Acceptance sampling is a form of inspection where samples are taken from lots or batches to determine if the quality meets predetermined standards. There are different types of sampling plans like single, double, and multiple sampling plans that specify the lot size, sample size, acceptance and rejection criteria. Operating characteristic curves show the probability of accepting lots with different quality levels. Acceptance sampling reduces inspection costs compared to 100% inspection but introduces risks of accepting bad lots or rejecting good ones.

1. Acceptance Sampling
- A form of inspection
PRESENTED BY : SENARATHNE D.M.U.S | S/09/598

2. Outline
 Introduction
 Usage
 Sampling Plans
 Single, Double and multiple Sampling Plans
 Operating Characteristic Curve and Acceptance Levels
 Sampling Risks
 Average Outgoing Quality
 Advantages and Disadvantages
 Conclusion
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3. Introduction
A form of inspection applied to lots or batches of
items before or after a process to judge conformance
to predetermined standards
It is a decision making tool by which a conclusion is
reached regarding the acceptability of lot.
acceptance sampling
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4. Acceptance Sampling Used in…
acceptance sampling
 When testing is destructive
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 When the cost of 100% inspection is extremely high and it is not
technologically feasible
 When the vendor has an excellent quality history, and some
reduction in inspection from 100% is desired, but the vendor’s
process capability is sufficiently low as to make no inspection an
unsatisfactory alternative

5. Sampling Plans
acceptance sampling
Sampling
plans
Attribute
sampling
Single
sampling
Double
Sampling
Variable
sampling
Multiple
Sampling
Sequential
Sampling
Sampling Plans specify the
lot size, sample size, number
of samples and
acceptance/rejection criteria.
Sampling plans involve
Random
sample
Lot
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6. Single Sampling Plan
acceptance sampling
 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
- cut off point) the whole lot is rejected; otherwise the whole lot is
accepted
Random
sample
(n items)
Lot (N
items)
Random
sample
(n items)
Lot (N
items)
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7. Double Sampling Plan
acceptance sampling
 A Double Sampling Plan allows the opportunity 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 (CL - lower level
of defectives, CU - upper level of defectives)
 Specifies the size of the second sample and the acceptance rejection
criteria based on the total number of defective observed in both
the first and second sample (CT- total allowable defectives)
 It works like the following example
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8. Double Sampling Plan…
acceptance sampling
First sample
inconclusive, take
second sample
First Random
sample
Lot
Accept Lot Reject Lot
CL CU
 Compare number of defective found in the first random
sample to CL and CU and make appropriate decision.
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9. Double Sampling Plan…
Lot First Random
Accept Lot Reject Lot
CT
 Compare the total number of defective in both samples to CT
and make the appropriate decision
sample
Second Random
sample
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10. Multiple Sampling Plans
acceptance sampling
 A Multiple Sampling Plan is similar to the double sampling plan in
that successive trials are made, each of which has acceptance,
rejection and inconclusive options.
 Which Plan you choose depends on
Cost and time
Number of samples needed and number of items in
each sample
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11. Operating Characteristic Curve(OCC)
 An Operating
Characteristic
Curve (OCC) is a
probability curve for a
sampling plan that
shows the
probabilities of
accepting lots with
various lot quality
levels (%defectives).
acceptance sampling
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0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
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Under this sampling plan, if the lot has 2%
defective
. the probability of accepting the lot
is 92% . the probability of rejecting
the lot is 8%
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Probability of acceptance
Lot quality (%defective)
If the lot has 10% defective
. it has a small probability (11%) of
being accepted . the probability of rejecting
the lot is 89%

12. Customers Acceptance Levels
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 Most customers understand that 100% inspection is impractical and are
generally willing to accept that a certain level of defectives will be produced.
 The Acceptable Quality Level (AQL) is the percentage level of defects at
which a customer is willing to accept as lot as “good”.
 The Lot Tolerance Percent Defective (LTPD) is the upper limit on the
percentage of defectives that a customer is willing to accept.
 Customers want lots with quality better than or equal to the AQL but are
willing to live with some lots with quality as poor as the LTPD, but prefer not
to accept lots with quality levels worse than the LTPD.

13. Defining good and bad lot
1
0.8
0.6
0.4
0.2
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Probability of acceptance
AQL LTPD Proportion non-conforming
Very Good
Ok! But
not great
Very Bad
Instead of good and bad
we will define “really
good”, “really bad”, “ok,
but not great”
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14. Customers Acceptance Levels…
 Therefore the sampling plan must be designed to assure the
customer that they will be receiving the required AQL and LTPD.
 The Consumer’s Risk is the probability that an unacceptable lot
(e.g. above the LTPD) will be accepted.
 The Producer’s Risk is the probability that a “good” lot will be
rejected.
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15. Sampling Risks
1
0.8
0.6
0.4
0.2
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
AQL
LTPD
Producer’s Risk = Probability acceptable
is rejected
Consumer Risk = Probability unacceptable accepted
Acceptable lot
Unacceptable lot
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16. Average Quality Of Inspected Lots
The result of acceptance sampling (assuming rejected lots are 100% inspected)
is that the level of inspection automatically adjusts to the quality of the lots being
inspected.
The Average Outgoing Quality (AOQ)is the average of rejected lots (100%
inspection) and accepted lots ( a sample of items inspected).
AOQ = 푃푎푐 × 푝
(푁−푛)
푁
where;
푃푎푐 = Probability of accepting a lot
푝 = Fraction defective
N = Lot size
n = Sample size
The maximum outgoing quality level is referred to as the AOQL
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17. Constructing OC Curve
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Probability of acceptance
Proportion non-conforming
0.677
Proportion
non-conforming
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Probability
of
acceptance
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0 1
0.01 0.986
0.02 0.922
0.04 0.677
0.06 0.416
0.08 0.226
0.1 0.112
0.15 0.014
OC curve for n=50, c=2 0.2 0.001

18. Advantages
 It is usually less expensive because there is less inspection.
 There is less handling of the product, hence reduced damage.
 It is applicable to destructive testing.
 Fewer personnel are involved in inspection activities.
 It often greatly reduces the amount of inspection error.
 The rejection of entire lots are opposed to the sample return of
defectives often provides a stronger motivation to the vendor for
quality improvements.
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19. Disadvantages
 There are risk of accepting “bad” lots and rejecting “good” lots.
 Less information is usually generated about the product or about
the process that manufactured the product.
 Acceptance sampling requires planning and documentation of the
acceptance sampling procedure whereas 100% inspection does
not.
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20. Conclusion
 Acceptance sampling is a statistical procedure used to determine
whether to accept or reject a production lot of material.
 A wide variety of sampling plans are available. Plans have an accepted
AQL & a rejected LTPD & an AOQL.
 Acceptance sampling tables are there to supply a set of accepted
procedures with known properties &verified results.
 Sampling provides rational means of verification that a production lot
confirms with requirements of technical specifications.
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21. THANK YOU
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