OPRE 6364 1 Acceptance Sampling
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OPR
E 63
641
Acc
epta
nce
Sampling
OPR
E 63
642
Acc
epta
nce
Sam
plin
g
●Ac
cept
/reje
ct e
ntire
lot b
ased
on
sam
ple
resu
lts●
Cre
ated
by
Dod
ge a
nd R
omig
durin
g W
WII
●N
ot c
onsi
sten
t with
TQ
M o
f Zer
o D
efec
ts●
Doe
s no
t est
imat
e th
e qu
ality
of t
he lo
t
OPR
E 63
643
What
is
acce
pta
nce
sam
plin
g?
Lot A
ccep
tanc
e Sa
mpl
ing
–A
SQC
tech
niqu
e, w
here
a ra
ndom
sam
ple
is
take
n fro
m a
lot,
and
upon
the
resu
lts o
f ap
prai
sing
the
sam
ple,
the
lot w
ill ei
ther
be
reje
cted
or a
ccep
ted
–A
proc
edur
e fo
r sen
tenc
ing
inco
min
g ba
tche
s or
lots
of i
tem
s w
ithou
t doi
ng 1
00%
insp
ectio
n–
The
mos
t wid
ely
used
sam
plin
g pl
ans
are
give
n by
Milit
ary
Stan
dard
(MIL
-STD
-105
E)
OPR
E 63
644
What
is
acce
pta
nce
sam
plin
g?
•Pu
rpos
es–
Det
erm
ine
the
qual
ity le
vel o
f an
inco
min
g sh
ipm
ent o
r at t
he e
nd o
f pro
duct
ion
–Ju
dge
whe
ther
qua
lity
leve
l is
with
in th
e le
vel
that
has
bee
n pr
edet
erm
ined
•Bu
t! A
ccep
tanc
e sa
mpl
ing
give
s yo
u no
idea
abo
ut th
e pr
oces
s th
at is
pr
oduc
ing
thos
e ite
ms!
OPR
E 63
645
Typ
es o
f sa
mplin
g p
lans
•Sa
mpl
ing
by a
ttrib
utes
vs.
sam
plin
g by
va
riabl
es•
Inco
min
g vs
. out
goin
g in
spec
tion
•R
ectif
ying
vs.
non
-rect
ifyin
g in
spec
tion
–W
hat i
s do
ne w
ith n
onco
nfor
min
g ite
ms
foun
d du
ring
insp
ectio
n–
Def
ectiv
es m
ay b
e re
plac
ed b
y go
od it
ems
•Si
ngle
, dou
ble,
mul
tiple
and
seq
uent
ial
plan
s
OPR
E 63
646
How
acc
epta
nce
sam
plin
g
work
s
•At
tribu
tes(
“go
no-g
o” in
spec
tion)
–D
efec
tives
-pro
duct
acc
epta
bilit
y ac
ross
rang
e–
Def
ects
-num
ber o
f def
ects
per
uni
t•
Varia
ble
(con
tinuo
us m
easu
rem
ent)
–U
sual
ly m
easu
red
by m
ean
and
stan
dard
de
viat
ion
OPR
E 63
647
Why
use
acc
epta
nce
sam
plin
g?
•C
an d
o ei
ther
100
% in
spec
tion,
or i
nspe
ct a
sa
mpl
e of
a fe
w it
ems
take
n fro
m th
e lo
t•
Com
plet
e in
spec
tion
–In
spec
ting
each
item
pro
duce
d to
see
if e
ach
item
mee
ts th
e le
vel d
esire
d–
Use
d w
hen
defe
ctiv
e ite
ms
wou
ld b
e ve
ry
detri
men
tal i
n so
me
way
OPR
E 63
648
Why
not
100%
insp
ection?
Prob
lem
s w
ith 1
00%
insp
ectio
n–
Very
exp
ensi
ve–
Can
’t us
e w
hen
prod
uct m
ust b
e de
stro
yed
to
test
–H
andl
ing
by in
spec
tors
can
indu
ce d
efec
ts–
Insp
ectio
n m
ust b
e ve
ry te
diou
s so
def
ectiv
e ite
ms
do n
ot s
lip th
roug
h in
spec
tion
OPR
E 63
649
A L
ot-
by-
Lot
Sam
plin
g P
lan
N(L
ot)
nC
ou
nt
Nu
mb
er
Co
nfo
rmin
g
Acc
ep
t o
rR
eje
ct L
ot
•Sp
ecify
the
plan
(n, c
) giv
en N
•
For a
lot s
ize
N, d
eter
min
e –
the
sam
ple
size
n, a
nd
–th
e ac
cept
ance
num
ber c
. •
Rej
ect l
ot if
num
ber o
f def
ects
> c
•
Spec
ify c
ours
e of
act
ion
if lo
t is
reje
cted
OPR
E 63
6410
The
Sin
gle
Sam
plin
g P
lan
•Th
e m
ost c
omm
on a
nd e
asie
st p
lan
to u
se b
ut n
ot
mos
t effi
cien
t in
term
s of
ave
rage
num
ber o
f sam
ples
ne
eded
•Si
ngle
sam
plin
g pl
anN
= lo
t siz
en
= sa
mpl
e si
ze (r
ando
miz
ed)
c=
acce
ptan
ce n
umbe
rd
= nu
mbe
r of d
efec
tive
item
s in
sam
ple
•R
ule:
If d
≤c,
acc
ept l
ot; e
lse
reje
ct th
e lo
t
OPR
E 63
6411
d≤c
?
Rej
ect l
ot
Yes
Acce
pt lo
t
Do
100%
in
spec
tion
Ret
urn
lot
to s
uppl
ier
Insp
ect a
ll ite
ms
in th
e sa
mpl
eD
efec
tives
foun
d =
d
No
Take
a ra
ndom
ized
sa
mpl
e of
siz
e n
from
the
lot N
The
Sin
gle
Sam
plin
g
pro
cedure
OPR
E 63
6412
Produce
r’s
& C
onsu
mer
’s R
isks
due
to m
ista
ken s
ente
nci
ng
•TY
PE I
ER
RO
R=
P(re
ject
goo
d lo
t)α
or P
rodu
cer’s
risk
5%
is c
omm
on
•TY
PE I
I ER
RO
R=
P(ac
cept
bad
lot)
βor
Con
sum
er’s
risk
10%
is ty
pica
l val
ue
OPR
E 63
6413
Qua
lity
Def
initi
ons
•Ac
cept
ance
qua
lity
leve
l (AQ
L)Th
e sm
alle
st p
erce
ntag
e of
def
ectiv
es th
at w
ill m
ake
the
lot d
efin
itely
acc
epta
ble.
A q
ualit
y le
vel t
hat i
s th
e ba
se li
ne re
quire
men
t of t
he
cust
omer
•R
QL
or L
ot to
lera
nce
perc
ent d
efec
tive
(LTP
D)
Qua
lity
leve
l tha
t is
unac
cept
able
to th
e cu
stom
er
OPR
E 63
6414
How
acc
epta
nce
sam
plin
g w
orks
•R
emem
ber
–Yo
u ar
e no
t mea
surin
g th
e qu
ality
of t
he
lot,
but,
you
are
to s
ente
nce
the
lot t
o ei
ther
reje
ct o
r acc
ept i
t•
Sam
plin
g in
volv
es ri
sks:
–G
ood
prod
uct m
ay b
e re
ject
ed–
Bad
prod
uct m
ay b
e ac
cept
edBe
caus
e w
e in
spec
t onl
y a
sam
ple,
not
th
e w
hole
lot!
OPR
E 63
6415
Acce
ptan
ce s
ampl
ing
cont
d.
•Pr
oduc
er’s
risk
–R
isk
asso
ciat
ed w
ith a
lot o
f acc
epta
ble
qual
ity
reje
cted
•Al
pha
α=
Prob
(com
mitt
ing
Type
I er
ror)
= P
(reje
ctin
g lo
t at A
QL
qual
ity le
vel)
= pr
oduc
ers
risk
OPR
E 63
6416
Acce
ptan
ce s
ampl
ing
cont
d.
•C
onsu
mer
’s ri
sk–
Rec
eive
shi
pmen
t, as
sum
e go
od q
ualit
y, a
ctua
lly b
ad
qual
ity
•Be
ta β
= Pr
ob(c
omm
ittin
g Ty
pe II
erro
r)=
Prob
(acc
eptin
g a
lot a
t RQ
L qu
ality
leve
l) =
cons
umer
s ris
k
The
OC
cur
ve fo
r a s
ampl
ing
plan
qua
ntifi
es th
ese
risks
OPR
E 63
6417
Take
a ra
ndom
ized
sa
mpl
e of
siz
e n
from
th
e lo
t of
unkn
own
qual
ity p
The
Sin
gle
Sam
plin
g
pro
cedure
Insp
ect a
ll ite
ms
in th
e sa
mpl
eD
efec
tives
foun
d =
d
d≤c
? No
Yes
Rej
ect l
ot
Acce
pt lo
t
Ret
urn
lot
to s
uppl
ier
Do
100%
in
spec
tion
OPR
E 63
6418
Oper
atin
g C
har
acte
rist
ic (
OC)
Curv
e
•It
is a
gra
ph o
f the
% d
efec
tive
(p) i
n a
lot o
r bat
ch v
s.
the
prob
abilit
y th
at th
e sa
mpl
ing
plan
will
acce
pt th
e lo
t•
Show
s pr
obab
ility
of lo
t acc
epta
nce
Pa
as fu
nctio
n of
lo
t qua
lity
leve
l (p)
•It
is b
ased
on
the
sam
plin
g pl
an•
Cur
ve in
dica
tes
disc
rimin
atin
g po
wer
of t
he p
lan
•Ai
ds in
sel
ectio
n of
pla
ns th
at a
re e
ffect
ive
in re
duci
ng
risk
•H
elps
to k
eep
the
high
cos
t of i
nspe
ctio
n do
wn
OPR
E 63
6419
Ope
ratin
g C
hara
cter
istic
Cur
ve
AQL
LTPD
β=
0.10
α=
0.05Probability of acceptance, Pa
{
0.60
0.40
0.20
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.80{
Proport
ion d
efec
tive
p
1.00
OC c
urv
e fo
r n
and c
OPR
E 63
6420
Type
s of
OC
Cur
ves
•Ty
pe A
–G
ives
the
prob
abilit
y of
acc
epta
nce
for a
n in
divi
dual
lo
t com
ing
from
fini
te p
rodu
ctio
n•
Type
B–
Giv
e th
e pr
obab
ility
of a
ccep
tanc
e fo
r lot
s co
min
g fro
m a
con
tinuo
us p
roce
ss o
r inf
inite
siz
e lo
t
OPR
E 63
6421
OC
Cur
ve C
alcu
latio
n
The
Way
s of
Cal
cula
ting
OC
Cur
ves
–Bi
nom
ial d
istri
butio
n–
Hyp
erge
omet
ricdi
strib
utio
n•
P a =
P(r
defe
ctiv
es fo
und
in a
sam
ple
of n
)–
Pois
son
form
ula
•P(
r) =
( (np
)re-
np)/
r!–
Lars
on n
omog
ram
OPR
E 63
6422
OC
Cur
ve C
alcu
latio
n by
Po
isso
n di
strib
utio
n
•A
Pois
son
form
ula
can
be u
sed
–P(
r) =
((np)
re-
np) /
r! =
Pro
b(ex
actly
rdef
ectiv
es in
n)
•Po
isso
n is
a li
mit
–Li
mita
tions
of u
sing
Poi
sson
•n≤
N/1
0 to
tal b
atch
•
Littl
e fa
ith in
Poi
sson
pro
babi
lity
calc
ulat
ion
whe
n n
is q
uite
sm
all a
nd p
qui
te la
rge.
•Fo
r Poi
sson
, Pa
= P(
r≤c)
OPR
E 63
6423
p
For u
s, P
a=
P(r≤
c)
OPR
E 63
6424
OC
Cur
ve C
alcu
latio
n by
Bin
omia
l D
istri
butio
n
Not
e th
at w
e ca
nnot
alw
ays
use
the
bino
mia
l di
strib
utio
n be
caus
e•
Bino
mia
ls a
re b
ased
on
cons
tant
pro
babi
litie
s–
N is
not
infin
ite–
p ch
ange
s as
item
s ar
e dr
awn
from
the
lot
OPR
E 63
6425
OC
Cur
ve b
y Bi
nom
ial F
orm
ula
.12
.115
.1
1 .1
62
.10
.223
.0
9 .3
00
.08
.394
.0
7 .5
02
.06
.620
.0
5 .7
39
.04
.845
.0
3 .9
30
.02
.980
.0
1 .9
98
P dP a
Usi
ng th
is fo
rmul
a w
ith n
= 5
2 an
d c=
3 an
d p
= .0
1, .0
2, ..
.,.12
we
find
data
val
ues
as s
how
n on
the
right
. Th
is g
iven
s th
e pl
ot s
how
n be
low
.
OPR
E 63
6426
The
Idea
l OC
Cur
ve
●Id
eal c
urve
wou
ld b
e pe
rfect
ly p
erpe
ndic
ular
fro
m 0
to 1
00%
for a
fra
ctio
n de
fect
ive
= AQ
L●
It w
ill ac
cept
eve
ry lo
t with
p ≤
AQL
and
reje
ct e
very
lo
t with
p >
AQ
L
p AQ
L
1.0
0.0
P a
OPR
E 63
6427
Prop
ertie
s of
OC
Cur
ves
•Th
e ac
cept
ance
num
ber c
and
sam
ple
size
nar
e m
ost
impo
rtant
fact
ors
in d
efin
ing
the
OC
cur
ve•
Dec
reas
ing
the
acce
ptan
ce n
umbe
r is
pref
erre
d ov
er
incr
easi
ng s
ampl
e si
ze•
The
larg
er th
e sa
mpl
e si
ze th
e st
eepe
r is
the
OC
cur
ve
(i.e.
, it b
ecom
es m
ore
disc
rimin
atin
g be
twee
n go
od a
nd
bad
lots
)
OPR
E 63
6428
Prop
ertie
s of
OC
Cur
ves
OPR
E 63
6429
Prop
ertie
s of
OC
Cur
ves
•If
the
acce
ptan
ce
leve
l c is
cha
nged
, th
e sh
ape
of th
e cu
rve
will
chan
ge.
All c
urve
s pe
rmit
the
sam
e fra
ctio
n of
sa
mpl
e to
be
nonc
onfo
rmin
g.
OPR
E 63
6430
Ave
rage
Outg
oin
g Q
ual
ity
(AO
Q)
•Ex
pect
ed p
ropo
rtion
of d
efec
tive
item
s pa
ssed
to
cus
tom
er
•Av
erag
e ou
tgoi
ng q
ualit
y lim
it (A
OQ
L) is
–The
“max
imum
” poi
nt o
n AO
Q c
urve
Nn
Np
Pinspection
rectifying
with
AOQ
a)
(−
=
OPR
E 63
6431
AOQ
Cur
ve
0.01
5AO
QL
Aver
age
Out
goin
gQ
ualit
y0.
010
0.00
5
0.10
0.09
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
AQL
LTPD
(Inco
min
g) P
erce
nt D
efec
tive
OPR
E 63
6432
Dou
ble
Sam
plin
g Pl
ans
•Ta
ke s
mal
l ini
tial s
ampl
e–I
f # d
efec
tives
< lo
wer
lim
it, a
ccep
t–I
f # d
efec
tives
> u
pper
lim
it, re
ject
–If #
def
ectiv
es b
etw
een
limits
, tak
e se
cond
sa
mpl
e
•Ac
cept
or r
ejec
t lot
bas
ed o
n 2
sam
ples
•Le
ss in
spec
tion
than
in s
ingl
e-sa
mpl
ing
OPR
E 63
6433
Mul
tiple
Sam
plin
g Pl
ans
•Ad
vant
age:
Use
s sm
alle
r sam
ple
size
s•
Take
initi
al s
ampl
e–I
f # d
efec
tives
< lo
wer
lim
it, a
ccep
t–I
f # d
efec
tives
> u
pper
lim
it, re
ject
–If #
def
ectiv
es b
etw
een
limits
, re-
sam
ple
•C
ontin
ue s
ampl
ing
until
acc
ept o
r rej
ect l
ot
base
d on
all
sam
ple
data
OPR
E 63
6434
Sequ
entia
l Sam
plin
g
•Th
e ul
timat
e ex
tens
ion
of m
ultip
le
sam
plin
g•
Item
s ar
e se
lect
ed fr
om a
lot o
ne a
t a ti
me
•Af
ter i
nspe
ctio
n of
eac
h sa
mpl
e a
deci
sion
is
mad
e to
acc
ept t
he lo
t, re
ject
the
lot,
or
to s
elec
t ano
ther
item
In S
kip
Lot S
ampl
ing
only
a fr
actio
n of
the
lots
sub
mitt
ed a
re in
spec
ted
OPR
E 63
6435
Cho
osin
g A
Sam
plin
g M
etho
d
•An
eco
nom
ic d
ecis
ion
•Si
ngle
sam
plin
g pl
ans
–hig
h sa
mpl
ing
cost
s•
Dou
ble/
Mul
tiple
sam
plin
g pl
ans
–low
sam
plin
g co
sts
OPR
E 63
6436
Take
a ra
ndom
ized
sa
mpl
e of
siz
e n
from
th
e lo
t of
unkn
own
qual
ity p
Des
ignin
g T
he
Sin
gle
Sam
plin
g
pla
nIn
spec
t all
item
s in
the
sam
ple
Def
ectiv
es fo
und
= d
d≤c
? No
Yes
Rej
ect l
ot
Acce
pt lo
t
Ret
urn
lot
to s
uppl
ier
Do
100%
in
spec
tion
OPR
E 63
6437
Pois
son
dist
ribut
ion
for D
efec
ts
•Po
isso
n pa
ram
eter
: λ=
np•
P(r)
= (n
p)re-
np/r!
= P
rob(
exac
tlyrd
efec
tives
in n
)•
This
form
ula
may
be
used
to fo
rmul
ate
equa
tions
in
volv
ing
AQL,
RQ
L, α
and β
to g
iven
(n, c
).W
e ca
n us
e Po
isso
n ta
bles
to a
ppro
xim
atel
y so
lve
thes
e eq
uatio
ns.
Pois
son
can
appr
oxim
ate
bino
mia
l pr
obab
ilitie
s if
nis
larg
e an
d p
smal
l.Q
. If w
e sa
mpl
e 50
item
s fro
m a
larg
e lo
t, w
hat i
s th
e pr
obab
ility
that
2 a
re d
efec
tive
if th
e de
fect
rate
(p) =
.0
2? W
hat i
s th
e pr
obab
ility
that
no
mor
e th
an 3
de
fect
s ar
e fo
und
out o
f the
50?
OPR
E 63
6438
Hyp
erge
omet
ricD
istri
butio
n•
Hyp
erge
omet
ricfo
rmul
a:
rdef
ectiv
es in
sam
ple
size
nw
hen
Mde
fect
ives
are
in N
.•
This
dis
tribu
tion
is u
sed
whe
n sa
mpl
ing
from
a s
mal
l po
pula
tion.
It i
s us
ed w
hen
the
lot s
ize
is n
ot s
igni
fican
tly
grea
ter t
han
the
sam
ple
size
. •
(Can
’t as
sum
e he
re e
ach
new
par
t pic
ked
is u
naffe
cted
by
the
earli
er s
ampl
es d
raw
n).
Q. A
lot o
f 20
tires
con
tain
s 5
defe
ctiv
e on
es (i
.e.,
p =
0.25
).If
an in
spec
tor r
ando
mly
sam
ples
4 it
ems,
wha
t is
the
prob
abilit
y of
3 d
efec
tive
ones
?
−−
=
NnMr
MN
rn
rP)
(
OPR
E 63
6439
Sam
plin
g Pl
an D
esig
n by
Bin
omia
l D
istri
butio
n
•Bi
nom
ial d
istri
butio
n:P(
xde
fect
ives
inn)
= [n
!/(x!
(n-x
))!]p
x (1-p
)n-x
Rec
all
n!/(x
!(n-x
))! =
way
s to
cho
ose
xin
n
Q. I
f 4 s
ampl
es (i
tem
s) a
re c
hose
n fro
m a
po
pula
tion
with
a d
efec
t rat
e =
.1, w
hat i
s th
e pr
obab
ility
that
a)
exac
tly 1
out
of 4
is d
efec
tive?
b)
at m
ost 1
out
of 4
is d
efec
tive?
OPR
E 63
6440
Solv
ing
for (
n, c
)
To d
esig
n a
sing
le s
ampl
ing
plan
we
need
two
poin
ts.
Typi
cally
thes
e ar
e p 1
= AQ
L, p
2=
LTPD
and
,
ar
e th
e Pr
oduc
er's
Ris
k (T
ype
I erro
r)an
d C
onsu
mer
's R
isk
(Typ
e II
erro
r), re
spec
tivel
y. B
y bi
nom
ial f
orm
ulas
, n a
nd c
are
th
e so
lutio
n to
Thes
e tw
o si
mul
tane
ous
equa
tions
are
non
linea
r so
ther
e is
no
sim
ple,
dire
ct s
olut
ion.
The
Lar
son
nom
ogra
mca
n he
lp u
s he
re.
OPR
E 63
6441
The
Lars
on
Nom
ogra
m
●Ap
plie
s to
sin
gle
sam
plin
g pl
an●
Base
d on
bin
omia
l di
strib
utio
n●
Use
s1-α
= P a
at A
QL
β=
P aat
RQ
L●
Can
pro
duce
OC
cu
rve
OPR
E 63
6442
Def
initi
ons
and
Term
sR
efer
ence
: N
IST
Engi
neer
ing
Stat
istic
s H
andb
ook
Acc
epta
ble
Qua
lity
Leve
l (A
QL)
: The
AQ
L is
a p
erce
nt
defe
ctiv
e th
at is
the
base
line
requ
irem
ent f
or th
e qu
ality
of
the
prod
ucer
's p
rodu
ct. T
he p
rodu
cer w
ould
like
to
desi
gn a
sam
plin
g pl
an s
uch
that
ther
e is
a h
igh
prob
abilit
y of
acc
eptin
ga
lot t
hat h
as a
def
ect l
evel
less
th
an o
r equ
al to
the
AQL.
Lot T
oler
ance
Per
cent
Def
ectiv
e (L
TPD
) als
o ca
lled
RQ
L (R
ejec
tion
Qua
lity
Leve
l): T
he L
TPD
is a
de
sign
ated
hig
h de
fect
leve
l tha
t wou
ld b
e un
acce
ptab
le
to th
e co
nsum
er. T
he c
onsu
mer
wou
ld li
ke th
e sa
mpl
ing
plan
to h
ave
alo
w p
roba
bilit
y of
acc
eptin
ga
lot w
ith a
de
fect
leve
l as
high
as
the
LTPD
.
OPR
E 63
6443
Type
I Er
ror (
Prod
ucer
's R
isk)
: Thi
s is
the
prob
abilit
y,
for a
giv
en (n
, c) s
ampl
ing
plan
, of r
ejec
ting
a lo
t tha
t has
a
defe
ct le
vel e
qual
to th
e AQ
L. T
he p
rodu
cer s
uffe
rs
whe
n th
is o
ccur
s, b
ecau
se a
lot w
ith a
ccep
tabl
e qu
ality
w
as re
ject
ed. T
he s
ymbo
l
is c
omm
only
use
d fo
r the
Ty
pe I
erro
r and
typi
cal v
alue
s fo
r
rang
e fro
m 0
.2 to
0.
01.
Type
II E
rror
(Con
sum
er's
Ris
k):T
his
is th
e pr
obab
ility,
fo
r a g
iven
(n, c
) sam
plin
g pl
an, o
f acc
eptin
g a
lot w
ith a
de
fect
leve
l equ
al to
the
LTPD
. The
con
sum
er s
uffe
rs
whe
n th
is o
ccur
s, b
ecau
se a
lot w
ith u
nacc
epta
ble
qual
ity w
as a
ccep
ted.
The
sym
bol
is
com
mon
ly u
sed
for t
he T
ype
II er
ror a
nd ty
pica
l val
ues
rang
e fro
m 0
.2 to
0.
01.
OPR
E 63
6444
Ope
ratin
g C
hara
cter
istic
(OC
) Cur
ve: T
his
curv
e pl
ots
the
prob
abilit
y of
acc
eptin
g th
e lo
t (Y-
axis
) ver
sus
the
lot f
ract
ion
or p
erce
nt d
efec
tives
(X-a
xis)
.
The
OC
cur
ve is
the
prim
ary
tool
for d
ispl
ayin
g an
d in
vest
igat
ing
the
prop
ertie
s of
a s
ampl
ing
plan
.
OPR
E 63
6445
Ave
rage
Out
goin
g Q
ualit
y (A
OQ
): A
com
mon
pr
oced
ure,
whe
n sa
mpl
ing
and
test
ing
is n
on-
dest
ruct
ive,
is to
100
% in
spec
t rej
ecte
d lo
ts a
nd re
plac
e al
l def
ectiv
es w
ith g
ood
units
. In
this
cas
e, a
ll re
ject
ed
lots
are
mad
e pe
rfect
and
the
only
def
ects
left
are
thos
e in
lots
that
wer
e ac
cept
ed. A
OQ
'sre
fer t
o th
e lo
ng te
rm
defe
ct le
vel f
or th
is c
ombi
ned
LASP
and
100
%
insp
ectio
n of
reje
cted
lots
pro
cess
. If a
ll lo
ts c
ome
in
with
a d
efec
t lev
el o
f exa
ctly
p, a
nd th
e O
C c
urve
for t
he
chos
en (n
,c) L
ASP
indi
cate
s a
prob
abilit
y p a
of
acce
ptin
g su
ch a
lot,
over
the
long
run
the
AOQ
can
easi
ly b
e sh
own
to b
e:
whe
re N
is th
e lo
t siz
e.
OPR
E 63
6446
Ave
rage
Out
goin
g Q
ualit
y Le
vel (
AO
QL)
: A p
lot o
f the
AO
Q(Y
-axi
s) v
ersu
s th
e in
com
ing
lot p
(X-a
xis)
will
star
t at
0 fo
r p=
0, a
nd re
turn
to 0
for p
= 1
(whe
re e
very
lot i
s 10
0% in
spec
ted
and
rect
ified
). In
bet
wee
n, it
will
rise
to a
m
axim
um. T
his
max
imum
, whi
ch is
the
wor
st p
ossi
ble
long
term
AO
Q, i
s ca
lled
the
AOQ
L.
Ave
rage
Tot
al In
spec
tion
(ATI
): W
hen
reje
cted
lots
are
10
0% in
spec
ted,
it is
eas
y to
cal
cula
te th
e AT
Iif l
ots
com
e co
nsis
tent
ly w
ith a
def
ect l
evel
of p
. For
a s
ampl
ing
plan
(n
, c) w
ith a
pro
babi
lity
p aof
acc
eptin
g a
lot w
ith d
efec
t le
velp
, we
have
ATI=
n +
(1 -
p a) (
N -
n)w
here
Nis
the
lot s
ize.
OPR
E 63
6447
Ave
rage
Sam
ple
Num
ber (
ASN
): Fo
r a s
ingl
e sa
mpl
ing
plan
(n, c
) we
know
eac
h an
d ev
ery
lot h
as a
sam
ple
of
size
nta
ken
and
insp
ecte
d or
test
ed. F
or d
oubl
e, m
ultip
le
and
sequ
entia
l pla
ns, t
he a
mou
nt o
f sam
plin
g va
ries
depe
ndin
g on
the
num
ber o
f def
ects
obs
erve
d. F
or a
ny
give
n do
uble
, mul
tiple
or s
eque
ntia
l pla
n, a
long
term
ASN
can
be c
alcu
late
d as
sum
ing
all l
ots
com
e in
with
a d
efec
t le
vel o
f p. A
plo
t of t
he A
SN, v
ersu
s th
e in
com
ing
defe
ct
leve
l p, d
escr
ibes
the
sam
plin
g ef
ficie
ncy
of a
giv
en lo
t sa
mpl
ing
sche
me.
OPR
E 63
6448
The
MIL
-STD
-105
E ap
proa
chA
Que
ry fr
om a
Pra
ctiti
oner
: Se
lect
ing
AQ
L (a
ccep
tabl
e qu
ality
leve
ls)
I'd li
ke s
ome
guid
ance
on
sele
ctin
g an
acc
epta
ble
qual
ity le
vel a
nd in
spec
tion
leve
ls w
hen
usin
g sa
mpl
ing
proc
edur
es a
nd ta
bles
. For
exa
mpl
e, w
hen
I use
M
IL-S
TD-1
05E,
how
do
I to
deci
de w
hen
I sho
uld
use
GI,
GII
or S
2, S
4?
--C
onfu
sed
in C
olum
bus,
Ohi
oW
. Edw
ards
Dem
ing
obse
rved
that
the
mai
n pu
rpos
e of
MIL
-STD
-105
was
to
beat
the
vend
or o
ver t
he h
ead.
"Y
ou c
anno
t im
prov
e th
e qu
ality
in th
e pr
oces
s st
ream
usi
ng th
isap
proa
ch,"
caut
ions
Don
Whe
eler
, aut
hor o
f Und
erst
andi
ng S
tatis
tical
Pro
cess
Con
trol
(SPC
Pre
ss, 1
992)
. "N
eith
er c
an y
ou s
ucce
ssfu
lly fi
lter o
ut th
e ba
d st
uff.
Abou
t the
onl
y pl
ace
that
this
pro
cedu
re w
ill he
lp is
in tr
ying
to d
eter
min
e w
hich
bat
ches
hav
e al
read
y be
en s
cree
ned
and
whi
ch b
atch
es a
re ra
w,
unsc
reen
ed, r
un-o
f-the
-mill
bad
stuf
f fro
m y
our s
uppl
ier.
I tau
ght t
hese
te
chni
ques
for y
ears
but
hav
e re
pent
ed o
f thi
s er
ror i
n ju
dgm
ent.
The
only
ap
prop
riate
leve
ls o
f ins
pect
ion
are
all o
r non
e. A
nyth
ing
else
is ju
st p
layi
ng
roul
ette
with
the
prod
uct."
OPR
E 63
6449
MIL
-STD
-105
E•
Orig
inal
ver
sion
(MIL
STD
105
A) is
sued
in 1
950
as
tabl
es; L
ast v
ersi
on (M
IL S
TD 1
05E)
in 1
989;
ISO
ad
opte
d it
as IS
O 2
859
•Pl
an c
over
s sa
mpl
ing
by a
ttrib
utes
for g
iven
lot s
ize
(N)
and
acce
ptab
le q
ualit
y le
vel (
AQL)
.•
Pres
crib
es s
ampl
e si
ze n
, acc
epta
nce
num
ber c
, and
re
ject
ion
num
ber r
•St
anda
rd in
clud
ed th
ree
type
s of
insp
ectio
n—no
rmal
, tig
hten
ed a
nd re
duce
d an
d gi
ves
switc
hing
rule
s•
Plan
s as
sure
pro
duce
r’s ri
sk (α
) of 0
.01
–0.
1. T
he o
nly
way
to c
ontro
l the
con
sum
er’s
risk
(β) i
s to
cha
nge
insp
ectio
n le
vel
OPR
E 63
6450
AQL
Acce
ptan
ce S
ampl
ing
by
Attri
bute
s by
MIL
STD
105
E
•D
eter
min
e lo
t siz
e N
and
AQ
L fo
r the
task
at h
and
•D
ecid
e th
e ty
pe o
f sam
plin
g—si
ngle
, dou
ble,
etc
.•
Dec
ide
the
stat
e of
insp
ectio
n (e
.g. n
orm
al)
•D
ecid
e th
e ty
pe o
f ins
pect
ion
leve
l (us
ually
II)
•Lo
ok a
t Tab
le K
for s
ampl
e si
zes
•Lo
ok a
t the
sam
plin
g pl
ans
tabl
es (e
.g. T
able
IIA)
•R
ead
n, A
c an
d R
e nu
mbe
rs
OPR
E 63
6451
MIL
-STD
-105
E
OPR
E 63
6452
OPR
E 63
6453
How
/When
would
you u
se
Acc
epta
nce
Sam
plin
g?
•Ad
vant
ages
of a
ccep
tanc
e sa
mpl
ing
–Le
ss h
andl
ing
dam
ages
–Fe
wer
insp
ecto
rs to
put
on
payr
oll
–10
0% in
spec
tion
cost
s ar
e to
hig
h–
100%
test
ing
wou
ld ta
ke to
long
•Ac
cept
ance
sam
plin
g ha
s so
me
disa
dvan
tage
s–
Ris
k in
clud
ed in
cha
nce
of b
ad lo
t “ac
cept
ance
” and
go
od lo
t “re
ject
ion”
–Sa
mpl
e ta
ken
prov
ides
less
info
rmat
ion
than
100
%
insp
ectio
n
OPR
E 63
6454
Sum
mar
y
•Th
ere
are
man
y ba
sic
term
s yo
u ne
ed to
kno
w
to b
e ab
le to
und
erst
and
acce
ptan
ce s
ampl
ing
–SP
C, A
ccep
t a lo
t, R
ejec
t a lo
t, C
ompl
ete
Insp
ectio
n,
AQL,
LTP
D, S
ampl
ing
Plan
s, P
rodu
cer’s
Ris
k,
Con
sum
er’s
Ris
k, A
lpha
, Bet
a, D
efec
t, D
efec
tives
, At
tribu
tes,
Var
iabl
es, A
SN, A
TI.
OPR
E 63
6455
Use
ful lin
ks
http
://w
ww
.bio
ss.s
ari.a
c.uk
/sm
art/u
nix/
mse
qacc
/slid
es/fr
ames
.htm
Acce
ptan
ce S
ampl
ing
Ove
rvie
w T
ext a
nd A
udio
http
://ie
w3.
tech
nion
.ac.
il/sq
conl
ine/
mils
td10
5.ht
ml
Onl
ine
calc
ulat
or fo
r acc
epta
nce
sam
plin
g pl
ans
http
://w
ww
.sta
ts.u
wo.
ca/c
ours
es/s
s316
b/20
02/a
ccep
t_02
red.
Acce
ptan
ce s
ampl
ing
mat
hem
atic
al b
ackg
roun
d
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