The document compares different acceptance sampling standards including MIL-STD-105E, MIL-STD-1916, ISO 2859, and ISO 3951, detailing their specific characteristics and limitations. It outlines the purpose of acceptance quality levels (AQL) and operating characteristic (OC) curves, and emphasizes the efficiency and cost-effectiveness of sampling over 100% inspection. Additionally, it explains various sampling processes and criteria for determining AQLs based on historical data and empirical judgment.

1. Acceptance Sampling
Comparison between:
MIL-STD-105E, MIL-STD-1916, ISO
2859, ISO 3951
AQLs, OC Curves
By Hassan Habib

2. Table of Contents
1. Introduction
2. Review of Basic Terminologies
3. Scope of Sampling Standards
4. Differences among the standards
5. Limitations
6. Information required for sampling practices
7. Sampling Processes
8. Switching Criteria
9. Sampling Tables
10.Determination of AQL
11.Purpose of OC curves
12.Conclusion

3. Introduction
• The standards under consideration are widely used for lot-by-lot acceptance
sampling
• These determine acceptance quality levels of parts produced in a
manufacturing organization to accept or reject lots based on percent non-
conforming
• Provide guidelines to judge whether acceptance quality level is within the
predetermined and agreed quality levels by the supplier and the consumer
• Conclusively, acceptance and rejection of the lots is decided by the samples
undertaken for checks and measurements
• Some of these standards deal with attributes and others deal with variables

4. Introduction
100% Inspection
• Costs are high
• Human Interaction makes it
less effective
• In certain cases, 100%
inspection is not possible
Sampling Inspection
• It takes less time and is less
expensive
• Calculated risks are involved
• Sampling inspection is a
must for destructive testing

5. Review of Basic Terminologies
Acceptance
• The act of an authorized representative of the government by which the
governments, for itself or as agent of another, assumes ownership of existing
identified supplies tendered or approves specific services rendered as partial or
complete performance of the contract
Critical Characteristic
• A characteristic that judgment and experience indicate must be met to avoid
hazardous or unsafe conditions for individuals using, maintaining or depending upon
the product; or that judgment and experience indicated must be met to assure
performance of the tactical function of a major item such as a ship, aircraft, tank,
missile, or space vehicle

6. Review of Basic Terminologies
Critical Non-Conforming Unit
• A unit of product that fails to conform to specified requirements for one or more critical
characteristic
Major Characteristic
• A characteristic other than critical, must be met to avoid failure or a material reduction
or usability of the unit of product for intended purpose
Major Non-Conforming Unit
• A unit of product that fails to conform to specified requirements of one or more major
characteristics, but conforms to all critical characteristics

7. Review of Basic Terminologies
Minor Characteristics
• A characteristic other than critical, or major whose departure from its specification
requirement is not likely not reduce materially the usability of the unit of product for its
intended purpose or whose departure from established standards has little bearing on
the effective use or operation of the unit
Minor Non-Conforming Unit
• A unit of product that fails to conform to specified requirements of one or more minor
characteristics, but conforms to all critical and major characteristics

8. Review of Basic Terminologies
Non- Conformance
• A departure from a specified requirement for any characteristic
Inspection
• Examining and testing supplies or services (including, when appropriate, raw
materials, components, and intermediate assemblies) to determine whether they
conform contract requirement
Non- Conforming Unit
• A unit of a product that has a one or more non conformance

9. Review of Basic Terminologies
Quality
• The composite of material attributes including performance features, and
characteristics of a product or service to satisfy a given need
Quality Assurance
• A planned and systematic pattern of all actions necessary to provide adequate
confidence that adequate technical requirements are established; products and
services conform to established technical requirements; and satisfactory performance
is achieved

10. Scope of Sampling Standards
MIL-STD-105 E
• Establishes lot or batch sampling plans and procedures of inspection by attributes
MIL-STD-1916
• The standard encourages organizations to submit to efficient and effective process control procedures
in place of prescribed sampling requirements. The goal is to support the movement away from AQL
based inspection strategy
ISO 2859
• Specifies sampling plans and procedures for inspection by attributes of discrete items. It is indexed in
terms of the Acceptance Quality Level (AQL)
ISO 3951
• Specifies acceptance sampling system of single sampling plans form inspection by variables
• Inspection procedure is to be applied to a continuing series of lots of discrete products all supplied by
one producer using one production process
• Single quality characteristic is taken into consideration, measurement error is negligible, and production
is distributed normally

11. Differences among standards
Sr. # Characteristic
MIL-STD-
105 E
MIL-STD-1916 ISO 2859 ISO 3951
1. Basics Attributes Attribute / Variables Attributes Variables
2.
Acceptance
Criteria
# of Non
Conformin
g products
/ AQL
# of Non Conforming
Products or s-
characteristic /
verification levels
No. of Non
Conforming
Products /
AQL
S-
characteristi
c / AQL
3. Distribution Any Any Any Normal only
4. Sample Sizes
Standard
Tables
Follows 105 E
Follows 105
E
Different
(usually
smaller)
5. Switching Standard Follows 105 E
Slightly
Different
Different

12. Limitations
Sr. # MIL-STD-105 E MIL-STD-1916 ISO 2859 ISO 3951
1.
Primarily for
continuous
series of batches
or lots / OC
curves to be
consulted
otherwise
Not intended
for use in
sampling of
destructive
tests
Not intended as a
procedure for
estimating lot
quality or for
segregating lots
Intended to be used for
parts produced from a
single production process
for discrete products
2.
Only for single feature
(quality characteristic)
3.
Intended to be used
where measurement error
is negligible and process
is stable

13. Information required for sampling practices
• This is usually known on lots submitted for
inspectionLot Size
• Given in inspection plans or proceduresInspection Level
• This is also known on lots submitted for
inspection. Will be discussed in detailAQL
• Single, Double or multiple
Type of sampling
to use

14. Sampling Process
Basic Process of Acceptance Sampling
Take a sample of
size ‘n’
Inspect all items
in the sample.
Determine actual
defectives ‘d’
Compare ‘d’ with
acceptance
number ‘c’
Accept lot if d<cReject Lot if d>c
Do 100%
inspection
Return Lot to
supplier

15. Sampling Process
Random Sampling
• Random sampling is giving every part in the lot an equal chance of being selected for
the sample regardless of its quality
Single Sample Plans
• Sample units inspected shall be equal to the sample size given by the plan. If the no.
of defectives is less than the acceptance number, the lot or batch shall be considered
acceptable. If it is equal to or greater than the rejection number the same shall be
rejected.

16. Sampling Process
Double Sampling Plans
• Sample is drawn as per the first sample size given by the plan. If the lot is accepted
as per the corresponding acceptance number, the lot is accepted, otherwise another
sample is drawn and is matched with the second acceptance number, if it is equal to
or less than this number, the lot is accepted, else it is rejected.
Multiple Sampling Plans
• In different standards normal sampling size is considered in the start and switching to
other inspection levels is done as and when is deemed necessary.
• Effected by the type of part that is being inspected. For expensive parts, destructive
testing, or harmful testing is to be carried out small sample sizes may be considered.
For MIL-STD-105 E inspection level III may be considered.

17. Switching Criteria
• Preceding 10 lots inspected under normal inspection
• Preceding 10 lots accepted with NC units equal or less
than limit number
• Production steady
• Approved by reasonable authority
Reduced
Inspection
Normal
Inspection
• Preceding 10 lots inspected under normal inspection
• Preceding 10 lots accepted with NC units equal or less
than limit number
• Production steady
• Approved by reasonable authority
2 out of 5 or less
consecutive lots not
accepted
5 consecutive lots
accepted
Tightened
Inspection
Discontinue
Inspection
5 lots not accepted
while on tightened
inspection
Suppliers improves
quality

18. Sampling Tables
Lot Size = 510, AQL=4.0%, General Inspection Level II
Step 1
• Find out the range in
which the lot size falls,
in our case it is 501-
1200
Step 2
• Find out the code letter
under the inspection
level straight across the
lot size. It is J for the
this example
Step 3
• Turn to sampling tables
to find J
Step 4
• Look across the code
letter and under the
required AQL (4.0%).
You will see Ac number
(7) and Re number (8)
Step 5
• Look under the sample
size column and find out
the sample size for this
lot
Step 6
• Carry out the inspection
to find defectives and
compare with Ac and Re
numbers

19. Determination of AQL
Acceptance Quality Levels / Limits Introduction
• It is defined as the maximum percent nonconforming (or the maximum number of non-
conformities per hundred units) that, for purposes of sampling inspection, can be
considered satisfactory as a process average.
• “Can be considered satisfactory” is interpreted as a producer’s risk or α. It varies from
0.01 to 0.1 in the standard.
• In percent non conforming plans, AQLs range from 0.01% to 10%
• These AQLs may be designated by groups or to individual features as critical, minor and
major non conformities

20. Determination of AQL
Basis of determining AQLs
• Historical Data
• Empirical Judgment
• Engineering information such as functions, safety, interchangeability, manufacturability
etc.
• Experimentation by testing lots with various percent nonconforming
• Producer’s Capability

21. Step 1
• Choose a normal
inspection plan and
start inspection
Step 2
• Inspect the whole lot
and find out the actual
percent nonconforming
parts
Step 3
• Compare this with the
OC curve for the given
lot size and acceptance
number
Step 4
• If expected acceptance
of the lot with given
percent nonconforming
is acceptable, continue
with the sampling plan
Step 5
• If expected acceptance
of the lot with given
percent nonconforming
is not acceptable,
change sampling plan
Step 6
• Redo Step 2 to 5 until a
sampling plan as per
the system capability is
chosen
Determination of AQL
Step for determination

22. Purpose of OC curves
Introduction
• It is a tool to determine the probability of acceptance of a lot with a certain percent
nonconforming products

23. Purpose of OC curves
Introduction
• The curves are generated based on the distribution of the data. Usually, the most
common distributions used are:
• Hypergeometric
• Binomial
• Poisson

24. Step 1
• Assume po value
Step 2
• Calculate npo value
Step 3
• Obtain Pa values from
Poisson table using
applicable c and npo
values
Step 4
• Plot point (100po, Pa)
Step 5
• Repeat 1, 2, 3, . . . To
plot the curve
Constructing an OC curve
• For N=3000, Sample size, n=89, acceptance number, c=2, with Poisson distribution,
where Pa=Probability of acceptance, po=Percent nonconforming
Purpose of OC curves

25. Constructing an OC curve
• For N=3000, Sample size, n=89, acceptance number, c=2, with Poisson distribution,
where Pa=Probability of acceptance, po=Percent nonconforming
Purpose of OC curves
Sr. # Po 100po N Npo Pa
1. 0.01 1.0 89 0.9 0.938
2. 0.02 2.0 89 1.8 0.731
3. 0.03 3.0 89 2.7 0.494
4. 0.04 4.0 89 3.6 0.302
5. 0.05 5.0 89 4.5 0.174
6. 0.06 6.0 89 5.3 0.106
7. 0.07 7.0 89 6.2 0.055

26. Constructing an OC curve
Purpose of OC curves
0.938
0.731
0.494
0.302
0.174
0.106
0.055
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4 5 6 7
OC curve for n=89, c=2
Pa

27. Conclusion
Outcomes
• The presentation depicted herein presents briefly an introduction of acceptance
sampling along with some major differences amongst the widely used sampling
standards
• After the introduction and statement of differences between the standards, limitations
of the same were discussed
• The purpose of AQLs, their determining factors and examples were discussed in
detail. A sample way to calculate AQLs was also stipulated.
• Finally, the purpose of OC curves was explained along with an example

28. Conclusion