chapter 10 lot-by-lot acceptance sampling for attributes.ppt

8/10/2019 CHAPTER 10 LOT-BY-LOT ACCEPTANCE SAMPLING FOR ATTRIBUTES.ppt

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Besterfield: Quality Control, 8thed.. 2009 Pearson Education, Upper Saddle River, NJ 07458.

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QualityControl

Chapter 9- Lot-by-Lot

Acceptance SamplingBy AttributesPowerPoint presentation to accompany

BesterfieldQuality Control, 8e

PowerPoints created by Rosida Coowar


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Learning Objectives

When you have completed this chapter you should be able to:

Know the advantages and disadvantages of sampling; the

types of sampling plans and selection factors; criteria for

formation of lots; criteria for sample selection; and decisions

regarding rejected lots

Determine the OC Curve for a single sampling plan

Determine the equations needed to graph the OC Curve for a

double sampling plan

Know the properties of OC Curves Know the consumer-producer relationships of risk, AQL, and

LQ


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Learning Objectives

When you have completed this chapter you should be able to:

Determine the AOQ curve and the AOQL for a single sampling

plan

Determine single sampling plans for stipulated producers risk

and for stipulated consumers risk

Upon completing this course, the students should be able to:

describe important concepts pertaining to quality, quality system and total quality management

apply the principles of probability and statistics in quality planning, control and improvement and

utilize appropriate statistical tools and techniques

undertake complete problem-solving cycle using appropriate quality improvement tools and

techniques

design a quality system and incorporate important quality elements necessary for its proper

functioning

implement the concept of total quality in engineering and non-engineering processes


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Fundamental AspectsAcceptance sampling has declined in importance due to SPC

Various acceptance sampling practices include statisticalacceptance sampling, fixed percentage, occasional random

checks, and 100% inspection

Acceptance Sampling is a form of inspection applied to lots or

batches of items before or after a process to judge conformanceto predetermined standards

Sampling plans are established by severity (critical, major and

minor)

A single sampling plan is defined by the lot size, N, sample size,

n, and the acceptance number, c

Performed where there is a consumer-supplier relationship

(consumer-supplier, two different plants, to departments, etc)


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Acceptance SamplingAcceptance Sampling is very useful when:

Large numbers of items must be processed in a short amount of

time

The cost of passing defectives is low

Fatigue/boredom is caused by inspecting large numbers of items

Destructive testing is required

Information concerning producers quality, such as and R, p

or c charts, and Cpkis not available

When automated inspection is not available

X


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Acceptance Sampling Three important aspects of sampling:

Involves random sampling of the entire lot

Accept and Reject Lots (does not improve the quality)

Lot Sentencing

Audit Tool Three approaches to lot sentencing:

Accept with no inspection

100% inspection

Acceptance Sampling


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Acceptance SamplingAdvantages compared to 100% inspection:

Less expensive

Reduced handling damage

Upgrade inspection job from monotonous piece-by-piece decisions to

lot-by-lot decisions

Reduces the amount of inspection error Stronger motivation for supplier to quality improvement due to

rejection of entire lots

Disadvantages

Risk of accepting bad lots and rejecting good lots

Less information generated

Requires planning and documentation

No assurance that entire lot conforms to specifications


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Sampling Plans

Sampling Plans specify the lot size, sample size, number of

samples and acceptance/rejection criteria

Sampling plans involve:

Single samplingDouble sampling

Multiple sampling

Sequential sampling

Randomsample

Lot


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Sampling Plans

Single Sampling Plan

N = lot size

n = sample size

c=acceptance number

If c or less non-conforming units are found in the sample, the

lot is accepted, else it is rejected


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Single Sampling Plan

A single sampling plan is one where: A representative sample of n items is drawn from a lot

size of N items

Each item in the sample is examined and classified as

good/defective

If the number of defective exceeds a specified rejection

number (c) the whole lot is rejected; otherwise the whole

lot is accepted


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Double Sampling Plan

ADouble Sampling Plan allows to take a second sample if

the results of the original sample are inconclusive Specifies the lot size, size of the initial sample, the

accept/reject/inconclusive criteria for the initial sample(N, n1, c1 (Ac), r1(Re))

Specifies the size of the second sample and theacceptance rejection criteria based on the total number ofdefective observed in both the first and second sample(n2,c2,r2)

If values are not given for r1 and r2, they are equal to c2+1


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First Randomsample

Lot

C1 r1

First sample inconclusive,

take second sampleReject LotAccept Lot

Compare number of defective found in the first random sample to C1

and r1 and make appropriate decision.



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C2

Reject LotAccept Lot

Compare the total number of defective in both lots to C2and make

the appropriate decision

Lot First Random sample

Second Random sample



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AMultiple Sampling Plan is similar to the double sampling planin that successive trials are made, each of which hasacceptance, rejection and inconclusive options

In sequential sampling plan, items are sampled and inspected

one after another. A cumulative record is maintained, and adecision is made to accept or not accept the lot as soon asthere is sufficient cumulative evidence

All four types of sampling plans can give the same results; thechance of a lot being accepted under a single sampling plan isthe same under appropriate double, multiple, and sequentialsampling plan


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Which Plan you choose depends on:

Cost and timeNumber of samples needed and number of items in

each sample


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Lot Formation

Lot formation can influence effectiveness of sampling plan

Considerations before inspection:

Lots should be homogeneous (same machine, same operator, sameinput material) otherwise sampling plan does not function properlyand it is difficult to take corrective action

Larger lots are more preferable than smaller lots to reduceinspection cost

Lots should be conformable to the materials-handling systems usedin both the vendor and consumer facilities (not to confuse betweenhomogeneous lot and packaging requirements)


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Random Sampling Samples should be representative of the entire lot with

each unit in the lot having equal likelihood of beingselected (random sampling)

Units selected for inspection should be chosen at random If random samples are not used, bias can be introduced If judgment methods are used to select the sample, the

statistical basis of the acceptance-sampling procedure islost Assign a number to each unit in the lot Use random numbers to determine which units to be sampled and

inspected (use Table of random numbers) Discard any number not appropriate

Many units already have serial numbers A unique number can be assigned indicating certain

location in the packing


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Random Sampling Liquid can be assumed to be homogeneous thus sample

taken anywhere Stratification may also be carried out during sampling


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Nonaccepted Lots A number of courses of actions can be taken:

1. Nonaccepted lot can be passed to production andnoncnonforming units sorted out by production personnel(unsatisfactory, defeats purpose of sampling, and slowsproduction)

2. Nonaccepted lot can be rectified at consumers plant by personnelfrom either the producers or consumers plant (consumer isaware of producers poor quality, transportation costs are saved,space must be provided at consumers plant)

3. Nonaccepted lot can be returned to producer for rectification(most appropriate course of action, results in long-run qualityimprovement, shipping costs paid both ways by producer,

producers employees are aware of poor quality

It is expected that nonaccepted lots will receipt 100%inspection and nonconforming units are discarded.

A resubmitted lot is not normally reinspected


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Statistical AspectsThe Operating Characteristic Curve:

Measures the performance of an acceptance sampling plan Plots the probability of accepting the lot versus the lot

fraction defective

Shows the probability that a lot submitted with a certain

fraction defective will be either accepted or rejected

1. Assume p02. Calculate np0value

3. Attain Pavalues from Poisson table using applicable cand np0values

4. Plot point (100p0, 100Pa)

5. Repeat steps 1, 2, 3 and 4 until a smooth curveobtained


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Operating Characteristic Curve

This curve plots the probability of accepting the lot (Y-axis)versus the lot fraction or percent defectives (X-axis)

The OC curve is the primary tool for displaying andinvestigating the properties of a Lot Acceptance SamplingPlan

There are two types of OC curves:

Type A

Gives the probability of acceptance of an individual lot comingfrom finite production

Type BGives the probability of acceptance for lots coming from a

continuous production

As n/N


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Statistical Aspects

OC Curve Properties

Acceptance sampling plans with similar properties can givedifferent OC curves

1. Sample size as a fixed percentage of lot size

2. Fixed sample size

3. As sample size increases, the curve becomes steeper4. As the acceptance number decreases, the curve becomes steeper

OC curve with n = 300 and c = 2 is steeper than that with n =50 and c = 0

Plans with c = 0 have the perception that nonconforming unitswill not be tolerated and should be used for criticalnonconformities

For major and minor nonconformities, c > 0 should beconsidered


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AnOperating Characteristic Curve (OCC) is a probability

curve for a sampling plan that shows the probabilities ofaccepting lots with various lot quality levels (% defectives).

0

0.1

0.20.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 .05 .10 .15 .20

Probability

ofaccepting

lot

Lot quality (% defective)

Under this sampling plan, if the lot has 3% defective

. the probability of accepting the lot is 90%

. the probability of rejecting the lot is 10%

If the lot has 20% defective

. it has a small probability (5%) of being accepted

. the probability of rejecting the lot is 95%

0.7

0.8

OCCs for Single Sampling Plans


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Consider a double sampling plan N = 2400, n1= 150, c1=

1, r1= 4, n2= 200, c2= 5, r2= 6 If there is one or fewer nonconforming unit on the first

sample, the lot is accepted

(Pa)I= P(1or less)IA second sample is taken only if there are 2 or 3

nonconforming units on the first sample

Then the lot can be accepted by obtaining:

Two NC on the first and 3 or less NC on second or

Three NC on first and two or less NC on second

(Pa)II= (P2)I(P3orless)II+ (P3)I(P2orless)II (Pa)combined= (Pa)I+ (Pa)II



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Inspect a sample

of 150 from lotof 2400

If 1 or lessNonconforming

units accept lots andstop

If 4 or moreNonconforming units

the lot is not acceptedand stop

If 2 or 3 nonconformingunits, inspect a second

sample of 200

If 5 or lessNonconforming units

On both samples,Accept the lot

If 6 or moreNonconforming units

On both samplesThe lot is not accepted

Figure 9-5 Graphical description of the double sampling plan: N=2400,n1=150,c1=1r1=4, n2=200, c2=5, and r2=6


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OCC for Double Sampling Plan


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OCC for a Multiple Sampling Plan


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Acceptable Quality Level (AQL)

Conflicting interest between consumer and producer when

acceptance sampling is used

Sampling carries risks of not accepting acceptable lots andof accepting unacceptable lots

Producers risk is the probability, for a given (n,c)

sampling plan, of rejecting a lot that has a defect levelequal to the AQL The producer suffers when this occurs,because a lot with acceptable quality was rejected. Thesymbol is commonly used for the Type I error and

typical values for range from 0.2 to 0.01 (typically 0.05) Pa= 1 - a


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Acceptance Quality Level (AQL) AQLacceptance quality limit

The AQL is a percent defective that is the base linerequirement for the quality of the producer's product. Theproducer would like to design a sampling plan such thatthere is a high probability of acceptinga lot that has a

defect level less than or equal to the AQL Consumers risk is the probability, for a given (n,c)

sampling plan, of accepting a lot with a defect level equalto the LTP or LQ. The consumer suffers when this occurs,because a lot with unacceptable quality was accepted.The symbol is commonly used for the Type II error andtypical values range from 0.2 to 0.01

LQ is limiting quality


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0.2

0.3

0.40.5

0.6

0.7

0.8

0.9

1

P

robability

ofac

cepting

lot

00.1

0 .05 .10 .15 .20 Lot quality (% defective)

AQL - percentage level of defects atwhich a customer is willing to accept

Acceptable Lot

Producers Risk = probability acceptable lot is rejected

OCC, AQL and Producers Risk


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0.2

0.3

0.40.5

0.6

0.7

0.8

0.9

1

P

robability

ofac

cepting

lot

00.1

0 .05 .10 .15 .20 Lot quality (% defective)

LTPD - upper limit on the percentage

of defectives that a customer is

willing to accept.

Consumers Risk = probability unacceptable is accepted

Unacceptable Lot

OCC, LTPD and Consumers Risk


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Average Outgoing Quality (AOQ) A common procedure, when sampling and testing is non-

destructive, is to 100% inspect rejected lots and replaceall defectives with good units. In this case, all rejected lotsare made perfect and the only defects left are those inlots that were accepted

The procedure is called rectifying inspection AOQ = (100p0)(Pa)

Rectifying inspection results in nonaccepted lots havingAOQ better than incoming quality

The limit of percent nonconforming is average outgoingquality limit (AOQL). A plot of theAOQ(Y-axis) versus theincoming lot p(X-axis) will start at 0 for p= 0, and returnto 0 for p= 1 (where every lot is 100% inspected and


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Average Outgoing Quality (AOQ) rectified). In between, it will rise to a maximum. This

maximum, which is the worst possible long termAOQ, iscalled the Average Outgoing Quality LevelAOQL.


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TheAverage Outgoing Quality (AOQ)is the average of

rejected lots (100% inspection) and accepted lots ( asample of items inspected)

Typically the term (N-n)/N is very close to 1; therefore, theequation most often used is:

ac

ac

N - nAOQ = P * p( ) where

N

P = Probability of accepting a lot

p = Fraction defective

n = sample size

N = Lot size

Average Outgoing Quality

AOQ = P *p where

P = Probability of accepting a lot

p = Fraction defective

ac

ac


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AOQ and Acceptance Sampling

Total Number NumberNonconforming

11 lots-

2% Nonconforming

11(3000)=33,000 33,000(0.02)=660

4 lots-

0% Nonconforming

4(3000)(0.98)=11,760 0

44,760 660

Percent Nonconforming (AOQ) = 660/44,760 X

100 =1.47%

Figure 9-15 contd.


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Average Sample Number (ASN) For a single sampling (n,c) we know each and every lot has

a sample of size ntaken and inspected or tested

For double, multiple and sequential plans, the amount ofsampling varies depending on the number of defectsobserved

For double sampling plan,

ASN = n1+ n2(1-P1)Where P1is the probability of a decision on the first sample

ASN curves are a valuable tool for justifying double or

multiple sampling when inspection costs are great becauseof inspection time, equipment costs, or equipmentavailability


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Average Total Inspection (ATI) When rejected lots are 100% inspected, it is easy to

calculate theATIif lots come consistently with a defectlevel of p.

ATI is the amount inspected by both the consumer andproducer

It assumes that rectified lots will receive 100% inspection For a lot acceptance sampling plan (LASP) with (n,c) and a

probability paof accepting a lot with defect levelp, wehave:

ATI=n + (1 - Pa) (N - n)

where Nis the lot size


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Sampling Plan Design Suppose is known and the AQL is also known then :

Sampling plan with stipulated producers risk (a, AQL) Sampling plan with stipulated consumers risk

Sampling plan with stipulated producers and consumers risk

can be designed


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Sampling Plan Design Stipulated Producers and Consumers risk

= 0.10 = 0.10AQL=0.9 LQ= 7.8

Find the ratio of P0.10/P0.95. From table 9-4 C is between 1and 2. Find n for c =1 and n for c =2 .


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Sampling Plan Design Have 4 plans

Select plan based on: Lowest sampling size

Greatest sampling size

Plan exactly meets consumers stipulation and is as close

as possible to producers stipulation Plan exactly meets producers stipulation and is as close

as possible to consumers stipulation


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Sampling Plan Design

An assembly plant plans a single sampling plan such that itslots of products that are no worse than 2% nonconformingis accepted at least 99% of the time. Recommend thepossible plans. Select a plan with higher consumersprotection. Draw the OC curve for the selected plan using 7

points. Table of Poisson distribution and np values forcorresponding c, a, and bvalues are given.


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THE END

IQ + EQ + SQ = TQ

We have indeed created man in the best of molds. (At-Tin: 4)

Taqwim: mold, symmetry, form, nature, constitution

chapter 10 lot-by-lot acceptance sampling for attributes.ppt

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