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Myth: “Acceptance sampling assures
good quality.”
Truth: Acceptance sampling provides
confidence that p (the population
fraction defective) is stable over a
long period of time and across many
lots.
The fundamental goal of acceptance
sampling is to reduce the amount of
inspection needed to verify that lots
of material have some predetermined
level of quality.
Truth: Acceptance sampling allows for
some predetermined level of
non-conformances
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

Modern production philosophies
like small batch sizes and
statistical process control by
variables data are making
acceptance by attributes
increasingly less effective.
To achieve the high levels of
quality that are being achieved in
a free market through
competition, it is getting
increasingly difficult for
acceptance sampling to meet its
goal with reasonable sample
sizes.
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
Part acceptance (old school)
◦ Acceptable Quality Limits (AQL)
◦ Incoming inspection

Process control (new school)
◦ Control charts
◦ Capability studies

Both ways have been used to
decrease consumer risk of
receiving non-conforming
product from suppliers
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
Very good at accepting very good
lots and rejecting very bad lots –
but what about in-between?
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

In the past AQL’s of 1% were
reasonable and process
capability was accepted at Cpk=1
Now we need much lower AQL’s
and Cpk much greater than 1
What happens to sampling?
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
Vendor certification
◦ Companies need to prove themselves
worthy
◦ Supplied data
◦ Auditing





No receiving inspection
Required SPC
Cpk>1.5 usually 2
Ever hear of PPAP, APQP, FMEA,
AS9102? If you haven’t its
coming.
Prove control and capability then sample
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


The home company tells us they put
about 13% RED M&Ms in their mix.
We have a lot (one bag) of delivered
M&Ms. We are randomly going to
sample a bag and we will only accept
the lot if the sample has 13% or less
red in it.
What is the probability of
accepting a sampled lot?
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


How does this correspond to
“Sampling Dilemma”?
What problems does this activity
cause? How does it add cost?
What if we increase the sample
size?
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
Type 1 (producer’s risk, alpha ) –
The probability that a hypothesis that
is actually true will be rejected
◦ The chance that a good lot will be rejected

Type 2 (consumer’s risk, beta ) –
The probability that a hypothesis that
is actually false will be accepted
◦ The chance that a bad lot will be accepted
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What happens to:
producer’s risk
consumer’s risk
as you increase your sample
size?
Why? What do we do?
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




Commonly referred to as OC Curves
Quantifies the producer’s and
consumer’s risk
Identified by the sample size (n) and
the maximum acceptance number (c)
Constructed from the Poisson
probability distribution
No perfect sampling plan exist, there
will always be some risk
Ideal OC Curve
1
Pa
0.75
0.5
0.25
0
1%
2%
Lot percent defective
3%
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
Characterized by
◦ Only two independent outcomes
◦ the average number of occurrences
per time period (pn=)
◦ used for rare events when n is large
and p is small
◦ Good to approximate the binomial
distribution

Constructed by
◦ using a Poisson probability table
Figure 13.2
◦ equation – the probability of exactly c
defectives in a sample of n (pn=)
e  pn ( pn) c
P (c ) 
c!
Poisson PDF
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1.
2.
3.
4.
5.
Choose p values between 0 and .09
Multiply each p value by n and
place it on the table
Make a percent column for p and
mark it 100p
Using Figure 13.2, start at the pn
value on the x-axis and go straight
up to the c= line. Then move
straight across to the y-axis. Read
the probability of acceptance.
Record the Pa value on the table
p
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
pn
100p
0
1
2
3
4
5
6
7
8
9
Pa
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
Pa
p
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
n=150
c=3
pn
100p
0
1
2
3
4
5
6
7
8
9
Pa
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1
2
3
4 5
100p
6
7
8
9
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

AQL
Defined as
◦ The maximum percent defective that is
allowed as a process average
◦ The level of quality of a submitted lot
that has a 95% chance of being accepted
◦ 1-AQL is the producer’s risk

Not the quality level that is being
produced or accepted
Not always the quality goal
In our exercise, it is .9%

How does sample size effect AQL?


◦ See figure 13.7
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
IQL
◦ The quality level that will be accepted
50% of the time.
◦ In our exercise, it is 2.5%
◦ How does sample size effect IQL?
 See figure 13.7

RQL
◦ The level of quality that will be
accepted only 10% of the time
◦ This is the consumer’s risk
◦ In our exercise, it is 4.5%
◦ How does sample size effect RQL?
 See figure 13.7
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AOQL
The maximum Average Outgoing
Quality
Found on the Average Outgoing
Quality (AOQ) curve
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

Shows the result of the incoming
inspection and sorting of rejected
lots
Outgoing quality is the quality
level expected from the process
of inspection
Assumptions
◦ The lots size and incoming quality
level is relatively consistent
◦ All the lots that pass go to
production
◦ All rejected lots are 100% inspected,
non-conforming units are replaced
with conforming units
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1. Create a table that includes;
1. a column for incoming percent defective
(100p)
2. percent accepted from the OC curve(Pa),
3. percentage rejected and fully sorted
(1-Pa)
4. and defects outgoing (Pa*100p)
2. Fill in the table
3. Graph the defects outgoing
4. Identify the AOQL
Incoming
Defective(%)
100p
0
1
2
3
4
5
6
7
8
9
Pa (%)
Rejected
(%)
1-Pa
Defects
Outgoing
Pa * 100p
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Incoming
Defective(%)

n=150
c=3
Pa (%)
Rejected
(%)
Defects
Outgoing
0
1
2
3
4
5
6
7
8
9
1.3
1.2
1.1
1.0
0.9
0.8
0.7
AOQ 0.6
0.5
0.4
0.3
0.2
0.1
1
2 3 4 5 6 7 8
Incoming Percent Defective
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
Variable
◦ Mil-Std-414
◦ ANSI/ASQ-Z1.9-1993

Attribute
◦ Mil-Std-105D
◦ ANSI/ASQ-Z1.4-1993
◦ Dodge-Romig Tables

Purpose
◦ Establishes sampling plans and
procedures
◦ Used as a reference to standardize
sampling
◦ To drive conformity on the switching
procedures between the use a
normal, tightened or reduced
sampling plan
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

Typically you are given a set of
criteria to use by your customer
You will need to know the
following:
◦
◦
◦
◦
◦
Inspection level
Lot size
Single, double or multiple inspection
Normal, reduced or tightened
AQL
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1.
2.
3.
Determine inspection level and lot size
Find inspection plan code letter
Determine if plan is single, double or
multiple inspection
4. Determine if plan is normal, tightened or
reduced
5. Find the correct plan chart
6. Based on code letter, determine sample
size needed
7. Inspect samples
8. Find the appropriate AQL column
9. Find the cell that connects the code letter
row to the AQL column
10. Find acceptance and reject numbers
1.
2.
If your sample has non-conformances equal
to or less than the Ac number, accept the lot
If your sample has non-conformances equal
to or greater than the Re number, reject the
lot
Use Table 13.10-13.14
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

Your customer requires you to use
MIL-STD-105D, single sampling,
normal inspection level II with an
AQL of 1%.
The shipment that arrived had a lot
quantity of 2000. You found the
sample size and determined there
are 3 non-conformances in the lot.
1. Do you accept or reject the lot?
2. What about a double inspection?
Why do a double inspection?
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



As batch sizes get smaller, the
effective number of parts requiring
inspection gets bigger (approaches
100%)
You can see this in the sampling
tables
As quality gets better, bigger and
bigger samples are needed to
detect a shift in the process average
Deming suggests a better (I think)
answer:
◦ Control the process with SPC.
 If it’s capable and in control, don’t inspect
any more than needed to keep it that way.
 If it’s not capable and in control, 100%
inspect.
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