668819271-presentation ACCEPTANCE-SAMPLING.pptx

15 - 1
a form of inspection applied to lots or
batches of items before or after a
process to judge conformance to
predetermined standards
Acceptance Sampling

Acceptance Sampling
• Acceptance sampling is a method used to accept or reject
product based on a random sample of the product.
• The purpose of acceptance sampling is to sentence lots (accept
or reject) rather than to estimate the quality of a lot.
• Acceptance sampling plans do not improve quality. The nature
of sampling is such that acceptance sampling will accept some
lots and reject others even though they are of the same quality.
• The most effective use of acceptance sampling is as an auditing
tool to help ensure that the output of a process meets
requirements.

When to use acceptance sampling?
• When testing is destructive.
• 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
• When the cost of 100% inspection is high.
• When 100% inspection is not technologically feasible or would
require so much calendar time and/or expenses.
• When there are many items to be inspected and the inspection
error rate is high.
• When the vendor has an excellent quality history, and some
reduction in inspection from 100% is desired.
• When there are potentially serious product liability risks.

Acceptance Sampling
• Purposes
– Determine quality level
– Ensure quality is within predetermined level

Advantages of Acceptance Sampling

Disadvantages of Acceptance Sampling
• Risks of accepting ”bad” lots and rejecting “good” lots.
In the “good” lot, there might be nonconformities.
• Sample provides less information than 100-percent
inspection
• Acceptance sampling requires more time on planning
and documentation of the acceptance sampling
procedure.

15 - 7
Sampling Plans specify the lot size, sample size, number of samples
and acceptance/rejection criteria. Sampling plans involve
. Single sampling
. Double sampling
. Multiple sampling
- Sequential Sampling
Random
sample
Lot
Sampling Plans

15 - 8
Lot Formations
Considerations before inspection:
• Lots should be homogeneous
Units in a lot should be produced by the same:
 machines,
operators,
from common raw materials,
approximately same time
• Larger lots more preferable than smaller lots
• Lots should be conformable to the materials-handling
systems used in both the vendor and consumer
facilities.

15 - 9
Random Sampling
• The units selected for inspection should be
chosen at random.
• Should be representative of all units in a lot
• Watch for Salting: Vendor may put “good” units on top layer of
lot knowing a lax inspector might only sample from the top layer
• Random samples are not used, bias can be
introduced.
• If any judgment methods are used to select the
sample, the statistical basis of the acceptance-
sampling procedure is lost.

15 - 10
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
Random
sample
(n items)
Lot (N
items)
Random
sample
(n items)
Lot (N
items)

(n,c)
Accept the lot
Reject the lot
d C
≦
d>C
(N, p)
Total number ： N
The proportion of defects :P
Where dis the number of the actual defects in the sample.

15 - 12






c
d n
N
d
n
K
N
d
K
a
C
C
C
c
d
P
0
)
*(
)
(
)
(
Probability of Acceptance :
N, lot size
K, total number of defective items in the lot
n, sample size
d, total number of defective items in the sample
c, acceptable limit of defective items in the sample

15 - 13
d
n
d
c
d
d
n
a p
p
C
c
d
P 



  )
1
(
)
(
0
Probability of Acceptance :
The lot size N is very large,
p is fraction defective,
d is the defective items in the sample and
c is the acceptable limit of defective items in
the sample.

Operating Characteristic (OC) Curve
• An Operating Characteristic Curve (OC) is a probability curve for a
specific sampling plan that shows the probabilities of accepting lots
with various lot quality levels (% defectives).
• Assists management to discriminate between good and bad lots
• Exact shape and location of the curve is defined by the sample size (n)
and acceptance level (c) for the sampling plan
15 - 14

15 - 15
Operating Characteristic Curve (OCC)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 .05 .10 .15 .20
Probability
of
accepting
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%

15 - 16
Operating Characteristic Curve (OCC)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 .05 .10 .15 .20
Probability
of
accepting
lot
Lot quality (% defective)
Under this sampling plan what is the probability of accepting a lot that
has 5% defectives?
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.

15-17
OC Curve (cont.)
OC curve for n and c
Proportion defective
AQL LTPD
Probability
of
acceptance,
Pa
 = 0.10
 = 0.05
1.00 –
0.80 –
0.60 –
0.40 –
0.20 –
–
|
0.02
|
0.04
|
0.06
|
0.08
|
0.10
|
0.12
|
0.14
|
0.16
|
0.18
|
0.20

Ideal OC Curve
• Suppose the lot quality is considered bad if p = 0.01 or more
• A sampling plan that discriminated perfectly between good and bad lots would
have an OC curve like:
15 - 18
1.00
0.04
0.01 0.02 0.03
Lot fraction defective, p
Probability of Acceptance, Pa

Ideal OC Curve (cont’d)
• In theory it is obtainable by 100% inspection Iif inspection were error free.
• Obviously, ideal OC curve is unobtainable in practice
• But, ideal OC curve can be approached by increasing sample size, n.
15 - 19

Producer and Consumer Risks in
Acceptance Sampling
• Most customers understand that 100% inspection is impractical and are
generally willing to accept that a certain level of defectives will be produced.
• AQL or Acceptable Quality Level
– is the percentage level of defects at which a customer is willing to accept
a lot as “good”.
• LTPD or Lot Tolerance Percent Defective
– is the upper limit on the percentage of defectives that a customer is
willing to accept.
15 - 20

• 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.
• 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.
15 - 21
Acceptance Sampling

• Because we take only a sub-sample from a lot, there is a risk that a good lot
will be rejected and bad lot will be accepted.
• The Producer’s Risk is the probability that a “good” lot will be rejected.
 (Producer’s Risk – a)
• The Consumer’s Risk is the probability that an unacceptable lot (e.g. above
the LTPD) will be accepted.
 (Consumer’s Risk – b )
15 - 22
Acceptance Sampling

Producer’s and Consumer’s Risk (cont’d)
Sampling Errors
Good
Lot
Bad
Lot Accept Reject
No Error
Type I Error
Producer’ Risk α
Type II Error
Consumer’s Risk β
No Error

Producer’s Risk - a
• Producer wants as many lots accepted by consumer as possible so
– Producer “makes sure” the process produces a level of fraction defective
equal to or less than:
p1 = AQL = Acceptable Quality Level
–
a is the probability that a good lot will be rejected by the consumer even
though the lot really has a fraction defective  p1
• That is, Lot is rejected given that process
has an acceptable quality level
P

 
  
 
Lot is rejected
P p AQL
  
 
 
a
P

1


15 - 25
OCC, AQL & Producer’s Risk
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability
of
accepting
lot
0
0.1
0 .05 .10 .15 .20 Lot quality (% defective)
AQL - percentage level of defects at
which a customer is willing to accept
“Acceptable Lot”
Producer’s Risk = probability acceptable lot is rejected

26
Consumer’s Risk - b
• Consumer wants to make sure that no bad lots are accepted
– Consumer says, “I will not accept a lot if percent defective is greater
than or equal to p2”
p2 = LTPD = Lot Tolerance Percent Defective
b is the probability that a bad lot is accepted by the consumer when the
lot really has a fraction defective  p2
• That is,
Lot accepted given that lot
has unacceptable quality level
P

 
  
 
Lot accepted
P p LTPD
  
 
 

15 - 27
OCC, LTPD & Consumer’s Risk
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability
of
accepting
lot
0
0.1
0 .05 .10 .15 .20 Lot quality (% defective)
LTPD - upper limit on the percentage
of defectives that a customer is
willing to accept.
Consumer’s Risk = probability unacceptable is accepted
“Unacceptable Lot”

• The sample size n and acceptance number c are the
solution to:
 


 







c
0
d
d
n
2
d
2
c
0
d
d
n
1
d
1
)
p
1
(
p
)!
d
n
(
!
d
!
n
)
p
1
(
p
)!
d
n
(
!
d
!
n
1


Designing a Single-Sampling Plan with a Specified OC Curve

29
Designing a Single-Sampling Plan with a Specified OC Curve
• Use a chart called a Binomial Nomograph to design
plan
• Specify:
 p1 = AQL (Acceptable Quality Level)
 p2 = LTPD (Lot Tolerance Percent Defective)
 1 – a = P[Lot is accepted | p = AQL]
 β = P[Lot is accepted | p = LTPD]

30
Use a Binomial Nomograph to Find Sampling Plan
• Draw two lines on nomograph
– Line 1 connects p1 = AQL to (1- a)
– Line 2 connects p2 = LTPD to b
– Pick n and c from the intersection of the lines
• Example: Suppose
– p1 = 0.01,
– α = 0.05,
– p2 = 0.06,
– β = 0.10.
Find the acceptance sampling plan.

Greek - Axis
p - Axis
p1 = AQL = .01
1 –  = 1 – .05 = .95
p2 = LTPD = .06

= .10
n = 120
c = 3
Take a sample of size 120.
Accept lot if defectives ≤ 3.
Otherwise, reject entire lot!

15-32
Rectifying Inspection Programs
• Acceptance sampling programs usually require corrective
action when lots are rejected, that is,
– Screening rejected lots
• Screening means doing 100% inspection on lot
• In screening, defective items are
– Removed or
– Reworked or
– Returned to vendor or
– Replaced with known good items

15 - 33
Inspection
Activity
Rejected Lots:
100%
Inspected
Accepted
Lots
Fraction
Defective
Incoming Lots:
Fraction Defective
Fraction
Defective = 0
Outgoing Lots:
Fraction Defective
0
p
0
p
1 0
p p

Rectifying Inspection Programs

Where to Use Rectifying Inspection
15 - 34
• Used when manufacturer wishes to know average level of quality
that is likely to result at given stage of manufacturing
• Example stages:
– Receiving inspection
– In-process inspection of semi-finished goods
– Final inspection of finished goods
• Objective: give assurance regarding average quality of material
used in next stage of manufacturing operations

15-35
Average Outgoing Quality: AOQ
• Quality that results from application of rectifying inspection
– Expected number of defective items that will pass on to customer
with a sampling plan
– Average value obtained over long sequence of lots from process
with fraction defective p
• N - Lot size, n = # units in sample
• Assumes all known defective units replaced with good ones,
that is,
– If lot rejected, replace all bad units in lot
– If lot accepted, just replace the bad units in sample
• Average outgoing quality limit (AOQL) is the maximum
outgoing quality level.
– maximum point on the curve
– worst level of outgoing quality
 
a
P p N n
AOQ
N



Development of AOQ
• If lot accepted:
Number defective units in lot:
• Expected number of defective units:
• Average fraction defective,
Average Outgoing Quality, AOQ:
  
# units
fraction
remaining
defective
in lot
p N n
 
   
    
 
 
 
   
Lot # defective
Prob
accepted units in lot
a
P p N n
   
     
   
 
a
P p N n
AOQ
N



Calculating the AOQL
EXAMPLE
Suppose that Noise King is using rectified inspection for its single-sampling plan.
Calculate the average outgoing quality limit for a plan with n = 110, c = 3, and N =
1,000. Calculate the probabilities of acceptance for values of the proportion
defective from 0.01 to 0.08 in steps of 0.01.
SOLUTION
Use the following steps to estimate the AOQL for this sampling plan:
Step 1: Determine the probabilities of acceptance for the desired values of p.
These are shown in the following table.
15-23

15 - 38
Proportion
Defective (p)
Probability of
Acceptance
(Pa)
0.01 0.974
0.02 0.819
0.03 0.581
0.04 0.359
0.05 0.202
0.06 0.105
0.07 0.052
0.08 0.024

Step 2: Calculate the AOQ for each value of p.
For p = 0.01: 0.01(0.974)(1000 – 110)/1000 = 0.0087
The plot of the AOQ values is shown in Figure (Next page)
For p = 0.02: 0.02(0.819)(1000 – 110)/1000 = 0.0146
For p = 0.03: 0.03(0.581)(1000 – 110)/1000 = 0.0155
For p = 0.04: 0.04(0.359)(1000 – 110)/1000 = 0.0128
For p = 0.05: 0.05(0.202)(1000 – 110)/1000 = 0.0090
For p = 0.06: 0.06(0.105)(1000 – 110)/1000 = 0.0056
For p = 0.07: 0.07(0.052)(1000 – 110)/1000 = 0.0032
For p = 0.08: 0.08(0.024)(1000 – 110)/1000 = 0.0017

Step 3: Identify the largest AOQ
value, which is the estimate of
the AOQL. In this example, the
AOQL is 0.0155 at p = 0.03.
AOQL
1.6 –
1.2 –
0.8 –
0.4 –
0 –
| | | | | | | |
1 2 3 4 5 6 7 8
Defectives in lot (percent)
Average
outgoing
quality
(percent)
Figure : Average Outgoing Quality Curve for the Noise King Muffler Service

15 - 41
Average Total Inspection (ATI)
)
)(
1
(
*
)
1
(
)
1
(
*
)
1
(
*
)
1
(
*
n
N
P
n
N
P
P
n
n
N
P
nP
n
n
N
P
n
P
ATI
a
a
a
a
a
a
a

















If lot is accepted:
Number of units inspected = n with a probability of
If lot is rejected:
Number of units inspected = N with a probability of
Average Total Inspection
a
P
a
P

1

15 - 42
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
Double Sampling Plan

15 - 43
First Random
sample
Lot
CL CU
First sample inconclusive,
take second sample
Reject Lot
Accept Lot
Compare number of defective found in the first random sample to CL
and CU and make appropriate decision.

15 - 44
CT
Reject Lot
Accept Lot
Compare the total number of defective in both lots to CT and make the
appropriate decision
Lot First Random sample
Second Random sample

(n1, c1)
Accept the lot
Reject the lot
dn1 c
≦ 1
dn1>c2
(n1+n2 , c2)
c1<dn1 c
≤ 2
Accept the lot
Reject the lot
d(n1+n2) c
≤ 2
d(n1+n2) >c2
(N,p)
15 - 45

• Probability of Acceptance
• ASN (Average Sampling Number)
15 - 46
Double Sampling Plan (cont’d)
)
(
)
( 2
2
1
1
1 c
d
d
P
c
d
P
P
P
P
P
a
II
a
I
a
a







)
1
(
)
1
)(
(
2
1
2
1
1
I
I
I
P
n
n
P
n
n
P
n
ASN








15 - 47
Example

• Solution:
15 - 48
279
.
0
)
95
(.
)
05
(.
)
1
(
1
0
50
50
1
0
50
50
1
1
1
1
1
1
1
1










d
d
d
d
I
a
d
d
d
d
I
a
C
P
p
p
C
P

• To obtain the probability of acceptance on the second
sample, we must list the number of ways the second sample
can be obtained. A second sample is drawn only if there are
two or three defectives in the first sample – that is if
15 - 49
2
1
1 c
d
c 

Decision
2 0 Accept
2 1 Accept
3 0 Accept
1
d 2
d
II
a
P

15 - 50
010
.
0
001
.
0
009
.
0
)
0
,
3
(
)
1
,
2
(
001
.
0
0059
.
0
220
.
0
)
95
.
0
(
)
95
.
0
.(
)
05
(.
)
0
(
)
3
(
)
0
,
3
(
.
2
009
.
0
037
.
0
261
.
0
)
95
.
0
(
)
95
.
0
.(
)
05
(.
)
1
(
)
2
(
)
1
,
2
(
.
1
2
1
2
1
0
100
0
0
100
3
50
3
3
50
2
1
2
1
1
0
100
100
2
50
2
2
50
2
1
2
1
1
1
1
1





































d
d
P
d
d
P
P
p
C
C
d
P
d
P
d
d
P
p
C
C
d
P
d
P
d
d
P
II
a
d
d
d
d
Therefore,

• Therefore,
15 - 51
289
.
0
010
.
0
279
.
0




 II
a
I
a
a P
P
P

15 - 52
N
p
n
n
N
P
n
N
P II
a
I
a
AOQ )]
(
)
(
[ 2
1
1 




)
1
(
)
( 2
1
1 a
II
a
I
a P
N
P
n
n
P
n
ATI 




sample)
first
on the
rejected
is
(Lot
sample)
first
on the
accepted
is
Lot
(
)
1
)(
( 2
1
1
P
P
P
P
n
n
P
n
ASN
d
d
d






For Rectifying Inspection:

• Sequential Sampling is an extension of the double-sampling and multiple-
sampling concept.
• In sequential sampling, we take a sequence of samples from the lot and allow
the number of samples to be determined entirely by the results of the
sampling process.
• In practice, sequential sampling can theoretically continue indefinitely, until
the lot is inspected 100%.
• In practice, sequential-sampling plans are usually truncated after the number
inspected is equal to three times the number that would have been inspected
using a corresponding single-sampling plan.
• If the sample size selected at each stage is greater than one, the process is
usually called group sequential sampling.
• If the sample size inspected at each stage is one, the procedure is usually
called item-by-item sequential sampling.
15 - 53
Sequential Sampling Plan

• Item-by-item sequential sampling is based on the sequential probability ratio
test (SPRT).
• The cumulative observed number of defectives is plotted on the chart.
• For each point, the abscissa is the total number of items selected up to
that time, and the ordinate is the total number of observed defectives.
• If the plotted points stay within the boundaries of the acceptance and
rejection lines, another sample must be drawn.
• As soon as the point falls on or above the upper line, the lot is rejected.
• When a cumulative plot falls on or below the lower line, the lot is
accepted.
15 - 54
Item-by-Item Sequential Sampling Plan

The equations for the two limit lines for specified values of p1, 1 – a, p2, and b
are
where
sn
h
X A 

 1
sn
h
XR 
 2
k
β
α
h







 

1
log
1
k
α
β
h





 

1
log
2
 
 










2
1
1
2
1
1
log
p
p
p
p
k
 
 
k
p
p
s










 2
1
1
1
log
(Acceptance line)
(Rejection line)
Item-by-Item Sequential Sampling Plan (cont’d)
15 - 55

15 - 56

• Example:
• For p1=0.01, α=0.05, p2=0.06, and β=0.10
• k=0.80066,
• h1=1.22
• h2=1.57
• s=0.028
15 - 57
(Reject)
n
X
and
Accept
n
X
R
A
028
.
0
57
.
1
)
(
028
.
0
22
.
1






15 - 58
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
Multiple Sampling Plan

15 - 59
Military Standard 105E
(ANSI/ASQC Z1.4, ISO 2859)

15 - 60
Description of MIL STD 105E
• Standard Sampling procedures for inspection by attributes were
developed during World War II.
• MIL STD 105E is the most widely used acceptance sampling system for
attributes in the world today. The original version of the standard, MIL
STD 105A, was issued in 1950. Since then, there have been four
revisions; the latest version was issued in 1989.
• MIL STD 105E is a collection of sampling schemes; therefore, it is an
acceptance sampling system.

15 - 61
• The standard provides for three types of sampling, single
sampling, double sampling, and multiple sampling.
• For each type of sampling plan, a provision is made for either
normal inspection, tightened inspection, or reduced inspection.
• Normal inspection is used at the stat of the inspection activity.
• Tightened inspection is instituted when the vendor’s recent
quality history has deteriorated.
• Acceptance requirements for lots under tightened inspection are
more stringent than under normal inspection.
• Reduced inspection is instituted when the vendor’s recent quality
history has been exceptionally good. The sample size used under
reduced inspection is less than that under normal inspection.
Description of MIL STD 105E (cont’d)

15 - 62
• The sample size used in MIL STD 105E is determined by the lot size
and by the choice of inspection level.
• Three general levels of inspection are provided.
 Level II is designated as normal.
Level I requires about one-half the amount of inspection as Level
II and may be used when less discrimination is needed.
Level III requires about twice as much inspection as Level II and
should be used when more discrimination is needed.
• There are also four special inspection levels, S-1, S-2, S-3 and S-4.
The special inspection levels use very small samples, and should
only be employed when the small sample sizes are necessary and
when large sampling risks can or must be tolerated.

15 - 63
Switching Procedures
Switching procedures between normal, tightened, and reduced inspection:
1. Normal to tightened. When normal inspection is in effect, tightened
inspection is instituted when two out of five consecutive lots have been
rejected on original submission.
2. Tightened to normal. When tightened is in effect, reduced inspection is
instituted when five consecutive lots or batches are accepted on original
inspection.

15 - 64
3. Normal to reduced. When normal inspection is in effect, reduced
inspection is instituted provided all four of the following conditions
are satisfied.
a. The preceding 10 lots have been on normal inspection, and none
of the lots have been rejected on original inspection.
b. The total number of defectives in the samples from the
preceding 10 lots is less than or equal to the applicable limit
number specified in the standard.
c. Production is at a steady state; that is, no difficulty such as
machine breakdowns, material shortages, or other problems
have recently occurred.
d. Reduced inspection is considered by the authority responsible
for sampling.
Switching Procedures (cont’d)

15 - 65
4. Reduced to normal. When reduced inspection is in effect, normal
inspection is instituted provided any of the following four conditions
has been met.
a. A lot or batch is rejected.
b. When the sampling procedure terminates with neither
acceptance nor rejection criteria having been met, the lot or
batch is accepted, but normal inspection is reinstituted starting
with the next lot.
c. Production is irregular or delayed.
d. Other conditions warrant that normal inspection be instituted.
5. Discontinue of Inspection. In the event that 10 consecutive lots
remain on tighten inspection, inspection under the provision of MIL,
STD 105E should be terminated, and action should be taken at the
vendor level to improve the quality of submitted lots.
Switching Procedures (cont’d)

66
Switching Rules for normal, tightened and reduced inspection
Start
Discontinue
inspection
10 consecutive lots
remain on
tightened
inspection
“or” conditions
• Lot rejected
• Irregular production
• A lot meets neither the
accept nor the reject
criteria
• Other conditions warrant
return to normal
inspection
“and” conditions
• production steady
• 10 consecutive lots
accepted
• Approved by
responsible authority
2 out of 5
consecutive lots
rejected
5 consecutive lots
accepted
Normal Tightened
Reduced

15-67
Step-by-Step Procedure
A step-by-step procedure for using MIL STD 105E is as follows:
1. Choose the AQL
2. Choose the Inspection Level
3. Determine the Lot Size
4. Find the appropriate sample code letter from Table 14-4.
5. Determine the appropriate type of sampling plan to use (single,
double, multiple).
6. Enter the appropriate table to find the type of plan to be used.
7. Determine the corresponding MIL STD 105E normal and reduced
inspection plans to be used when required.
• Normal Sampling Plan is to be used as long as supplier is producing
the product at AQL quality or better
• MIL STD 105E provides procedure for switching to tightened or
reduced inspection if there is an indication that the supplier’s quality
has changed.
Step-by-Step Procedure of MIL STD 105E (cont’d)

15 - 68
Table 14.4 presents the sample size code letter for MIL, STD 105E
Tables 14-5, 14-6, and 14-7 presents the single sampling plan for
normal, tighten, and reduced inspection level respectively
Example:
Suppose a product is submitted in lots of size N=2000, AQL=0.65%
From Table 14.4 the code letter under general inspection level II is K
For single sampling plan:
From Table 14.5 under normal inspection level n=125, c=2
From Table 14.6 under tighten inspection level n=125, c=1
From Table 14.7 under reduced inspection level n=50, c=1

15-69
Sample Size Code Letters (MIL STD 105E, Table 14.4)
Lot or Batch Size S-1 S-2 S-3 S-4 I II III
2 to 8 A A A A A A B
9 to 15 A A A A A B C
16 to 25 A A B B B C D
26 to 50 A B B C C D E
51 to 90 B B C C C E F
91 to 150 B B C D D F G
151 to 280 B C D E E G H
281 to 500 B C D E F H J
501 to 1200 C C E F G J K
1201 to 3200 C D E G H K L
3201 to 10000 C D F G J L M
10001 to 35000 C D F H K M N
35001 to 150000 D E G J L N P
150001 to 500000 D E G J M P Q
500001 and over D E H K N Q R
Special Inspection Levels
General Inspection
Levels
Other charts and tables are available on the courses website under resources.

15 - 70
Normal Inspection Single Sampling (MIL STD 105E, Table 14.5)

15 - 71
Tighten Inspection Single Sampling (MIL STD 105E, Table 14.6)

15 - 72
Reduced Inspection Single Sampling (MIL STD 105E, Table 14.7)

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