Acceptance Sampling plans

Nestlé Research Center

Acceptance Sampling plans


Konsep Dasar

Prosedur pengambilan keputusan thdp produk

yg datang atau sudah dihasilkan perusahaan

Ada 3 metode :

1. Tanpa inspeksi

2. Inspeksi 100%

3. Sampel penerimaan (Acceptance Sampling)


Acceptance Sampling

Bukan alat pengendalian/teknik perbaikan

kualitas

Sbg alat inspeksi bahan baku/produk sesuai dg

spesifikasi atau tidak

Bentuk inspeksi antara prsh dg supplier,

konsumen atau antar divisi dalam prsh

Dasar perkiraan keputusan penerimaan atau

penolakan produk


Alasan Penggunaan...

Pengujian destruktif

Biaya inspeksi tinggi

100% inspeksi butuh waktu lama

Uji kinerja prsh thdp produk yg dihasilkan


Keunggulan...

Lebih murah

Minimalkan kerusakan dan perpindahan

tangan

Mengurangi kesalahan inspeksi

Memotivasi supplier bila ada penolakan bahan

baku


Kelemahan...

Resiko penerimaan produk “cacat” dan

penolakan produk “baik”

Informasinya “sedikit” ttg produk

Butuh perencanaan dan dokumentasi prosedur

pengambilan sampel


Macam pengujian...

1. The PRODUCER TEST

Sebelum produk dikirim ke konsumen

2. The CONSUMER TEST

Setelah produk dipakai oleh konsumen

Nestlé Research CenterJanuary 2004 NRC PGi8

Types of Acceptance sampling plan

C la ssif ica tio n o f a cce p tan ce sa m p lin g p la ns

Single

Double, m ultiple

Sequential

Item sam pling

Bulk sam pling

By attributes By variables

Acceptance sam pling plans


Sampling by attributes concept

sampling Inspect & count number of defectives

Acceptance number

Accept lotReject lot

N

n

c

Nestlé Research CenterJanuary 2004 NRC PGi

Acceptance Sampling methodA C C E P T A N C E S A M P L IN G

A C C E P T L O T

R E T U R N L O T T O S U P P L IE R 1 0 0 % IN S P E C T IO N

D E C IS IO N

R E JE C T L O T S A M P LE A G A IN

D E C IS IO N

IN S P E C T S A M P LET yp e t it le h e re

T A K E S A M P LE


A Two-Stage Acceptance Sampling

Inspect Inspect nn11 items items

Find Find xx11 defective items in this sample defective items in this sample

xx11 << cc11 ? ?

xx11 >> cc22 ? ?

Inspect Inspect nn22 additional items additional items

AcceptAcceptthe lotthe lot

RejectRejectthe lotthe lot

xx1 1 + + xx22 << cc33 ? ?

Find Find xx22 defective items in this sample defective items in this sample

YesYes

YesYesNoNo

NoNo

NoNoYesYes

FirstFirstStageStage

SecondSecondStageStage


The Outcomes of Acceptance SamplingThe Outcomes of Acceptance Sampling

Type I and Type II ErrorsType I and Type II Errors

CorrectCorrectDecisionDecision

Type II ErrorType II ErrorAccepting aAccepting a

Poor-quality lotPoor-quality lot

CorrectCorrectDecisionDecision

Type I ErrorType I ErrorRejecting aRejecting a

Good-quality lotGood-quality lot

RejectReject HH00

Reject the LotReject the Lot

AcceptAccept HH00

Accept the LotAccept the Lot

HH0 0 TrueTrueGood-Quality LotGood-Quality Lot

HH0 0 FalseFalsePoor-Quality LotPoor-Quality LotDecisionDecision

State of the LotState of the Lot


Indeks Kualitas AS

AQL (Acceptable Quality Level) Tipe I Error

LQL (Limiting Quality Level) Tipe II Error

IQL (Indifference Quality Level)

AOQL (Average Outgoing Quality Level)


AQL (tipe I Error)

Tingkat kualitas menurut produsen

Proporsi maksimum dari kesalahan/cacat yg

diperbolehkan

Probabilitas penerimaan produsen 95-99%

% maksimum ketidaksesuaian per 100 unit produk

Resiko produsen (α) = resiko yg diterima produsen

krn menolak produk BAIK

Jika AQL kecil, Pa mendekati 1.

Probabilitas kesalahan tipe I =α=1-Pa sekitar

0,05/0,01


LQL (Tipe II Error)

LTPD (Lot Tolerance Percent Defective)

Tingkat kualitas menurut konsumen

Kualitas ketidakpuasan/tgk penolakan dg LQL rendah

Resiko Konsumen (β) = resiko dialami konsumen krn

terpaksa menerima produk CACAT / tidak sesuai

β=probabilitas menerima produk cacat pd LQL

Jika p (prob.menolak produk CACAT) besar, konsumen

ingin Pa mendekati 0 (kecil biasanya 0,1)


IQL

Tingkat kualitas antara AQL dan LQL

Tingkat kualitas pd probabilitas penerimaan 0,5

untuk rencana sampel ttt

Fokus pd supplier internal dan eksternal bhw

produk yg diinspeksi diharapkan dpt memenuhi

spesifikasi


AOQL

Perkiraan hubungan bagian kesalahan produk

sebelum inspeksi (INCOMING QUALITY) atau p dari

bagian sisa kesalahan stlh inspeksi (OUTGOING

QUALITY)

AOQ = p x Pa

Incoming Quality BAIK--> Outgoing Quality HRS BAIK

Incoming Quality BURUK-->Outgoing Quality TETAP

BAIK (asumsi tdk ada kesalahan selama inspeksi)


Evaluasi Kinerja Sampel

Bermacam-macam pengukuran :

1. Kurva OC (Operating Characteristic)

2. Kurva AOQ (Average Outgoing Quality)

3. Kurva ATI (Average Total Inspection)

4. Kurva ASN (Average Sample Number)


OC Curve Kurva Karakteristik Operasi

Kurva probabilitas penerimaan thdp produk yg

dihasilkan

Hubungan antara Pa dan p

Rumus Pa = P(d ≤ c)

Pa = probabilitas penerimaan

c = cacat produk maksimum yg disyaratkan

d = jumlah cacat yg terjadi

p = bagian kesalahan dalam produk


Binomial Probability Function for Acceptance Sampling

Probability of Accepting a Lot (Pa)

f xn

x n xp px n x( )

!!( )!

( )( )

1

where:where:nn = sample size = sample sizepp = proportion of defective items in lot = proportion of defective items in lotxx = number of defective items in sample = number of defective items in sample

ff((xx) = probability of ) = probability of xx defective items in sample defective items in sample


Pa = P (d ≤ c)

Pa = ∑ n! Pd (1-p) n-d

d! (n-d)!

Nilai Pa terlihat pada Tabel DISTRIBUSI BINOMIAL


Operating Curves

Operating Curve

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.00% 0.02% 0.04% 0.06% 0.08% 0.10% 0.12% 0.14%

Expected proportion of defectives

Pro

bab

ilit

y o

f ac

cep

tan

ce:

P(.

)

c=0

c=1

c=2

c=3


= 0.05 producer’s risk for AQL

= 0.10

Consumer’s risk for LTPD

Probability of Acceptance

Percent Defective

Bad lotsIndifference zoneGood lots

LTPDAQL

0 1 2 3 4 5 6 7 8

10095

75

50

25

10

0


OC Curves for Different Sampling Plans

1 2 3 4 5 6 7 8 9 100

% Defective in Lot

P(Accept Whole Shipment)

100%

0%

LTPDAQL

n = 50, c = 1

n = 100, c = 2


AOQ Curve

Mengukur rata-rata tgk kualitas output dr hasil

produksi yg banyak dg proporsi kerusakan p

N - byknya unit yg dihasilkan

n - unit sampel yg diinspeksi

p - bagian kesalahan/kerusakan = p

Pa – probabilitas penerimaan = Pd

N

)nN)(P)(P(AOQ ad


Contoh ...Single Sampling

Diketahui N = 2000 n = 50 c = 2Proporsi kesalahan np' Probabilitas penerimaan (Pa)

0,01 0,05 0.990,02 1,00 0.920,03 1,50 0.81

0,10 5,00 0.130,11 5,50 0.09

0,15 7,50 0.02

Secara TABELARIS


Secara MATEMATIS

Pa = P (d ≤ c)

Pa = ∑ n! Pd (1-p) n-d

d! (n-d)!

Maka P (d ≤ 2 ) = P (d =0,1,2) = P(d=0)+P(d=1)+P(d=2) = 0,544

Asumsi p = 0,05

P(d=0) = 50! (0,05)0(1-0,05) (50-0) =

0! (50-0)!

P(d=1) = 50! (0,05)1(1-0,05) (50-1) =

1! (50-1)!

P(d=2) = 50! (0,05)2(1-0,05) (50-2) =

2! (50-2)!


Example: Acceptance Sampling Example: Acceptance Sampling

An inspector takes aAn inspector takes a sample sample

of 20 items from a lotof 20 items from a lot. His. His

policy is to accept a lot ifpolicy is to accept a lot if

no more than 2 defectiveno more than 2 defective

items are found in the sample.items are found in the sample.

Assuming that Assuming that 5 percent of a5 percent of a

lot is defectivelot is defective, what is the probability that he , what is the probability that he willwill

accept a lot? Reject a lot?accept a lot? Reject a lot?


Secara TABELARIS

np = (20)(0,05) = 1 Pa = .920



0 (20 0)20!(0) .05 (1 .05) .3585

0!(20 0)!f

1 (20 1)20!

(1) .05 (1 .05) .37741!(20 1)!

f

2 (20 2)20!(2) .05 (1 .05) .1887

2!(20 2)!f

PP(Accept Lot) = .3585 + .3774 + .1887 = .9246(Accept Lot) = .3585 + .3774 + .1887 = .9246

PP(Accept Lot) = (Accept Lot) = ff(0) + (0) + ff(1) + (1) + ff(2)(2)

n n = 20, = 20, cc = 2, and = 2, and pp = 5% (.05) = 5% (.05)


n n = 20, = 20, cc = 2, and = 2, and pp = .05 = .05


PP(Reject Lot) = 1 – (Reject Lot) = 1 – PP(Accept Lot)(Accept Lot)

= 1 - .9246 = 1 - .9246

= .0754= .0754


Double-sampling plans Contoh :

n1= 50 c1 = 1

n2 = 100 c2 = 3


Secara TABELARIS

P` = 0,01--> n1p` = 0,5

n2p` = 1,0

Sampling I Sampling II TotalPa Total Pa(I) Pa (II)

p ≤ 1 ,910,076

- - ,910p ≤ 2 ,986 p ≤ 1 ,736 ,056p ≤ 3 ,998 ,012p ≤ 0 ,368 ,004Jumlah ,970

p ≤ c p ≤ c


P` = 0,02--> n1p` = 1,0

n2p` = 1,5


p ≤ 1 ,736,184

- - ,736p ≤ 2 ,920 p ≤ 1 ,406 ,075p ≤ 3 ,981 ,061p ≤ 0 ,135 ,008Jumlah ,819

p ≤ c p ≤ c


P` = 0,06--> n1p` = 3,0

n2p` = 6,0


p ≤ 1 ,199,224

- - ,199p ≤ 2 ,423 p ≤ 1 ,017 ,004p ≤ 3 ,647 ,224p ≤ 0 ,002 ,0005Jumlah ,2035

p ≤ c p ≤ c


P =0,08 n1p = 50.0,08 = 4,0

n2p = 100.0,08= 8,0

Sampling I Sampling II Total

P (d ≤

c)

Pa Tot Pa-I P (d ≤

c)

Tot Pa (II)

P (d

≤1)

.092 .092 - - .092

P (d

≤2)

.238 .146 P (d ≤1) .003 .00044

P (d

≤3)

.433 .195 P (d ≤0) 0 0

Jumlah .09244


Single Sampling dg N = 5000 n =40 c =4 ( asumsi

p = 0,01 ; 0,05 ; 0,6 scr matematis dan tabel)

Double Sampling dg N = 5000

n1 = 40 c 1 = 1

n2 = 60 c2 = 5

dg p = 0,01 ; 0,04 ; 0,6 scr tabel

Documents

Acceptance Sampling plans