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.

pdf

Acce

ptan

ce s

ampl

ing

mat

hem

atic

al b

ackg

roun

d