .. c u s t od ian . .1 t h i.
. t a nd a rd .
>. Re com m en ded cor rec t ion . . s dd lt len n , o r d e le t ion . .h ou ld be
dd r . . . .d t o t h e St a n brd i. a t io r . Divi. iom , Of fic . o f t h e As . im ta .t Se c .. .
a a r y of De f.a .e (Su@y an d Logis t ic .), Wa .h in @an Z5 . D. C.
I l .
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-- .,-...,--
..
UJlvl-hn- ls
INTRODUCTION . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . .
SECTION A
GENERAL
D&9tiRIPT30N OF
t ibfPL3 t 4G PL. J S . . . . .
Tab le, :
Table A-1 U3LCon ve ra ion Table . . . . . . . . . . . . . . .
Table A-2 Sam p le Size Code t iNe r s . . . . . . . . . . . . . .
Table A-3
Opera t i ng Char.c t er i* t ie Curve. 10. Sampf iq
Plm m of S.c t iOa B, C, an d D (Graph - for
San @. Sis e t ie Le t t e r s B t hough Q) . .
SECTION
B
VAR3ABIL1TY UN3U40WK-STANDARD
DEV~TION METHOD
Par: J SINGLE SPECIFICATION LIMIT . . . . . . . . . . . . . .
Ex8 m pl. *:
Exam p le B- I
Exam ple B-2
Table. :
Tr eble E.- I
Table B-Z
Exam ple of Cdca fa t to iw:, S im gle
sPec iflca t iOn fAm il-Fo rm 1 . . . . . . . . . . .
Exam ple of Ca lcu la t ion s: Sin ~le
Sp*c ific a t ie a Lt m it -l%rm 2 . . . . . . . . . . .
M..t e r Tabie for Norm a l n d Tigh t eo ed
3 n m pec t i0 n (Form l-Sin n le fAm it ) . . . . .
Maa t e r Table for Redu eed im pec t ion
(sOr rn l-s in gl. LiJ n ii) . . . . . . . . . . . . . .
Pa r t H
DOUBLE SPECIFICATION Uh UT . . . . . . . . . . , .
Examp lea :
Exam ple B-3
Exa rn @e B-4
T, b lem:
Table B- 3
Table B-4
Table B-5
t iam ple of Cdc rda t iom m : Double Spec ifi .
c 8 t ioa LAn it -Ck e AQL va i.4 fa r Upper
an d Lawe r Spec ific a t ion Lim it Com bin ed
Exam ple o f Ca lcu la t in na : Double Spec ifi-
c a t ion Um it -DIffe r em AC3L va lu e s for
Uppe r su d
fmwer
Spec ific a t ion Um it m .
Mm m t e r Ta ble
fo r
Normal
n d Tigh t en e d
Im pec t i .n (Double Lim it an d f%rm 2 -
si I l le LiIni f ) . . . . . . . . . . . . . . . . . .
Mss ie r Table fo r R=du ced fa sp ec t iom
(Dou ble LIm it mn d Form Z-Sin gle Lim it )
Table for
3SatimatiaE
t h e Lot P. r c en t
De fe c t ive . . . . . . . . . . . . . . . . . . . . .
. . .
. . .
. . .
. . .
. . .
Pa r t f3 J
EST1MATION OF PROCESS AVZSAGE AND
C3UTE- FOR RZDUCEL AND TIGHTENED
INSPECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table , :
Table B-6
Table B-?
Table L-8
APP=dk B . . . . . .
Va lu e . o f T for Tigbt en ad k p 8 c t i0 1 1 . . . . . .
~t s of Es t im a t ed k ; P.r c en t
De fe c t ive fa r Rodu c=d In spec t ion . . . . . . . .
Va lu e . o f F for h 4 a s im um St an da rd
Devia fio a .[MBD) . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
‘iii
Esu
“ii
1
:
5
3 5
3 7
3 8
3 9
4 0
4 1
4 3
4 4
4 5
4 6
4 7
5 ? .
5 4
5 6
5 8
5 9
. . . . ..-
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comzNls-cOfmffwd
P*T5
u DOUBLE 5PECfF1CAT10N LlhffT . . . . . . . . . . . . .
3hampfe*:
3 k Am pfe D-3 Es am pk a f Cdc t d a t ion w Double SpecUi-
c a t ion L6 m it -Oa* AOL vah m UpPa r an d
fm we r Spe c ific a t ion . fAm it Com birm d . . . . .
Exu n p le D-4 Em m p le
of
.Ca lc u la t iom s: Dou ble +pecUi -
c -t ion L6m it -D3 ffe r e u t AOL va lu e - fo r
UpVr d kwe r Spec ifica t ion
Limits . . . .
Tables :
Table D-3
Mas t e r T*le fo r Norm al a n d Tigh t en ed
fn . p e c t im (Dou ble Lim it an d Form Z-
Simgleumlt) . . . . . . . . . . . . . . . . . . . . .
T.bla D-4
Master
T&ble fo r Redu ced 3 nop .c t iom
[Oou bk Lim it . .d Form Z-Sin gle Lim it ) . . . .
T.ble D-5 T-ble fo r Es t im a t in g t h e fa t Pe rc en t age
De fe c t ive . . . . . . . . . . . . . . . . . . . . . . . .
P*r t Ul
SST1MATION OF PROCB AVESAG C AND
CSJ T&R3A FOR REDUCED AND TIGHTENED
INSPECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tsble :
Table D-6 Va lu e . o f T fo r Tigh t en ed fr t . p e c t ion . . . . . .
Table D-7 Lim it - o f Ec t in u t od IAX Per cen t
De fe c t ive fo r Redu c ed h m pec fiom . . . . . . . .
APP* 6 D........ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
-
9 5
9 7
9 8
9 9
1 0 1
1 0 3
1 0 4
1 0 6
1 0 8
1 1 0
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mlL-8’m-414
llhfislm?
INTRODUCTION
Th i. St am dardwa . p repm red t o m ee t growin g IIeeo fo r t be U. o f s t an da rd
u ’n p liq p t m m for J am pec t ion by va r i*ble . in t i~r n m a t n p rocu rem en t , DIIpp ly
an d .t orage , an d m a in t en an ce ia .p c iion opa r a t iozm . Tbe va r ia bf. . sam pJ &s
p lan e .pp ly t o n @e qu a lit y ch a ra c t e r is t ic wh ich can be rn e a .t irm d on c o a t t n -
t m .. s ca le , an d for wh ich qua lit y i.
xpr e s s ed in t e rm . cd pe rcen t d e fe c t iu e . Th e
t h eory u n c le r lyin g t h e deve lop rn e .t o f t h e war i.bt e . .an ip lim ~ p lau a , in c lu d in g t h e
opa ra t iq c h a ra c t =r im tic c u rve .. a .awn e . t h a t rn ea .u rem .m t. of t ba qu a t t t y ch a r .
c te r i s t i c re in depen den t, id en t ic s lfy d i.t ribu fed n orm al ran dom var isblea .
1 . com pa r ium wit h a t fr ibu t a .
..mpfing pfmn.,
war lah e s u m p fia g p lam m
h ave t be dvan t a~e of um mfly r em dt in ~ & cm m ide rsble .avin em in am ple -
fo r .xm n pa rabl. a . .u r u ic e . . t o t h e cor rec t n es s . of d ec is ion . in ju dgin g . . in le
qua lit y ch a rac t e r is t ic , or fo r t h e .a rn e sam ple s ize . gr ea t e r a .m ir an ce is ob-
t a in ed u s in g va r ia ble , p lan ..
At t r ibu t e . s am plin g p fan . h a ve t h e advan t a ge of
grea t e r s im plic it y , o f be in g app lic able t o e it h e r .in gle or rn u t t ip le qu a lit y ch a r -
ac t e r is t i c . , an d of requ ir in g n o k n owledge abou t t h e d is t r ibu t ion of t h e con t lau eu .
rn . a .u r. rm en c.
of any d t he
qu alit y c fu r. t xe ridc ..
It 1 0 im por fsm t t o m ot . t fu t va r ia ble . .am p t fm p ph a .
rm m ot t o be um .d
i.d i. c r irn in a t . ly , , im pfy bec .u .e . it i. p o ..ible t o obf.in vaxi.bk . t n ea .u ra r n em t
,d a t a . fn con m lde rq app fie a t lon . wh e re t h e rm rm at it y or ir t d e~n de .ce
. smnp -
t ion . m ay be qu e .t icm cd , t h e u se r i. dvi.e d t o cm -..u lt h i. t e ch n ica l agen cy
to
de t ci-rh in . t he fe . . ib ilit y of a pp fi ca lion .
Th i8 Sra n da rd 1 . d ivid ed in t o fou r .e c t im m . Sec t ion A desc r ibe . @n . ra t
p roc t t lu r . a o f t h e .am plim g p la n . . Se c fic .m . B u t d C de .c r ib . .Pc ifi. p roc edu r e .
an d pp lic a t ion . of t h e .a rn p Iin g p lan . wh en w.=ia bilit y i. u n k n ovr . , In Sec t ion B
t h e .s t ir n .t e
of
lo t .%an d . r d d .vi. t ion i. u s ed .s lh . fn . i. 1 0 . an
.timat. of t h e
u n k n c .w. va r iabilit y , an d in Se c t ion C t h e ave r age ram s . of t h e su n p f. 1 * u sed .
Sec t ion D de sc=ibes t h e p lan . wh en va r ia bilit y is k n own .
Each
of Sec t iono B. C,
an d D i. d ivid e d in t o fbr ee p a r t .: (l) SAMPJ IIW PIUM
for t h e Sin gle S~c ifieu iom Lim it Ca .e , 1 1 1 )Sam pfim g Plan s for t h . m ubl. Spc -
ific . t ion Lim it Case , an d (3 J J )Procedu re . J orEs t h n a t ion cd Proce .. Ave ra ge an d
Cr it e r ia fe r Tigh m n ed r id Redu ced J a . p ec t ion .
For t ba
n gle s ~c ific at io n
lim it ca . e , Lh e
ccep t a bilit y t r it e r io . i . giv=n im t wo foran .: Form 1 am d Form Z.
Eit h e r o f t h e fon n c m ay be u .ed ,
i -i ci t h e y rc id e t t t ic t i a . t o .a in p le s is e -d
de c i ion fo r lot c cep t abilit y or re je e t a bilify . III d ec id in g wh e t h e r w u .= Form 1
or FQrrn Z, t h e followin ~ po iDt . sh ou ld be bo=n . in m in d . Form I p rovide . t h e lot
ccep t abilit y c r i~. r ion wit hou t t it n .t ir t g 1 0 I p e rcen t d e fe c t ive . Th e Form 2 1 0 1
acc ep t abilit y c r it er ion r equ ire . em t irn at es of J ot pe rcen t d e fec t ive . Th em e e li -
m a t e . a t .o .r . ~qu im d for e s t izn a t bn of t h a p roea
a ve rage .
Ope r a t in g Ch a rac t e r is t ic Cu rve . fn Table A-3 h ow fh e r=la t ioa .ft ip be t weem
qu a lit y an d pe rcen t o f lot . expe c t e d t o be c ce~able for
the
q u a li t y c b ar a c t a ri .t i c
in m ~e t .d . A. s t a t ed , t h e . e Ope r a t in g Ch a rac fe r i ‘t ic Cu r -. a re &sed 0 1 1t be
.. u rn pia r i t ha t m eam . m m en t. re .ek c t ed a t ra adan alrom a c io rsn ti d is t ribu t ion .
Th e corre s p end i ng u n p fin ~ p la n . in Sec t iW. S, C. ~d D w. m m st cbed
. c los e ly ., p o.. ib le ~de r
.y . t em Of f ix ed .unpfe .Ise wit h re . pcc t t o t h e ir
Opc ra lin g Ch a rac t e r is t ic Cu ? we s . O~raUn g Ch s ra c t e r is t jc Cum . in T.bf. A-3
h ..= be en com pu t ed for t h e .m plin g
p]an.
b. .. d or j t h . . .t im a t e o f lo f .t u d a rd
devia t ion e f u n kn own ..r i.bilit y , Th y a re equ lly .pp lie .ble ior .a r n p lln s p lan .
h oed on t h . ave raga r an ge of the .awIp I. o f u n fm own va r iabilit y an d t hem e bam .d
o n k n own va ria bUit y .
C.r t a im c ln ..cm r i. :ic . con ce rn in g t h e su n p liag ph m . in S. .t iom . B am d C
-d t bosa la S9 c t ion D dwu fd b, m ou d . Pk n . baa .d on fba m t im a& ot u mk =0 9m
War ia blllt y re qu ire fe~r .M@e wit . fo r cm ~ra~e . ..”ra n ca -ba a t b
d.
Mate
of lcM .t aad a rd t iwl.s i~ i. “. .d t h an _bg. ib .~..a e ru a~. d ffn .-+
in u .ed : on fh e o t t wr t id , p lan . Vsbg t h e .W~.gG r~ge of t h e AM@. r .qu ira
VII
-—
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mb61v—414
11 J une 19s7
m ph r com puu t t m m . Pla rm um ln n bm =va r iabllt t y -qu t re con *l&rablT f-r
s am p le t m k fa r com wrabk am UJ rMC* t ba I ich =r o f t h e p la n s whw =TIabt u t y
1 s u ak am : @we we r ,
tba
roqu ir=m w.t of k um II -rk biUt y Is t n s en t am .
Th e u se r 1 s . dvis e d t o co .m ilt MS t ec t a lca l~u c~ bdom WPIYLW cun p t ia j
p ia no U.t n g bDOwa w8 rIAbu uy.
Ta t h B-8 p rovids va lu e s o f t be f~c t o r F t o com pu t e t fia m axfm um s t an da rd
dewia t ion h fsD. Th e h fSD se -s M ~u id e fo r t h e m agn it ud e of t h t e a t ir n a t e o f
lot s t an da rd de -s c ion wh en u -in Plazm for t bm dou ble s p c ff ica t ion lim it c --e ,
ba sed on t h e in t im at e o f lot . t a a~rd devia t ion of u n .bn - .a r im tdUt y . Sim ifAr ly
Table C-8 p rovid es vm lu e - of t h e Iac t o r f t o c om ~t e t h e m axim um ave r age ran ge
MAR. Th e MAR or .ew m a g de fo r t be m agn it u d e of
the
ave rage ruige of t h e
“k e do .bfe .p ec ific .t ia . lim it . . . . . ba .ed . . t h e
n p le wk . u s in p la nm for t
a ve r age range
of the cunple of unbam w ar iddl i t y . Tba edmate
of lo t tmd a r d
devia t ion or ve r age ran ge of t h e
m pk , U it is Iem t h m t h e h fSD or MAR.r e .
=c t ive ly . h s lps *O im mu re . bu t doe . m ot gu a rm t .e , lo t accep t . bfllt y.
AU
ymbols and t h e ir d efin it io n . re gim n III t h a a -ix t o P a r t J U cd t h e
a pp lic able *c t im .
h Ulum t ra t im of t h e com ~t iom an d p roc .du rm a .~ed IIJ
t h e .un p lin g p lan s i. give . i. t h e
n m p lec u f Pa r t - I an d 1 1
of t be spplk able
.ec t ion .
Th e com p ut at hm m irwolve s im ple r it hm et ic ope ra t ion . su ch am .dd it in a,
u bt ra c t io”. m ult ip lic u ion , &d d Ivim ion of m wn bera , or
m ost , t h e t a k in g of
.qu a re root o f
n um be r . Th e u se r sh ou ld becom e fu n ilia rwit h t h e g.n e ra l p ro -
cedu re . of Sec t ia n A. an d r e fe r t o sh e pp lica ble se c t ioa fo r de t ailed iawt ru ct iom
rega rd ing pcc ific p rocedu re .. c orn pu . ion s . m d t able s fo r [h e Barn p lia g p lan ..
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~14
11 Jmfe 14s7
...
SECTION A
GENERAL DESCRIPTION OF SAMPLING PLANS
Al. SCOPE
All Pu r
+’
Th i 8 Sam m krd =s t ablim h es
m mp ln n g P anm an d p rocedu re s for in opec -
t icm by va r iable
fo r use in Government
P*.c . rem e.t . s .pp fyu ad s t ora~., and rnAJl-
tetts.cc inspect ion op8 ra t i0 r Im . wh en .pp li -
c abfe t h is St an d a rd h a ll. be re fe r en ced in
t he spec ific a t ion , con t rzc t , o r in 8pcc t ie n in -
. t ru c t ic .r . m ,
an d t h e p rovis ion , se t fo r t h
h e re in s h a ll ovem .
Al. ? III*PC
c t ion . lnm pec lion i. t iw p ro . . . .
o f m ea su r , n s .
xam in in g. t es t in g. gagin g. 0 .
o t h e rwise com pa r in g t h e “u n it o f p rodu c t ”
(See Al .4 ) wit h t he ap pk abfe requ ir em em la .
AI.3 ln s pcc t i- by Var iable s . Inspect ion by
va r iable s i . in spe c t ion wh ere in r+ spec ifie d
qu a lit y ch a ra c t e -r i. t ic (Se e AI.5 ) on a u n it
o f p roeu c t i . m ea su red on . con t in u ou s
.c a le . .u . h . pou n d -. iwh eo, fe e t p e r s e c -
on d , e t c ., An d rn eam trem e . t is r e cu rd . d .
A1 .4 Un it o f Produ c t . Th e u n it o f p rodu c t
i . t h e en t it y o f p rod u c t in .xc t ed in orde r
t o dew r rn in e it ; m ea su rable qu a lit y ch a r -
c t e r is t ic . Th im m ay be a s in gle a r t ic le , a
pa ir . a
e t .
com pon en t of an en d p rodu c t ,
or t h e en d p rodu c t it s e lf. Th e u n il o f p rod -
u c t m ay or m ay K.t be t h e su n e
s t h e u n it
o f pu rch am e,
su pp ly , p rodu c t ion , or
t h i pme r . t .
A 1 .5 Qu a lit y Ch ara c t e r is t ic . Th e qu a lit y
ch a rac t . r ia t ic fo r va rxable e in . p e c t i4 n is
t h a t ch a ra c t e r is t ic e f i u n it o f p ,odu c t t h a t
is a c t u a lly m .a . u zed , t o d e t e rm im con for -
m an ce wit h give n r eq uir em e n t .
A1. b Spec ific a t icm Lim it . . Th e pecl f lca-
t ion Iim t t(e )
is t h e r equ i r e rn cn t t h a t
qu a lit y ch ara c le r i. t ic .h ou ld m ee t . Th i*
req .~rem en t m ay be exp ren m d n . u ppe r
p r c~f ic a t ion lim it ; o r 6 lower pac ific a t ion
lim it , c a lle d h e re in
. in ~le s pe cific at io n
lim it ; or bo lh u ppe r an d lower .~c ifie a t iem
lim it . , c a lled h e re in a dou ble ~cif icmion
l imi t .
A 1 .7 Sam p li.~ Plan s . A s am p lin g p fan 1 .
a PrOCedUr* *h *c h
pec iiie s t h e rm xn be r c .<
un i ts o f p rod u c t from lo t wh ic h r e t o h
it m pec t ed , a r id t h . c r i l. r ion Xor a e c ep fabil -
it y o f t h e lo t . Sam p lin g p fa zm de s ip a t ed in
t h i. St an da rd a re
pp lic able t o t he in sPc -
t fon of ch gfs qu a lit y cba ra c t e r i-fk e of a
unitof p rodu c t . Tfm se p fwm m ay be u s ed
wh e t h er p ra cu rem rm l in spec t ion i.
per.
km ’rm d a t t h e p lan t o f p rim e c oa tr ac t? r .
wbcon t r ac t or or ven dor . o r t d e st in a t io n ,
-d -S90 may be u aod wh en AppTOPrU1 O in
ppfy and s to ra ge . an d m a in fa na ac e fL1 8pe c-
t i on o fm r at t om .
A3 . CLASSIPTCAITO? f OF DEFECTS
AZ. I Mt t h odof Cia8 s ifr in g~fe c t @. As f8m -
. ific a t , c .n a l d e fe c t - . . t h e rm in e ra t io . o f
de fe c t . o f t h e u n it o f p rodu c t c la a s ifi. d
ac cord in g t o t h e ir irn p or fa a c e . A d e fe c t 1 9
devia t ion of t h e u n it of p rodu ct fr -a m , r e -
qu ir em en t . o f t he spec ific a t ion s; d rawiags ,
Pu rch a .e da~c r ip fia ”. , a n d aay cbu~c
t h e r e t o in t h e con t r ac t or
order.
Defec t s
n orm a lly be lon g t o on e o f fh e fOllO*g
c la s se s ; h owever . d e fe c t s m ay be p lk ced k
ot h er c iao . cs .
AZ. 1 .1 Cr it ic a l De fe e t o . A c r it ic a f de fe c t
i. .“ . t h a t iu d em e. t an d axm rien ce in d ic a t e
cou le r e eu lt ;. . h a za rdou . “or u n s s fe con d i-
t ion s for in d ivid u a l. u . in g or m .im ain in g
t h e p rodu c t ; or , fo rm ajn r en d it . r n 9 u n it ~of
p rodu c t , su ch a . sh ip s , aircraft, or famba.
d .f. c t t h a t cou ld p reven t fm r for rn a a co of
their t ac t ic -i fu m ct ion .
A2 . I.2 Ma jor De fe c t s . A m a jor de fe c t i8 a
de fe c t . o t he r t h an c r it ic a l, t ha f cou t d re s u lt
in fa ilu r e , o rm at er it lly r edu ce t he u s abilit y
of t he u n it o f p rod u c t for it s in ten ded fm rp obe .
A2. I .3 Minor Defec t s . A m in or de fe c t is
on . t h a t doc n not mater i a l l y reduce t h e u sa -
bili t y of t h e u n it o f p rod u c t fo r it m in t em &d
Pu rpo sa . o r i- d ep r fu rc from s t ab l i s lmd
a t an d ard 9 h a t in g .0 s ign Ui CUIt bOa C in I OrI
t h e e ffe c t ive u .e or ope ra t ion of t h@ un it .
A3 .
PERCENT DE
FECTTVE
A’3 .1 =.PT89 .8 8 . Of NO. CMt fO_
co . Tt i
e$ fcn t of nonconformance of p ro
du es 9 fn ff
be exp re -s cd i. t e rm s of pe rcen t &fae t ive .
A3 .Z Pe rcen t f%.fe e t iwe . Tbe pe rc en t d .-
fec t iv-.~ac t er im t ic of I i%.
lox of p rodv;t ”i. t h ~ n um be r of u n it . o f p rad -
u c t de fe c t iwe for t ha t c fu ra c t c r i. t ic d ivid ed
by t h e t a t a f n um be r o f u n it m o f p rodu c t An d
m ult id im d by on . h un dred . Exp re ss ed
m an
.aua t i o rx Percen: rk fe c t iv8 -
Num be r of Ae fe c t ive a x 1 0 0
Num bs r o f d t m
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.—. — . . .
Mk+m +la
lx Jlfffe 1957
Ad. ACCEPTABLE QUALITT LEVEL
A4 . 1 Acc e@abZc Ou a iil
bwl. Tba =-
a CBOm ln af
value xp r*s .e .i in fa rm . o f p e rc aa t d8 f*c -
t ive .Pc if ie d for
s bigle qu Uit y c ha ra ct er -
ia t ic . Gr t a in n um e r ied va ft ws o; AOL
r=~im g f
ram
.0 4 t o 1S.0 0 pa rce .n t am
hO-a
i. Table A- 1 . Wh e . . ran - of AOL VUW-
i. .p e c ifie d . it d u ll h e t rea t ed s if it wore
equ a l t o t he WdUC of AQL for wh ich
mfa2 i 0 c
p lms re lu -wh ed an d wh ich i~ bc lu ded
wit h in t h e AOL ran ge . Wh en t h e •~c~t e d
AOL i- a pa r t icu la r va lu e ot h e r t b& t ivm e
for wh ich oam plh g p fan m r e fu rn ich ed , t he
AOL, wh ich i- t o be u sed in
pP2 yih g t he
yovi.ion s o f t h is St an da rd , .It afl be ., .h o~
m Table A- 1 .
A4 .2 Spec ify in g AOL1 c . Tin pa r t icu la r AOL
vafu e le be u sed
fo r n gle qu alit y ch ar -
c t a r im tic o f a given p rodu c t m us t be pe e -
ified . fn t h e CM. of a dou ble
Pc i f i . a thm
l imi t . it h . r an AOL va lu e it PcUied fo r
t h e t ot a l p e rc en t d e fec t i.. m u a id a of ba t h
u p~r -d lower spe c ifica t ion Um it a , o . t -e
AOL va lu e . a re sp ec ified . om . fo r t h e
upper
l im i t
an d an ot h e r fo r t h e lower Ifm it .
AS. SUBJ bflmAL OF PRODUCT
A5 . I la t . Th e t s r rn ,,1 ov h a ll n m m n ,vir t -
cp ec t i~lo t , -’ i.e ., a co llec t ion
of
u n it . o f
p rodu c t fr om wh ich s am ple is d r am ad
in ope c~t d t o d e t e rm ”m e com plh rm e wit h fh e
a cc ep t ab ilit y c rit e rio n .
A5 . 1 .1 Form a t ion of Lot s . Each la ; sh a ll,
s fa r m la p r ac t ica ble , con .iwt o f un it . cd
p rodu c t of .in gla t ype , gssd e , ~Ass , s ize ,
or corn po. it k n m an u fac t u re d u n de r e .. e n -
r i.Ily t he sam e con dit im it .
A5 .2 Lot Sis e . Th e lot im 1 . t h a n um be r
of u n it . d p rodu c t in lo t , an d m ay d iffe r
f r em the quant i t y
de .i r.a t md h fbs com t rae t
or o rd e r a , lo t fo r p ro d”c tla r. ,
b ip rne l l t .
or Et he r Pu rpo .. ,.
A6 . LOT ACCEP TABILITY
A6 . I Acce Sabfiit y Cr ife r ien . Th e
cca@-
bilit y o f a lot o f material
i kn i t id br
imapc:kta ddf be de t en n h .d byum of ~
of t h e .am plin g p la it . a . .oe ia f.d~t b. .pec -
ffie d va lu e
of t he
AOL{S). Tbi. St an da rd
p rovid e 8 am pliag p la a . baa ad om baowa 4
b- va r ia bilit y . fn t h e Ia t fa r can
t wo a ffa m at ivo m et +,
m provit id , -
ba red on t h e e t fma i a
of
im fa t t da rd d ov i.
a t ioa and
the die r on lb am rqe
ran ge of
t h e t -fa t e . Th ese .r . r . f. r r e d t o . . t h e
s t an da rd dowia t io . m e t h od an d t be rinse
m et h od . For t h a case of a s in gle cp ee ifie a -
t ia t l u n lit , lb ac c .p t a biu ~ c r it e r ion I-
A6 .2 Ch oice of Sa rn fAim Pla in . Su n pUaB
~D u d PIWCEOU-9 a :e p ro -d ad in d8C -
t ion B if Var idd lit y 1 0 u abn own am d t h e
. t a ad am f de r f.u ion m a t h d is m wd, h Soc -
t icm C U va r iabilit y i wu nbaewn a? id t he r an ge
m at bod i c u ced . an d in Sec fioa D if .a r iabUit y
is bn own . Urdesa ot krwi.e
pc ffied , u n .
b-n va r ia biUt y, d=rd dewia fim m et h od
u n F4 1 r t d p lan s . an d t h e ceef=ablfifv crl -
terbr. d Farm 2 (fo r t h e 9 ic @e sp ec ific at io n
iim it c a se ) Aa if be u sed .
A7 . SAMPLE SELECTION
A7. I Det e rm in a t ion of Sam p le Sis e . Th e
.Un p l. ., - h , t h a m m’lfmr of u n t t m o f prod -
u c t d rawn frc an
lo t . Re t a t i~ sam ph a Iws
m Aes im a t ed by cu t e le t t e r s . Th e
8ampf4
s is e cod= Ie t te r“d epc it ds on
the.inq=ticm
le .ve : an d t h e lot
1=4 . Th ere
m
f iva h-
• f=c t iOale=J~: L U. fU. IV. -d v. f f~e-~
o t h e rwh e pec ffiod Ia -fm ct ien Ieva l IV sh ali
k u sed . Th e
u n p le .i.e cod . le t t e r app li-
cable t o t h e .p c ifi.d iz i.p ec t im l.we l a r id
fo r lo t s of given s is e .h d l be obt a in e d fr om
Ta ble A-2 .
NOTICE-5P. c ia l Rese rva t icm for
Cr it ic a l Ch ara ck rn B1 ic 8 . Tbe Go.e r rm ’i.n t
r e . e .vo. t be
rm hl t o in
sm c t em ryu n it m b-
m k kd h y t h e ;u pp fie r fos c r it ie t i e t ir .c -
t e r imko , uad to re jec t t h e rem ain de r o f t h e
lo t Immed la fe ly a ft e r
defec t is
fou ud . Tbo
GOvem irn en t t im o rc r :r vee t h t r igh t t o am -
p fe fo~ c rit icm f
d. f.c t c evm r y
le t au bm it t ad
by t k
u ppUer a r id t o r e jec t an y I-* if A
sam p le dr .wm t h rnre fr~ is fo -d t o
con ta in
ow or more.
c r it ic t i d a fec t s.
A7 .2 Dr .wim B of Sam ple s . A sam ple 1 0 om .
or m e re u n it . o l p roduc t d rawn from . lo t .
Un It c o f t t n m un fdo Aa2 i be , ,a l~c t ,d wit h -
O* re ard t o
t?bdr
q.safi ty .
Proe . du re fo r 8 t Lm a t fm g 2 2 n p r ee om m
awrage @ cr it e r ia for t icbt an ed an d re -
dweed in . fm c ft a n ba red = t h Um pac t h n
rom iit o o f pm eed in c lot s a re p rovid ed in
Pa r t u f
of
dac t iorm B. C. an d D.
AS. SPECIAL PVOCEOURE POR APPLI-
CATION .F
MIXED VARIABLBS-
AlTT21BLfTES BA?APLJ NG PLANS
8
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lu prwid=d for t in Miad w8*bl9D-
t r lbcuaa -Wunpumg phm m bon 1 8 ad t h a t
tbOM h ,T=t ih A-S a - z-t W dk.]
Condlt lon A. Amptm wwI&mc. oximta
W t bm produ c t cubm it t od fo r
iaapctioa IS
m hc t od by Ch Up fli, Z t O m ea t t fM ,IWXiZ
Ik a t lan lt m it (s ) by c reem ln g p roee m
f r m n Ia rae r qu s .m tit y of p roduc t wh ich 1 .
n ot be in g produ ced wlt bln t ba ,Pc lfica t ion
Ilmlt(al.
Codlt iaQ B. Ot h e r con d lt iorm ads t
tbt
warrant tb=
u , . o f a .a r lablac -
m t t ribu t em • ar a~i4 is *-.
A9 .2 De fin it io n..
A9 .Z. 1 in .pac t lom by At t r lbu t 8s . fn sp ec t ioa
by t ribu te . I* in wpec t koa wbardc.
tba unit
of p roduc t is Ch sd fied s im ply m defec t ive
or m an dc fec t iwe wit h reap ac t t o a given re -
qt iir e .m om 07 s .t o f n qu t rnm en tm .
A9 .Z.Z Min d Var iabla -Attr ib* ln m P 8 c -
t i o n .
t in nd va r im h le
-a t t ribu t es in m p8 ct io n
~m gpcc t ion of
arnfie by
stt
i bu ta
. in
dd it ion t o in sp ec t ion by va r iable . m m lready
m ad . of previo.a unp le , before . de-
e k i,on .ao ~o.,*: ca~qs i iv.o r . *I- c -bili~ ~
M ct ih m t ie . ‘. ‘-
A9 .3 Se le ct io n of Sam p lir t c Plan s . Th e
m iaad *a r lable . . a t t Yi - S -p lm g p lan
s t a ll h
e lec t ed in UCOdUICe wit h t h n
fcdlovim~
A9 .3 .1 Se lec t t h e vs r lableo vn p liag p lm
M ccordu aca wit h Sec t ion
B, C, O, b.
A
lot
mcdm
Ui* ccef%abi
m e of
the fo uo ’wln ’ Com t it ie m . i. .*tL.fic. .
Camdltkm A. 7 bo lot com ~i4 s wit h
t tn app rsp rm ta va r ia b1 4 cca*bllIt y cr l -
terlm of section
B, C. or D.
Caa6itLm
B. Th e Is t cm IPU*s +t b
t be ccep t abif it y c r it a r km of pragrapb
11.1.2 of bAIL-sTD- 05 .
A9 .4 . 1 U Cond it ion A ia n ot a t ie fie d, p ro.
coed ir i a ccord an ce wit h t k
t t t i bu t e
oM’l -
p lir ig p lan t o m ee t Con d it ion B.
A9 .4 .2 lf Con d it ion B ia n ot ca t i;lied , t h e
lot doe n ot m ee t t he 8 cc epabilicy c r lt e r ian .
A9 .5 Se=r lt Y of Iaaopae t ion . Th e p roce -
du re s fo r .ever i ty f m .p ec t i.m re l=rred to
in ~ra r raph A8 are net
ppfic sbl. fo r
m ixed Vazia ble . .a t t r ibum . in m~c t ion .
NOTICE- Wh en Go ue rr m te m t d ra win ..
SPed fiCa t iOm n , or ot hc .r d a t a re u .e4 t a r
UIY prm me ot h e r t h an In con n ec t ion wlt b a
de fin it ely re lam d Gove rn men t p rocu rem en t
opa ra t loa . t h m Lbit .d St a t e s Gow rru n en t
t be=aby im zu r , n o re . pm . ibilit y or m y ob-
liga t ion wbt coevc r ; an d t h e fac t t h a t t h e
Co.e rn nt ezt t m ay h ave form .la t d. f.r n im bed .
or In u Iy way
pp lied t h e a id Lr swi ag s,
wcifica t ion a , or ot h e r da t a (* II@ t . ‘=
rm ~ard ed by im plica t ion or ot he rwim e
in
m Y m -e r lice rm in g t h e t ild e r or an y ot h a r
p c r*On or corpora t ion , or con vey in g an y
r igh t s or p rm is . ion
to
m -n ufbc t ufe , u **.
or
e ll aay pa t en t ed in ven t ion t h u m ay in
m n 7 =*T h ra~-t d t br e t o .
a
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ror spd5 6 d A03 . va3 u .eI
a 23 6 q WiIh in m m u r-go t
— to 0.049
0.050 t o 0.069
0.070 t o 0 .1 0 9
O.lloto 0.164
0.165 t o 0 .Z19
0 .Z8 0 t o 0 .4 3 9
0 .4 4 0 t o 0 .6 9 9
0 .7 0 0 Ie 1 .0 9
1 .1 0 t o 1 .6 4
).6 5 t o 2 .7 9
2.80 t o 4 .3 9
4 .4 0 t o 6 .9 9
7 ,0 0 t o 1 0 .9
1 1 .0 0 t o 1 6 .4
Use t h h AQl
Vazue
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
““”
m
m
61 0 1J OIB35DF31
1 1 1 t o
1 8 0 Be&c I
1 8 1 t o
3 0 0 Et DFH_j
301 to 500 C32GIK
501 to
800 DFHJ L
80 1 t “ 1 .3 0 0
I
EGIKL
1 .3 01 t o
3 .2 0 0 FHJ LM
3 .ZO1 t o 8 .0 0 0 Gl
Lh i N
8 .0 0 1 t o 2 z ,0 0 0 HJ MNO
m
mple .i;e code le t t e r . given in body of
Uble re app li. abze wh en t h e in d ica t ed in -
p t c t im leve lw are t o be “m ed .
4
.
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mL-sm-414
11 Smn 1
TAB- A-S
OpraCinC Clmr.ete.si.tic CtMW9. for Su n @iD* Plan .
o f t %c t i~m B, C, 4 D
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T
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U
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h t t p : /
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s s
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2 0 0 8 - 0
6 -
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VARIABIIJ TY
SSCTIW B
uNKNowN-sTANDAmf DEvlAnoN
Parf I
S INGLE S PE UF 3 CAT1 0 N LUA3T
S1.
SAMPIJNG
PLAN FOR SINGLE
SPECIFICATION LXM ’T
Th i. pAr l Of t h e St an da rd deoc r ibe . t h e
p rocedu r e* fo r u s . wh h p lan i fo r
oingle
ap e .ifiu t ion lim it wh en va r ia bilit y y of fh e
lot wit h re .pe c t t o t h e qu a lit y ch a ra e%er i. -
t ic i. u n k n own n d t h e .t an da rd devia t ion
m et h od ia u ed . Th e a cc ep t abilit y c r it er ion
i. given in t wo equ iva le n t io rm 9. Tbeoe a re
id e n t ified a s Form 1 -d Form .2 .
B1 .1 Use of Sam Pt in fl Pla J w. To de t e r -
m in . wh s t h e r t h e lo t m e=t . t h e cc ep t -
a bilit y c r it e r ion wit h re sp ec t t o
pa r t i c u -
la r qu a lit y c fu ra c t e r is t ic a .u d AQL. -Iu e .
t h e a pp lica ble cam p lin g p lan sh a fJ be u c ed
in
ccordan ce wit h lb. p r ovia ion m of S.c -
u c .n A, Gen e ra i Desc r ip t ion of
Samplmg
Plan. .-d th.. e i n %hi, part Of th. Standard.
B 1 .2 Drawi. .qo f Sam plem . AfI .am plew ha l l
be d rawn in accordan ce -’t h p a r agr aph A7 . Z.
B1 . 3 Det e rm in a t ion of Sam p le Size Code
~. Th e .sm pla
zce cod
l e t t e r
h a
be se le c t e d fr om Table A-Z in c co rd anc e
wit h p a ra s raph A7 . 1 .
B2 SELSCTING THE SAMPLING PM
WHEN FORhf 1 IS USED
BZ. 1 Maa t e r s am plin g Table s . Th = m u t e r
an m lm n t a ble s fo r m lan a ba sed or . -r ia -
bilit ~ -MI for ~ n gle s pe cific at io n
lim it vben u s in g t h e c t a ad a rd devia t ion
me t h o d r e T ab le s B-1 .nd B-Z, Table B- I
in .m =d le r n orm .] an d t igh te r .e d ir iap e c t ion
a r t < Table B - Z for r edu ced
imspeet io i t .
B 2 . Z Obt ain in g
t he Sa? n Plin K
PIan.
Th e
.m np l. t ig p lan con s.s t . .1
.unple .i.e 8d
m
~nociafed
Cc.eptability COtI.unt. 1 The
s am p lin g p lan i. obt a in ed from Ma t e r
Table B-1 -, B-.? .
B2 .2 .1 Sam Ie Sis e . Th e ample . is e - Z*
~h oum m t e m a .,. . t a bl - e o.-. . p -.fin g *O
.-.1 . ..cn ple ic e c u t e t e t t e r .
BS. Z.2 Accepu bility brmant. The acc.p
dility
c oru taa f k . c or r eewm t
. g t o t b emun
p le s ize m en t ion ed ia pn agraph B2 .2 .1 ,
in d icm ed in t h e colum n of t h e n u s t e r t a
cor r e~pm xlin g t o t be app lic able A(2 L va l
Table B-1 i. e n t e r ed from t h e fop fo r n
m a l in opec fion
n d fr om t h e bo t t om
t igh t en ed in sp ec t ion . Sam plin g p lu m for
duced
in spe c t ion a re p rovidd_ in Table B
B3. LOT-BY-WT ACCEPTABILITY PR
CEDURES WHEN PURIM 1 LS USE
B3. 1 Accep t abilit y Cr it er ion . Tbe degr
o f c on fo rm an ce of q
u afit y c b8 ra c t er ic t i
wit h r e sp e c f lo s in gle sp ec ifica t ion lim
.W1 be ju dg.d by t h ~, qu sn t it y (u -XJ I*
fl-L)/ i. .
B 3 .2 . Corn t a t ien . Tt It fo llowin g qu an t
.h a ff b- (“-X)/ ’ ., (x-L)/ . , d
pen d iagon wh e t h e r t he sp e c ifica t ion lim it
~ qpe r o r lower lim it , +e r e
U i. t k u ppe r spe c ifica t ion lim it .
L i- t be lower sp ec ific a t ion lim it ,
X i. t h e sam p le m ean . a n d
. i. t h e .t irn at e o f lot sn &rd de .r la t io
B3 .3 Acc
ability Crite rfon. Cumpare
abifttywmst-nt k. ff (u-x)/m or (x- f.)/a
equal to .ar gre8ter tlun k, the lot meets t
=cc~tiIf.fty criterion: if (U-X)1.** (X-f-)1
ia l.mm Uu8 k or nerative, 3hrm the M &
not meef the •=e~llity c r i t e r ion .
M. t 3 1 J M3 t MRY FOR OPXRATION O
~~MNG PLAN WREN FORM s
Th e foLIowfn r ‘soP* •~m ar is e ‘h e Pr
=~u . . . t . . . . m llowed :
(1 ) Da t e r rn irw t h e sxm ple . i.e code lt
t e r from Table A-2 by um in g t h e le t s is e a
in .p cc fion leee l.
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MIL-m-414
11 Jt333e1957
(2)
Obfa i. Pk . from Mam er Tab)= B-1
or B-z by .e lee t in g t h e sam p le s ize n an d
t he ac . .p t abill$ y con st an t k .
(3 ) Se lec t a t ran dom t h e sam pl= of n
unit. lrorn t h e le t ; in spe c t n d record t h e
m ea . u re r n em of sh e qu a lit y c h arac t er is t ic
fe r each u t iit o f
the sample.
(4 ) Cm n p .t e t h e s .m p Ie mean ~ an d
e s t ima t e
of lot
s t s ”da rd dcvis t ic .n . . an d
ISO com pu t e t h e quan t it y (u -X)1 . fo r an
u pe r sp e c ifica t ion lim it V or t h e q~n t it y
A-L)/ . fo r
k .wer .pe c it ic a t io~ lid s 3 . .
1 5 ) M t h e quan t it y (u -X)/ s o r (X-W.
i. equal co or greater
t h an k , t h e 1 0I m ee t s
t h e
c .e p t .bilicy c r it e r ion : it ’ (u -X)/ . or
(X-L)/. i. [e..
(ha--- k or negat ive, t hes
the
lot doe’ rwtmeel
Ih ea cc ep t t ii lily c rit e r io n.
B5.
SELECTING THE
SAMPL3NG P2AN
WNEN
FOfUd Z 5S
USED
S3 5 .1 h 4a sc c r Sam plin g Table .. Th . m a. t e r
.am pJ mg t able s fo r p la n s ba sed on va r ia bil -
it y u n kn own for a s in gle spe c ifica t ion lim it
wh en u s in g t h e m ~n d -rd deriatitm method
sre Table. B-3
nd
B-4 of Pa r t If. Tsble
B-3 is u se d fo r n orm a l a“d ai~h t en ed
inm pec -
eion
an d Table B-4 .fc .r red uced .in sp ec tion .
B 5 .Z Obla in in ~
t he Sam plin g
Plan .
Th e
sa rn p li”~ p lan co. s s .t s of . .u n p l. , Ize a n d
sn s soc ia t ed m axim um alk .w=ble pe rcen t
d a$ e c live . Th e sam p lin ~ p lm i. ob ta ined
from MaDt e r Table B-3 or B-4 .
6 5 .2 .1 Sam ple Size . T)M
m n p le m ic e n is
h ewn m t h e m a . t c r t a ble co r t e sp en d in ~ 1 0
each sam >le .iz . code le t t e r .
1 3 5 ..? .Z Ma xi m . m Allo w8 ble Percent Defee-
t$ve.
The rrm xim .t n
llowable p .=. en t d e -
=live M for am ple s t im a t e. c or re sp on d .
im g t o t h e .un p le s ize m =n t ion ed in
pa :a grm ph 9 5.2 .1 is it td ica t ed in
t he c olum n
of t h e n m .t e r t a ble .xxr e .pon d iy t g t o t h e
Pp lic=ble AOL va lu e . Tabl. B-3 i. =n t =,.d
from t be t op fo r n orm al in spec t ion -d fr om
t h e bot t om lo, lsghter.ed in. peetion. Sam -
-li>g plan. lcIr reduced i n spec t ion r m p ro -
d-l ea ,. ~a~,e ~-, .
B6 .1 Accep t abilit y Cr it e r ion . Th e dc~re e
of c on fo rm an ce Of a qu a llt y ch ar ac t er is t ic
wit h re sp ec t m
a i.n gle s pe cific at ion lim it
hall
b, ju dged h y t h e pe rcen t o f rm n em -,
Iorm ,n g p rodu c t ou t s id t t h e u ppe r or low+r
cpe c ift ea t ion lim it . Th e pe r cen t age of Ma -
coa fo rming
product is
cs t im at t d by wiie r ia ’
T~le B-5 wit h t h e qu glit y in dex an d t h e
s amp l e
ize .
B6. Z GE-I
u t a t io” o f Qt ufit
~-lity~-X)~rnpE~
if t h e spe c ifica t ion lim it i. a u ppe r lim it
U, or OL . (X- L)/t if it is a Io-e r J im it L.
Th * q ua at it ie .. X
m d s .
r e t h e rnp l .
m e a n n d e .t im m e of lot s t an da rd devia t ion .
re spec t ive ly .
W.
~
-ii-t-d
P.,. em
d.f=~ti- in d
lo t
bove t h e u ppe r sp e c ifica t ion lim it ,
or
by ?z.. th. es t im at ed pe rcen t d e fe c t ive be low
t he lower .p ec ifi ca t ian lim it .
Tb e
s t ima t e d
Pc*.=.: d e fec t ive PU or
PL i .
obt ain ed by
en t e r in a Tabk B-5
w it h Ou or QL
an d t h e
ppropr ia t e anple s ize .
336 . 4
Acceptability Criterion. Gmpare the
es t im at e d lot pe re en t de Ie c t ive pU or pL wit h
t he m axim um allowable pe rc en t d e fec t ive M.
U PU Or Pl, 1 . eqUf t o or lea s
thn U, the
lot rneets the
a cc ep ta bilit y c rit e r io n;
i f Pu
or p~ is greaier t han M or
if Qu or Q is
,n ega t ive , t hen
t he 10: does not meet
\ h e
a cc ep ta bilit y c rit e r io n.
B7 . SIJ 7 1SMARY FOR OPERATION
OF
SAMPL3NG PL.AN WHEN PORM 2 3 S
USED
Th e fe llc .rn ng s t ep . .um rn ar iz .e t he p ro -
cedure. to be fallc.u.ed,
(1 ) De t erm in e t he m ple .i=e code le t -
t e r from Table A-2 byu . in g t h e lot s ize m d
t he in spec t ion leve l.
(Z) Obt a in p la n from Mas t e r T=ble B-3
or B-d by .e le c fi.~ t h e .u n p le .ixa n
attd
t he m axim um allowable pe rc en t d e fe c t ive M.
(3 ) S ele ct
t
ran dom t h e
ample of n
unit. frmn the Io f; in sp ec t UId re cord
t he
m. a s u r e r n emt
of
t h e qua lit y ch a rac t . r im ic
cm each .u n h of t h e
amp l e .
(4 ) Cm npu t e3 h = sam ple m ean X a r id t h e
e c t im a le o f lo t . t a ”d a rd devfa t ia n . .
(5 ) Com pu t e t h e qu a lit y in d ex Q
(U-X)/ *
if n upp. r .p e.ific . t ie , . lim it
J f i:
P.*ifie d . or OL = (x. L)/ . if lc t we rspec -
iiic a t ion 1 ;... ;. L
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Mu.-sm4l4
11
J uoe 1 9
fi) ff t he e . t im a t ed lo t p er ce rn de fec tive
is~r ea t e r t l.an U Orif QuOr C3~ is a ep t i
PU Or PL i. ~ud to or 1... than the max i .
r
h en t h e lot doe . m l m ee t t h e c cepm bi
m um .d lowable p e rc en t d e fe c t ive M.
the lot criterion.
meet. the
cc.pt~bil$ty criteriom if PU Or PL
EXAMPLS B-1
Exm n p le o f Ca lc ufa t io .s
Sin gle Spe c i ica t lon Lim it -Form I
Va r ia bilit y Un kn own - St an da rd Devia t ion
Method
ExAm ple Th e rn .t im um t em pe ra t u r e
o f o per at io n
fo r ce r :a in devic . i. .p e c ifi.d . .? 09 ”
A lot o f 4 0 it em . i. s u bm it t ed fo r in sp ec t ion . Zn . p ec t ion Z-eve l IV, n orm al in sp e c
t ion , wit h AQL = 1 -% i . t o be u , c d .
From Table s A-2
n d B-1 i i. a e e : t h a t
m arn p lc 0 1 s is e 5 i. r equ ired . Su ppose t h e m ea su rem en t . obt a in e d a re
. 1 .s3
Exp lana t ion
(975 )2 / 5
1 90 ,4 3 5 - 1 9 0,1 2
3 1 0 / 4
-s
9 7 5 1 5
[2 0 9 - 1 9 5 )/ S .8 1
S. . Table B-1
Se e Pa r&. B3 .3
Th e lo t rneetm the .cceptabiltty c r it e r ion . m in ce (U. ~)/ s is ~r em t=r t h an k .
NOTE: If n gle lower sp c ffiea t {on lim it L is given . fh e n com pu fe t h e q~n t ilY ~-~)f~ i
Iin . 1 0 -d com ~re il wit h k , t h e lo t m ee t . t h e =cc ep t 8 bilit y *r ii=. iQn . if (~-Ll/ * i
equ a l t o o r gre a fe r t h an k .
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...
TABLE B-1
Standard Deviatiom Methc.d
MIster Table Far Normal &.d
T i~ h te n e d fn . p e ct lo .
for PlaIJsBased on Variability Unknown
[Sin gle Sp ec ific at io n Lim it – Fo rm 1 )
Sample size
code letter
B
c
Ac c e p t ab le (
.25
.40
kk
k
2.00
1.88
2.11 1.98
2.2o 2.06
2.24 ,?,11
3..26 2.14
-
allty
.—
.65
T
$
. CVC IS (n o rma l i n s p ec t i on )
m
Gi-
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,;l5
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
T
0.00 15.00
k k
.566
. 341
. .
.6 1 7 .3 9 3
. 67S
. 4s5
.7 s5 .5 1 6
. 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
1.03
—
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
v
1.34
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
I
.42 2.3?.
1.09
1.12
1.14
+
.886
.664
.917
.69s
.936
.71,?
.946
.723
.969 .145
.971
.746
I
.4 7 2 .3 6
g
2.50 11.40
J
K
2,61
.?.65
?.,66
—
2.71
2.77
2.80
2.51 2.41
1
.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 .4 7 2 .3 3
.4o i .6 5
1.73
1.76
1:76
1.1s
1.18
1.18
I
,54 2.45
L
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 2.61
L
50
zoo
2.96
2.97
—
.065
Z.84
2.85
-t
2.73 2.6.?
.15
.2510
I
,0(
—
alit,
Z.50 ,0.00
A21AOL wdue8 ye knpercent de-a.
AcceptableC lightened inspectio
1:::,
V.V
,tern hth. lot
m u s t b e in s pe ct e d.
[Irst
tunpllq plan belcw
rrow, that is, both sample OIZ.Sas well ao k va2ue. When nample sise equdt er e=ceedo lot ~~
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TABLE 23-2
“S t anda rd Deviallm Method ~E
Maater Table for Reduced lnmc.ectimfor Plana Breed On Varlabilitv Unkmwm
(Sin gle Sp ’c .ifi. .t l.n Lit ni t -F . r m I )
I I
uality Levelo
EEE
“Ac
x
—
k
—
I
SampIe size
I
Sunp l e
Code
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
i
Zoo
Z.11
.40
—.
k
—.
I
—
.—
1,65
i.75
1.84
-L
k
m
I
.$ 8
1.9a
—
1.9a
J+~~
.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
1.50
I
Z.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--
.79
1.6S
1.8Z
1.69
1.8z
1.69
2.06 1.47
.53
t-t
Z.4Z
Z.)z
Z.58
Z.47
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