JF608: Quality Control - Unit 5

www.themegallery.com
UNIT 5 :UNIT 5 :
ACCEPTANCE SAMPLING
© Mechanical Engineering Department

LOGOOUTLINEOUTLINE
 Introduction
 Advantages and Disadvantages
 Sampling Plans
 Operating Characteristic Curve (OCC)
 Single Sampling Plans

LOGOINTRODUCTIONINTRODUCTION
 Acceptance sampling is a process that helps
to determine whether to accept or reject the
sample being observed
DefinitionDefinition

 Determine quality level
 Ensure quality is within predetermined level
PurposePurpose

 Untuk menentukan penerimaan & kualiti
bahan mentah yang masuk
produk separa-siap
produk siap yang keluar
 Untuk mengawal & memperbaiki kualiti
produk
Kegunaan PenerimaanKegunaan Penerimaan
PersampelanPersampelan

1. Homogenus
 semua proses mesti sama
2. Lot dalam jumlah yang besar
 supaya dapat mengurangkan kos
pemeriksaan
Syarat Persampelan Pada LotSyarat Persampelan Pada Lot

1. Membahagi produk kepada ‘inspection lots’.
2. Ambil sampel dari setiap lot secara rawak.
3. Buat pemeriksaan dan tentukan kualiti.
4. Terima atau tolak berdasarkan pemeriksaan
terhadap sampel.
Langkah Dalam OperasiLangkah Dalam Operasi
PersampelanPersampelan

LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
AdvantagesAdvantages DisadvantagesDisadvantages
Economical and take less time Risks of accepting “bad” lots
and rejecting “good” lots
Less handling damage Added planning and
documentation
Fewer inspectors Sample provides less
information than 100-percent
inspection
Applicability to destructive
testing
Entire lot rejection (motivation
for improvement)
Reduce the amount of
inspection error

LOGOSTATISTICAL SAMPLING DATASTATISTICAL SAMPLING DATA
 Sampling to accept or reject the immediate lot of
product at hand.
 Go / no-go classification
each part either classified as defective or good
classification can be based on a set of attributes
 Attributes
 Defectives - refers to the acceptability of product
across a range of characteristics
 Defects - refers to the number of defects per lot,
may be higher than the number of defectives

LOGO
Defect merupakan sebarang ‘non-conforming unit’ bagi
produk terhadap piawaian.
1.Kerosakan kritikal :
memberi kesan terhadap keadaan merbahaya dan tidak
selamat untuk pengguna produk tersebut.
2.Kerosakan major :
memberikan kesan terhadap kegagalan produk dari segi
fungsinya.
3.Kerosakan minor :
memberi kesan terhadap ketrampilan tetapi tidak pada
funsinya.
Jenis-Jenis Kerosakan / KecacatanJenis-Jenis Kerosakan / Kecacatan
(Defect)(Defect)
STATISTICAL SAMPLING DATASTATISTICAL SAMPLING DATA

When can acceptance sampling be applied?When can acceptance sampling be applied?
At any point in production
The output of one stage is the input of the
next

Sampling at the Input stage
 Prevents goods that don’t meet standards
from entering into the process
 This saves rework time and money

Sampling at the Output stage
 Can reduce the risk of bad quality being
passed on from the process to a consumer
 This can prevent the loss of prestige,
customers, and money

Sampling at the Process stage
 Can help adjust the process and reduce the
amount of poor quality in production
 Helps to determine the source of bad
production and enables return for
reprocessing before any further costs may be
incurred

Lot received for inspection
Sample selected and analyzed
Results compared with acceptance criteria
Accept the lot
Send to production
or to customer
Reject the lot
Decide on disposition

Typical Application of Acceptance SamplingTypical Application of Acceptance Sampling
Based on the observations made, the
decision is made to either accept or reject
the entire shipment

Typical Application of Acceptance SamplingTypical Application of Acceptance Sampling
The decision to accept or reject the
shipment is based on the following set
standards:
 Lot size = N
 Sample size = n
 Acceptance number = c
 Defective items = d
• If d <= c, accept lot
• If d > c, reject lot

Types ofTypes of Acceptance SamplingAcceptance Sampling PlansPlans
Single-sampling plan
Double-sampling plan
Multiple-sampling plan

Single Sampling PlanSingle Sampling Plan
(n,c)
Acc the lot
Reject the lot
d <C
d>C
(N, p)
Lot Size ： N
The proportion of defects :P
Where d is the number of the actual defects in the sample.

Double Sampling PlansDouble Sampling Plans
Define:
 n1 -- sample size on first sample
 c1 -- acceptance number for first sample
 d1 -- defectives in first sample
 n2 -- sample size on second sample
 c2 -- acceptance number for both samples
 d2 -- defectives in second sample
Take sample of size n1
 Accept if d1 ≤ c1; reject if d1 > c2;
 Take second sample of size n2 if c1 < d1 ≤ c2
 Accept if d1+d2 ≤ c2; reject if d1+d2 > c2

Multiple-sampling planMultiple-sampling plan
(n,p)
Acc the lot
Reject the lot
dn1<c1
dn1>c1
(n1+n2)
c1<dn1<r1
Acc the lot
Reject the lot
d(n1+n2)<r2
d(n1+n2)>r2
(n1+n2+n3)c2<d(n1+n2)<r2

Faktor Pemilihan Plan PersampelanFaktor Pemilihan Plan Persampelan
1. Ringkas
• single sampling adalah yang paling senang
• multiple sampling adalah yang paling sukar
2. Kos Pendatbiran
• kos untuk latihan, pemeriksaan, penyimpanan rekod adalah
paling sedikit bagi single sampling
3. Maklumat kualiti
• single sampling akan memberi lebih banyak maklumat berkaitan
paras kualiti setiap lot
4. Bilangan unit-unit yang akan diperiksa
• Bilangan yang banyak diperiksa adalah pada single sampling
5. Kesan Psikologi
• Lebih rendah bagi multiple sampling kerana peluang kedua masih
ada

Operating Characteristic CurveOperating Characteristic Curve
The curve or graphs show the
probability of a lot being accepted
for various value of incoming
quality

Operating Characteristic CurveOperating Characteristic Curve
ProbabilityofAcceptingLot
Lot Quality (Fraction Defective)
100%
75%
50%
25%
.03 .06 .09
α = 0.10
90%
β = 0.10
AQL
LTPD
Indifferent
Good Bad

• Producers Risk
– The risk associated with a producer rejecting a
lot of materials that actually have good quality
• Also referred to as a Type I Error or α
• Consumers Risk
– The risk associated with a consumer accepting a
lot of materials that actually have poor quality
• Also referred to as a Type II Error or β

 PRODUCERS RISK:
RISK ASSOCIATED WITH REJECTING A LOT OF GOOD QUALITY
 CONSUMERS RISK:
RISK ASSOCIATED WITH ACCEPTING A DEFECTIVE LOT
Action Good Lot Poor Lot
Consumer Accept Correct
decision
Error
Producer Reject Error Correct
decision

Acceptable Quality Level (AQL)
• Maximum percent defective that is acceptable
 = P(rejecting lot | p = AQL)
• Corresponds to higher Pa (left-hand side of OC Curve)
Lot Tolerance Percent Defective (LTPD)
• Worst quality that is acceptable (accepted with low
probability)
 = P(accepting lot | p = LTPD)
• Corresponds to lower Pa (right-hand side of OC Curve)

OC Curve Calculation
Two Ways of Calculating OC Curves
 Binomial Distribution
 Poisson Formula
Binomial Distribution
 Cannot use because:
• Binomials are based on constant probabilities.
• N is not infinite
• p changes
A Poisson formula can be used

OC Curve Calculation
Find your sample size, n
Find your fraction defect p
Multiply n*p
From a Poisson table find your PA

Operating Curves
p : actual proportion defective items
(probability of a part being defective)
d : number of defective items in the batch
n : sample size
,2,1,0
!
)(
0)1(}{
==
≤≤−





==
−
−
d
d
enp
ndpp
d
n
dxprob
npd
dnd Binomial
approx.
Poisson
approx.

Example: Acceptance probability
9662.0
0867.02169.03614.03012.0)02.0|3(
0867.0
!3
21
)02.0|3(
2169.0
!2
21
)02.0|2(
3614.0
!1
21
)02.0|1(
3012.0
!0
21
)02.0|0(
2.13
2.12
2.11
2.10
=
+++==≤
=
⋅
===
=
⋅
===
=
⋅
===
=
⋅
===
−
−
−
−
pxprob
e
pxprob
e
pxprob
e
pxprob
e
pxprob
= probability of acceptance the lot.
Suppose n = 60, p =0.02, and c=3.

For each value of p, we can compute the
probability of acceptance:
p 0.02 0.04 0.06 0.08 0.1
μ = np 1.2 2.4 3.6 4.8 6
prob(x<=3) 0.9662 0.7787 0.5153 0.2942 0.1512
How does the operating characteristic curve change
when:
• c increases?
• n increases (for fixed c/n)?
• lot size N increases?

n = 60
c = 3
AQL LTPD
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5 6 7 8 9 10 11 12
Percent defective
Probabilityofacceptance
Β =.10
(consumer’s risk)
α = .04 (producer’s risk)

Given,
N = 2500
n = 50
c = 2
Construct OC Curve using Poisson
Formula
Example

Solution
Selected, p µ= np d = 0 d = 1 d = 2 Pa
0.01 0.5 0.607 0.303 0.076 0.986
0.02 1.0 0.368 0.368 0.184 0.920
0.03 1.5 0.223 0.335 0.251 0.809
0.04 2.0 0.135 0.271 0.271 0.677
0.05 2.5 0.082 0.205 0.257 0.544
0.06 3.0 0.050 0.149 0.224 0.423
0.07 3.5 0.030 0.106 0.185 0.321
0.08 4.0 0.018 0.073 0.147 0.238
0.09 4.5 0.011 0.050 0.112 0.174
0.1 5.0 0.007 0.034 0.084 0.125

Solution
Fraction defective in lot
N = 2500
n = 50
c = 2

TYPES OF INSP. AND SWITCHINGTYPES OF INSP. AND SWITCHING
1. NORMAL - WITH NORMAL LEVEL OF DEFECTS
o dilakukan pada peringkat permulaan pemeriksaan &
sekiranya kualiti produk adalah baik & sekata
2. TIGHTENED - WITH HIGH LEVEL OF DEFECTS
o dilakukan apabila kualiti pengeluar menjadi semakin teruk
& kurang berkualiti berbanding pemeriksaan biasa.
o bilangan produk yang diperiksa bertambah berbanding
pemeriksaan biasa.
3. REDUCED - WITH OUTPUT REDUCED DEFECTS
o dilakukan apabila kualiti produk adalah cemerlang.
o bilangan produk yang diperiksa akan berkurangan
berbanding pemeriksaan biasa.

ExampleExample
Suppose a product is submitted in
lots of size N = 2000. The AQL is
0.65% through normal single
sampling plan and inspection of level
II

SolutionSolution
Given N = 2000 and level II, refer code letter in
the table
Code Letter = K
From Table II-A ( single and normal
inspection ) and AQL =0.65%
Accept = 2 Reject = 3

SolutionSolution
So the sampling plan to use is
n = 125 ( 2,3 )
Take 125 samples and
Accept if defective ≤2
Reject if defective ≥3

ExampleExample
Determine a single normal sampling
plan if AQL = 0.4%, using Level I
inspection and lot size is 1000

SolutionSolution
Given N = 1000 and level I, refer code letter in
the table
Code Letter = G
n = 32

ExampleExample
Suppose a product is submitted in lots of
size N = 2000. The desired AQL is 0.65%.
Determine the single sampling plan for
normal, tighten and reduce using level III
inspection.

SolutionSolution
Given N = 2000, AQL = 0.65% and level III
Type Code
Letter
Sample
Size
(n)
Accept
(Ac)
Reject
(Re)
Normal L 200 3 4
Tighten L 200 2 3
Reduce L 80 1 4

ExerciseExercise
Dengan menggunakan Jadual MIL-STD-105D/Z1.4, Code
Letter L dan AQL = 0.65%, keputusan pemeriksaan 8 lot
terakhir adalah seperti berikut :
Lot Defect
I 1
II 4
III 5
IV 1
V 3
VI 0
VII 2
VIII 2
Apakah keputusan anda jika;
i.Using normal inspection for Lot I
ii.Using tighten inspection for Lot IV
iii.Using reduce inspection for Lot VIII
iv.Using normal inspection for Lot VI
v.Using reduce inspection for Lot V

SolutionSolution
Accept (Ac) Reject (Re) Result
i 3 4 Accept
ii 2 3 Accept
iii 1 4 Reject
iv 3 4 Accept
v 1 4 Reject

ExerciseExercise
A lot size of 1000 pieces is being
inspected for attribute, single sampling
plan normal inspection level II with an
AQL of 1.0% using ANSI/ASQ Z1.4.
Using a Poisson Distribution, construct
OC Curve at appropriate n and c

SolutionSolution
Given N = 1000 and level II, refer code letter in
the table
Code Letter = J
n = 80

SolutionSolution
p µ=np x=0 x=1 x=2 Pa
0.01 0.8 0.449 0.359 0.144 0.953
0.02 1.6 0.202 0.323 0.258 0.783
0.03 2.4 0.091 0.218 0.261 0.570
0.04 3.2 0.041 0.130 0.209 0.380
0.05 4.0 0.018 0.073 0.147 0.238
0.06 4.8 0.008 0.040 0.095 0.143
0.07 5.6 0.004 0.021 0.058 0.082

SolutionSolution
Fraction defective in lot
N = 1000
n = 80
c = 2

LOGO
Click to edit company slogan .

JF608: Quality Control - Unit 5

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to JF608: Quality Control - Unit 5

Similar to JF608: Quality Control - Unit 5 (20)

More from Asraf Malik

More from Asraf Malik (20)

Recently uploaded

Recently uploaded (20)

JF608: Quality Control - Unit 5