JF608: Quality Control - Unit 5

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UNIT 5 :UNIT 5 :ACCEPTANCE SAMPLING

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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

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



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 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




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 of Types of Acceptance SamplingAcceptance Sampling Plans Plans

Single-sampling planDouble-sampling planMultiple-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.


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



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



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)



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, 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.



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?



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)



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.


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


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


SolutionSolution

So the sampling plan to use is n = 125 ( 2,3 )

Take 125 samples and Accept if defective ≤2Reject if defective ≥3


ExampleExample

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


SolutionSolutionGiven 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.


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


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


SolutionSolutionGiven N = 1000 and level II, refer code letter in the table

Code Letter = J n = 80




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


SolutionSolution

Pro

babi

lity

of a

ccep

tanc

e

Fraction defective in lot

N = 1000n = 80c = 2

LOGO

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JF608: Quality Control - Unit 5