11 sampling tech 3new - student

8/8/2019 11 Sampling Tech 3new - Student

1/26

Lot-by-lot

Acceptance SamplingTechniques

byAttributes

Assoc. Prof. Ir. Dr. Cheong Kuan Yew

School of Materials & Mineral Resources Engineering

Engineering Campus

Universiti Sains Malaysia


2/26

Topic Outcome:

At the end of this topic, student will be able to:

Describe the consumer-producer relationship

from a OC curve.

Determine and explain producers risk,consumers risk, AQL, and LQ.

Apply a sampling plan.


3/26

Topic Outline:Introduction

Consumer-Producer Relationship

Producers Risk ( ) & AQL

Consumers Risk ( ) & LQ


4/26

(1) Introduction


5/26

Introduction

An OC curve can be plotted for any combination of sample

size (n) and acceptance number (c). Each combination results in a different curve.

Some of the most important things to remember about OC

curves can be seen by comparing the curves.

DIFFERENT n: A larger sample size tends to result in a

steeper curve such a plan is said to have greater

discriminating power than plan with smaller sample size

and shallower curve.

DIFFERENT c: a larger c tends to change the shape of the

curve, creating a flat shoulder at the top while retaining a

thin tail at the bottom.


6/26

OC curve has 3 parts

1.0

0.5

05.0 10.0

Pro

bab

ilityofAcc

ep

tance,P

a

[orPer

centofLotsA

ccepted,100

Pa

]

Percent Nonconforming (100p0)

Shoulder (or peak) at the top

It shows the quality of the product thatwill be accepted by sampling plan

without question.

Thin part of the tail atthe bottom

It shows the quality of

the product that is almost

certain to be rejected bythe plan.

Middle portion between shoulder and

tailAt exact centre of the curve, where the Pa

is 50%, product of corresponding quality

has 50-50 chance of being either rejected

or accepted.


7/26

In general, engineer should make sure that the shoulder

of the curve corresponds to the product he/she is willing to

be accepted and that the tail of the curve corresponds to

the product he/she is willing to be rejected.

Maximum economy is likely to be obtained when theprocess is running at or near its capability level and

when this level matches the shoulder of the OC curve to

be used.


8/26

(2) ConsumerProducer Relationship


9/26

Producers Risk

AQL


10/26

Producers Risk (Producers Risk ( )) It is defined as the probability or risk of rejecting a lot

when the quality of the lot is acceptable.

What does this mean to an engineer?

The risk for a good product to be rejected a lost to an

organization.

Example:

A process capability is 99%. Customer is willing to accept 1%

nonconforming units. However, during inspection a certain

percentage of lots still rejected ever though the percent of

nonconforming is less than 1%.


11/26

How to estimate Producers Risk ( )

1) Plot OC curve for the sampling plan.

2) Find the percentage nonconforming (100p0) in the

process.

Rough estimation can be done if no exact data is

available.

However for a more accurate check, a processprocesscapability studycapability study is preferable.

1) Use the process capability percentage to determine the

probability of acceptance (Pa) on the OC curve.

2) Producers Risk ( ) = 1 - Pa


12/26

Q & A:

Process Capability = 99%

1.Sampling Plan, N=3000, n=80, c=0





Find the Producers Risk for the above sampling plans

according to the stated process capability.


13/26

OC Curve

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6


Perce

ntofLotsAcc

epted(100Pa)

c=4

c=3

c=2

c=1

c=0

Process Capability = 99%

100p0 = 1%

c 100Pa 100

0 44.9% 55.1%

1 80.9% 19.1%

2 95.2% 4.8%

3 99.1% 0.9%

4 99.8% 0.2%

Percentage of LotsNOT Accepted (Pr)


14/26

It is associated with producers risk.

It is a numerical definition of an acceptable lot. It is the maximum percent nonconforming that can be

considered satisfactory for the purposes of acceptancesampling.

It is a reference point on the OC curve and is notmeant to convey to the producer that any percentnonconforming is acceptable.

It is a statistical term and is not meant to be used by

general public.

Producer only can guarantee an acceptable lot when 0%nonconforming or the number nonconforming in the lotless than or equal to acceptance number, c.

Acceptable Quality Level (AQL)


15/26

Producers quality goal is to meet or exceed the

specifications so that no nonconforming units are

present in the lot.

A sampling plan should have a low Producers risk for

quality that is equal to or better than the AQL.

Example:

Sampling plan: N=4000, n=300, and c=4, AQL=0.7%.

What is the non-acceptance probability?


16/26

OC Curve

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3


Perce

ntofLotsAcc

epted(100Pa)

(AQL, 1-100Pa)

93%

Comment:

Producers risk = 7%

Product that is 0.7%

nonconforming will have

a non-acceptanceprobability of 0.07 or

7%.

7 out of 100 lots that

are 0.7%

nonconforming will not

be accepted by the

sampling plan.


17/26


18/26

Consumers Risk

LQ


19/26

Consumers Risk ( ) It is defined as the probability or risk of accepting a bad

lot based on a sampling plan.

It is expressed in terms of probability of acceptance.

To estimate consumers risk:

Plot OC curve for a sampling plan.

Find out the percent nonconforming that theconsumer wants to reject.

Find this value on the OC curve and determine theprobability of acceptance. This gives the risk ofaccepting unsatisfactory quality provided the productof such poor quality is actually submitted.


20/26

Q & A:

Consumer wants to reject product that is 4% nonconforming.

1. Sampling Plan, N=3000, n=80, c=02. Sampling Plan, N=3000, n=80, c=1

3. Sampling Plan, N=3000, n=80, c=2

4. Sampling Plan, N=3000, n=80, c=35. Sampling Plan, N=3000, n=80, c=4

Find the Consumers Risk ( ) for the above sampling plans.


21/26

OC Curve

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6


Perce

ntofLotsAcc

epted(100Pa)

c=4

c=3

c=2

c=1

c=0

c 100Pa=100

0 4.1%

1 17.1%

2 38.0%

3 60.2%

4 78.1%


22/26

It is associated with consumers risk.

It is a numerical definition of a nonconforming lot.

It is the percent nonconforming in a lot for which (for

acceptance purposes) the consumer wishes the

probability of acceptance to be low.

For previous example, LQ = 4% for 100 = 5% (for c=0)

lots that are 4% nonconforming will have a 5%

chance of being accepted. 1 out of 20 lots that are

4% nonconforming will be accepted by this samplingplan.

Limiting Quality (LQ)


23/26


24/26

Design of Sampling Plan


25/26

Design of Sampling Plan

Rule of Thumb

A sampling plan should not be adopted without seeing

the OC curve!!!!!


26/26

END

11 sampling tech 3new - student

Documents