Lesson 15
Acceptance Sampling
a form of inspection applied to lots
or batches of items before or after a
process to judge conformance to
predetermined standards
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Acceptance Sampling
Acceptance 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
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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 sampling
. Double sampling
. Multiple sampling
Lot
Random
sample
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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 - cut off point) the whole lot is rejected; otherwise
the whole lot is accepted
Lot (N
items)
Random
sample
(n items)
Lot (N
items)
Random
sample
(n items)
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Double Sampling Plan
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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Double Sampling Plan
Lot
Accept Lot
First Random
sample
First sample inconclusive,
take second sample
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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Double Sampling Plan
Lot
First Random sample
Second Random sample
Accept Lot
Reject Lot
CT
Compare the total number of defective in both lots to CT and make the
appropriate decision
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Multiple Sampling Plan
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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Acceptance Sampling
Purposes
Determine quality level
Ensure quality is within predetermined level
Advantages
Economy
Less handling damage
Fewer inspectors
Upgrading of the inspection job
Applicability to destructive testing
Entire lot rejection (motivation for
improvement)
Disadvantages
Risks of accepting “bad” lots and
rejecting “good” lots
Added planning and documentation
Sample provides less information
than 100-percent inspection
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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).
Probability of accepting lot
1
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%
0.9
0.8
0.7
0.6
0.5
0.4
If the lot has 20% defective
. it has a small probability (5%) of being accepted
. the probability of rejecting the lot is 95%
0.3
0.2
0.1
0
0
.05
.10
.15
.20
Lot quality (% defective)
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Operating Characteristic Curve (OCC)
Under this sampling plan what is the probability of accepting a lot that
has 5% defectives?
Probability of accepting lot
1
0.9
0.8
Approximately 80%
This sampling plan may not be
acceptable to customer. Therefore,
this sampling plan may not be
acceptable for meeting the
customers level of quality.
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
.05
.10
.15
.20
Lot quality (% defective)
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Customer Acceptance Levels
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.
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Customer Acceptance Levels
Therefore the sampling plan must be designed to assure the customer
that they will be receiving the required AQL and LTPD.
The AQL and LTPD are dependent on many things (reliability, liability,
competitor quality levels, etc.) and will vary by industry and by customer.
Typically industry standards are set because suppliers have more than
one customer and customers have more than one supplier.
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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OCC, AQL & Producer’s Risk
1
Producer’s Risk = probability acceptable lot is rejected
Probability of accepting lot
0.9
0.8
0.7
0.6
0.5
AQL - percentage level of defects at
which a customer is willing to accept
0.4
0.3
0.2
0.1
0
0
.05
.10
.15
.20
Lot quality (% defective)
“Acceptable Lot”
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OCC, LTPD & Consumer’s Risk
1
Probability of accepting lot
0.9
0.8
0.7
LTPD - upper limit on the percentage
of defectives that a customer is
willing to accept.
0.6
0.5
0.4
0.3
0.2
0.1
Consumer’s Risk = probability unacceptable is accepted
0
0
.05
.10
.15
.20
Lot quality (% defective)
“Unacceptable Lot”
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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).
N-n
AOQ = Pac * p(
) where
N
Pac = Probability of accepting a lot
p = Fraction defective
n = sample size
N = Lot size
The maximum outgoing quality level is referred to as the AOQL.
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OCC
Example: Create an Operating Characteristic Curve for the sampling plan: Lot
Size = N = 2000, sample size = n = 10, reject if number defectives > C = 1.
Answer the following questions.
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Operating Characteristic Curves
What is the probability of
accepting a lot which has
2.5% defective?
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Operating Characteristic Curves
What is the Producer’s risk if the
AQL is 1%?
.0043
Mouse over the “Producer’s
risk” cell to see the explanation.
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Operating Characteristic Curves
What is the Consumer’s risk if the
LTPD is 6%?
.8824
Mouse over the “Consumer’s
Risk” cell to see the explanation.
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Operating Characteristic Curves
What is the AOQ curve?
What is the AOQL?
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Homework
Read and understand all material in the chapter.
Discussion and Review Questions
Recreate and understand all classroom examples
Exercises on chapter web page
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