jf608: quality control - unit 5
TRANSCRIPT
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
LOGOINTRODUCTIONINTRODUCTION
Determine quality level Ensure quality is within predetermined level
PurposePurpose
LOGOINTRODUCTIONINTRODUCTION
Untuk menentukan penerimaan & kualiti bahan mentah yang masuk
Untuk menentukan penerimaan & kualiti produk separa-siap
Untuk menentukan penerimaan & kualiti produk siap yang keluar
Untuk mengawal & memperbaiki kualiti produk
Kegunaan Penerimaan Kegunaan Penerimaan PersampelanPersampelan
LOGOINTRODUCTIONINTRODUCTION
1. Homogenus semua proses mesti sama
2. Lot dalam jumlah yang besar supaya dapat mengurangkan kos
pemeriksaan
Syarat Persampelan Pada LotSyarat Persampelan Pada Lot
LOGOINTRODUCTIONINTRODUCTION
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 Operasi Langkah Dalam Operasi PersampelanPersampelan
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGAdvantagesAdvantages 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 classificationeach part either classified as defective or goodclassification 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 / Kecacatan Jenis-Jenis Kerosakan / Kecacatan (Defect)(Defect)
STATISTICAL SAMPLING DATASTATISTICAL SAMPLING DATA
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
When can acceptance sampling be applied?When can acceptance sampling be applied?
At any point in productionThe output of one stage is the input of the
next
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
When can acceptance sampling be applied?When can acceptance sampling be applied?
Sampling at the Input stage Prevents goods that don’t meet standards
from entering into the process This saves rework time and money
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
When can acceptance sampling be applied?When can acceptance sampling be applied?
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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
When can acceptance sampling be applied?When can acceptance sampling be applied?
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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
Types of Types of Acceptance SamplingAcceptance Sampling Plans Plans
Single-sampling planDouble-sampling planMultiple-sampling plan
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
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.
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGDouble Sampling PlansDouble Sampling PlansDefine:
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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGFaktor Pemilihan Plan PersampelanFaktor Pemilihan Plan Persampelan
1. Ringkas• single sampling adalah yang paling senang• multiple sampling adalah yang paling sukar2. Kos Pendatbiran• kos untuk latihan, pemeriksaan, penyimpanan rekod adalah
paling sedikit bagi single sampling3. Maklumat kualiti• single sampling akan memberi lebih banyak maklumat berkaitan
paras kualiti setiap lot4. Bilangan unit-unit yang akan diperiksa• Bilangan yang banyak diperiksa adalah pada single sampling5. Kesan Psikologi• Lebih rendah bagi multiple sampling kerana peluang kedua masih
ada
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
Operating Characteristic CurveOperating Characteristic Curve
The curve or graphs show the probability of a lot being accepted for various value of incoming quality
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGOperating Characteristic CurveOperating Characteristic Curve
Pro
bab
ility
of
Acc
epti
ng
Lo
t
Lot Quality (Fraction Defective)
100%
75%
50%
25%
.03 .06 .09
α = 0.1090%
β = 0.10
AQ
L
LT
PD
IndifferentGood Bad
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING• 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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING 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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGAcceptable 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)
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
OC Curve Calculation
Find your sample size, nFind your fraction defect pMultiply n*pFrom a Poisson table find your PA
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGOperating Curvesp : actual proportion defective items
(probability of a part being defective)d : number of defective items in the batchn : sample size
,2,1,0!
)(
0)1(}{
==
≤≤−
==
−
−
dd
enp
ndppd
ndxprob
npd
dnd Binomialapprox.
Poisson approx.
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGExample: 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
epxprob
epxprob
epxprob
epxprob
= probability of acceptance the lot.
Suppose n = 60, p =0.02, and c=3.
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGExample: Acceptance probability
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 6prob(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?
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGExample: Acceptance probability
n = 60c = 3
AQL LTPD
00.10.20.30.40.50.60.70.80.9
1
1 2 3 4 5 6 7 8 9 10 11 12
Percent defective
Pro
ba
bili
ty o
f ac
ce
pta
nc
e
Β =.10(consumer’s risk)
α = .04 (producer’s risk)
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
Given, N = 2500n = 50c = 2
Construct OC Curve using Poisson Formula
Example
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGSolutionSelected, p µ= np d = 0 d = 1 d = 2 Pa
0.01 0.5 0.607 0.303 0.076 0.9860.02 1.0 0.368 0.368 0.184 0.9200.03 1.5 0.223 0.335 0.251 0.8090.04 2.0 0.135 0.271 0.271 0.6770.05 2.5 0.082 0.205 0.257 0.5440.06 3.0 0.050 0.149 0.224 0.4230.07 3.5 0.030 0.106 0.185 0.3210.08 4.0 0.018 0.073 0.147 0.2380.09 4.5 0.011 0.050 0.112 0.1740.1 5.0 0.007 0.034 0.084 0.125
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGSolution
Fraction defective in lot
Pro
bab
ility
of a
cce
pta
nce
N = 2500n = 50c = 2
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLINGTYPES OF INSP. AND SWITCHINGTYPES OF INSP. AND SWITCHING1. NORMAL - WITH NORMAL LEVEL OF DEFECTSo dilakukan pada peringkat permulaan pemeriksaan &
sekiranya kualiti produk adalah baik & sekata
2. TIGHTENED - WITH HIGH LEVEL OF DEFECTSo 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 DEFECTSo dilakukan apabila kualiti produk adalah cemerlang.o bilangan produk yang diperiksa akan berkurangan
berbanding pemeriksaan biasa.
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
SolutionSolutionGiven 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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
SolutionSolution
So the sampling plan to use is n = 125 ( 2,3 )
Take 125 samples and Accept if defective ≤2Reject if defective ≥3
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
ExampleExample
Determine a single normal sampling plan if AQL = 0.4%, using Level I inspection and lot size is 1000
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
SolutionSolutionGiven N = 1000 and level I, refer code letter in the table
Code Letter = G n = 32
From Table II-A ( single and normal inspection ) and AQL =0.4%
Accept = 0 Reject = 1
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
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.
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
SolutionSolutionGiven N = 2000, AQL = 0.65% and level III
Type Code Letter
Sample Size (n)
Accept (Ac)
Reject (Re)
Normal L 200 3 4Tighten L 200 2 3Reduce L 80 1 4
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING 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 2VIII 2
Apakah keputusan anda jika;i.Using normal inspection for Lot Iii.Using tighten inspection for Lot IViii.Using reduce inspection for Lot VIIIiv.Using normal inspection for Lot VIv.Using reduce inspection for Lot V
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING SolutionSolution
Accept (Ac) Reject (Re) Resulti 3 4 Acceptii 2 3 Acceptiii 1 4 Rejectiv 3 4 Acceptv 1 4 Reject
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
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
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
SolutionSolutionGiven N = 1000 and level II, refer code letter in the table
Code Letter = J n = 80
From Table II-A ( single and normal inspection ) and AQL =1.0%
Accept = 2 Reject = 3
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
SolutionSolutionp µ=np x=0 x=1 x=2 Pa
0.01 0.8 0.449 0.359 0.144 0.9530.02 1.6 0.202 0.323 0.258 0.7830.03 2.4 0.091 0.218 0.261 0.5700.04 3.2 0.041 0.130 0.209 0.3800.05 4.0 0.018 0.073 0.147 0.2380.06 4.8 0.008 0.040 0.095 0.1430.07 5.6 0.004 0.021 0.058 0.082
LOGOACCEPTANCE SAMPLINGACCEPTANCE SAMPLING
SolutionSolution
Pro
babi
lity
of a
ccep
tanc
e
Fraction defective in lot
N = 1000n = 80c = 2
LOGO
Click to edit company slogan .