Quality Control
Chapter 10- Acceptance
Sampling Systems
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Outline
 Lot-by-lot acceptance sampling plans for
attributes
 Acceptance sampling plans for continuous
production
 Acceptance sampling plans for variables
Besterfield: Quality Control, 8th ed..
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Learning Objectives
When you have completed this chapter you should
be able to:
 Determine the sampling plan using ANSI/ASQ Z1.4.
 Know the switching rules for ANSI/ASQ Z1.4.
 Categorize the various sampling plan systems in
terms of lot-by-lot, continuous production,
attributes or variables.
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Learning Objectives-cont’d.
When you have completed this chapter you should
be able to:
 Describe the various sampling plan systems and
know their function (advantages, disadvantages,
purpose etc.).
 Determine the sampling plan using the Dodge Romig
Tables
 Construct the OC Curve for a chain sampling plan.
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Learning Objectives-cont’d.
When you have completed this chapter you should
be able to:
 Be able to use the Shainin Lot Plot Method.
 Determine the sampling plan ANSI/ASQ S1
 Determine whether a lot is accepted or rejected
using ANSI/ASQ Z1.9
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Lot-by-Lot Acceptance Sampling
Plans for Attributes
 Devised in 1942 at Bell Labs
 Later became MIL-STD-105E
 ISO-2859
 ANSI/ASQ Z1.4
 Wording & terminology changes
 Additional tables added
Besterfield: Quality Control, 8th ed..
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ANSI/ASQ Z1.4
 This standard is applicable to:
 End items
 Components and raw materials
 Operations
 Materials in process
 Supplies in storage
 Maintenance operations
 Data or records
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ANSI/ASQ Z1.4
 Intended to be used for a continuing
series of lots, but may be designed for
isolated lots.
 Standard provides for single, double, and
multiple sampling plans.
 Provision is also provided for normal,
tightened, or reduced inspection.
 Plan is specified by the AQL, and sample-
size code.
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ANSI/ASQ Z1.4
 Normal inspection is used at the start of
inspection with changes being a function of
recent quality history.
 Tightened inspection:
 Generally used when producer’s recent
quality history has deteriorated.
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ANSI/ASQ Z1.4
 Reduced inspection:
 Used when the producer’s recent quality
history has been exceptionally good.
 Decision concerning what type of plan to use is
left to the responsible authority.
 Nonconformities are classified such as critical,
major…
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ANSI/ASQ Z1.4
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Sample Size Code Letters
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Comparison of Inspection levels
100
95
= 0.05
Percent of Lots Accepted (100Pa)
80
60
I = 1/2 n
II = n
III = 2n
40
III
II
I
20
100=10
0
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4
6
Percent Nonconforming (100Pa)
8
10
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ANSI/ASQ Z1.4
 AQL
 The AQL is the most important part of the
standard since the AQL and sample size dictate
the plan used.
 AQL is defined as the maximum percent
nonconforming that can be considered
satisfactory as a process average.
Satisfactory = Producer’s risk, α
Usually 0.05
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ANSI/ASQ Z1.4
AQL
AQL is specified by contract or
responsible authority.
AQL may be determine from
historical data, empirical judgment,
engineering information,
experimentation, producer’s
capability, consumer’s
requirements.
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ANSI/ASQ Z1.4
 AQL
 AQL is specified by contract or responsible
authority.
 AQL may be determine from historical data,
empirical judgment, engineering information,
experimentation, producer’s capability,
consumer’s requirements.
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ANSI/ASQ Z1.4
 Sample Size
 Determined by lot size and inspection
level
Use of sample-size code
 Inspection level is determined by the
responsible authority.
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ANSI/ASQ Z1.4
 Sample Size
 Different levels of inspection provide
approximately the same protection to the
producer, but different protections to the
consumer.
 Plan provides for “special” levels to be
used where relatively small sample sizes
are necessary and large sampling risks
must be tolerated. (S-1, S-2, S-3, S-4)
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ANSI/ASQ Z1.4
 Implementation
Determine lot size
Determine inspection level
Find sample-size code letter in table
Determine AQL
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ANSI/ASQ Z1.4
 Implementation cont’d.
Determine type of sampling plan
Find sampling plan in appropriate table
Start with normal inspection and change
to tightened or reduced based on
switching rules
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AQL
What an AQL means is that as long as a
supplier maintains his/her process average (%
defective) at the assigned AQL or lower, there
is a very high probability that shipments from
that supplier, when inspected using ASQ Z1.4
sampling plans, will be accepted.
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AQL
By the same token, there is a very high
probability that shipments, when inspected
using ASQ Z1.4 sampling plans, will be rejected
if a supplier's process average (% defective)
remains higher than the assigned AQL.
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ANSI/ASQ Z1.4
 Single sampling plans
Start by identification of AQL, lot size,
inspection level, and type of sampling
plan.
Locate appropriate plan parameters in
tables.
 Double and Multiple Sampling
Similar procedures as single sampling
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ANSI/ASQ Z1.4
 Normal, Tightened, and Reduced Inspection
 Start with normal inspection
 Switching Procedures
 Normal to tightened
Institute when 2 out of 5 consecutive lots not accepted
on original inspection
 Tightened to normal
Institute when 5 consecutive lots accepted
If not, then discontinue inspection under this plan
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ANSI/ASQ Z1.4
 Switching Procedures
 Normal to reduced
 Institute when: (all of the following)
 Preceding 10 lots on normal inspection have
been accepted
 Total nonconforming in preceding 10 samples
is less than number identified in Table 10-5.
 Production is at a steady rate
 Reduced inspection is considered desirable by
responsible authority
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ANSI/ASQ Z1.4
 Switching Procedures
 Reduced to normal
Institute when: (any of the following)
A lot is not accepted
Sampling procedure terminates with neither
acceptance or rejection criteria have been met
Production is irregular or delayed
Other conditions
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ANSI/ASQ Z1.4
 Standard is designed for use where units of product
are produced in a continuing series of lots or
batches.
 If a sampling plan is desirable for a lot or batch of an
isolated nature, it should be chosen based on the
Limiting Quality (LQ) and consumer’s risk, b.
 These tables are included in the standard, but not
the textbook.
 Or use ANSI/ASQ Standard Q3
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ANSI/ASQ Standard Q3
 Standard is used for inspection of isolated
lots by attributes.
 Provides indexed tables by Limiting
Quality, LQ.
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ANSI/ASQ Standard Q3
 Two Schemes:
1. Used for lots that are isolated or mixed or
that have an unknown history as far as all
parties know.
Lot size and LQ must be known.
Nominal values of the LQ are based on
b=0.10
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ANSI/ASQ Standard Q3
 Two Schemes:
2. Used when a vendor is producing a
continuous stream of lots and sends one
or a few to a customer who will consider
them as isolated lots.
Occurs frequently when purchasing
small quantities of raw materials.
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Dodge-Romig Tables
 A set of inspection tables for lot-by-lot
acceptance sampling by attributes.
 Tables are based on Limiting Quality (LQ)
and Average Outgoing Quality Limit (AOQL).
Tables for single and double sampling
 Advantage that the plan provides a
minimum amount of inspection for a given
inspection procedure.
Desirable for in-house inspection
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Dodge-Romig Tables
Limiting Quality – LQ
Based on the probability that a particular lot,
which has percent nonconforming equal to the
LQ, will be accepted.
Probability is the consumer’s risk, β = 0.10
LQ plans give assurance that individual lots
of poor quality will rarely be accepted.
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Dodge-Romig Tables
 Observations about the LQ tables:
As the lot size increases, the relative
sample size decreases.
The tables extend until the process
average is one-half of the LQ.
As the process average increases, a
corresponding increase occurs in the
amount inspected.
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Dodge-Romig Tables
 Average Outgoing Quality Limit – AOQL
Applicable when the inspected lot is a
convenient subdivision of a flow of
product for materials handling purposes
(non-homogeneous)
AOQL plan limits the amount of poor
outgoing quality on an average basis, but
gives no assurance on individual lots.
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Dodge-Romig Tables
 Process average
 Obtained by the same techniques as for
p-charts
First 25 lots the average percent nonconforming
is obtained
 Type of nonconformance
 Dodge-Romig tables do not provide for different
categories or tightened inspection
Different LQ or AOQL values may be used
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Chain Sampling Inspection Plan
 A special type of lot-by-lot acceptance sampling
plan for attributes designated as “Chain Sampling
Plan ChSP-1”.
 Applicable to quality characteristics which involve
destructive or costly tests.
 Use of small sample sizes
 Acceptance number, c=0
Poor shape of OC curve at the producer’s risk
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Chain Sampling Inspection Plan
 Chain sampling uses the cumulative results of
several samples
Determination of the value of i, the
number of previous samples, is
determined by analysis of the OC curves
for a given sample size.
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Chain Sampling Inspection Plan
 Procedure:
 For each lot, select a sample of size
n and test each for conformance to
specifications.
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Chain Sampling Inspection Plan
 Procedure:
 If the sample has 0 nonconforming units,
accept the lot; if the sample has 2 or
more nonconforming units, do not accept
the lot; and if the sample has 1
nonconforming unit, it may be accepted
provided that there are 0 nonconforming
units in the previous
i samples of size n.
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Chain Sampling Diagram
Current Lot
i previous lots
n=5
c=0
Secondto-Last
Lot
Last Lot
Accept if 0 Nonconforming Units &
in n =5 or if 1 Nonconforming Unit
Zero Nonconforming Units in i
Previous Lots
Figure 10-4 Chain Sampling Diagram
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Chain Sampling Inspection Plan
Conditions for use of the Chain Sampling Plan:
1. The lot should be one of continuing
series of product that is sampled in
substantially the order of production
2. The consumer can normally expect
the lots to be essentially the same
quality.
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Chain Sampling Inspection Plan
Conditions for use of the Chain Sampling Plan:
3. The consumer has confidence in the
producer not to occasionally send an
unacceptable lot that would have the
optimum chance of acceptance.
4. The quality characteristic is one that
involves destructive or costly tests.
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Sequential Sampling
 Used for costly or destructive tests
 Subgroup size of 1 – item by item plan
 Sequential sampling is similar to multiple sampling,
except sequential sampling can, in theory, continue
indefinitely.
 In practice, the plan is truncated after the number
inspected is equal to three times the number inspected
by a corresponding single sampling plan.
 Based on the Sequential Probability Ratio Test
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Sequential Sampling Plan
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Sequential Sampling Plan
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Skip Lot Sampling
 Designated SkSP-1 and based on AOQL.
 A single sampling plan for minimizing
inspection costs when there is a continuing
supply of lots of raw materials, component
parts, subassemblies, and finished parts from
the same source.
 Applicable to chemical and physical
characteristics that require laboratory analysis.
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Procedure for SkSP-1 Plans
Begin by inspecting every lot
When i consecutive lots are
found to be conforming
Discontinue inspection of every lot
Inspect a fraction, f, of the lots
In a random manner
When an inspected lot is found
nonconforming
Figure 10-7 Procedure SkSP-1 plans
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ANSI/ASQ S1
 Provides procedures to reduce the
inspection effort when the supplier’s
quality is superior.
 A skip-lot scheme used in conjunction
with attribute lot-by-lot plans given in
ASQ Z1.4
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ANSI/ASQ S1
 Requirements to use ANSI/ASQ S1
1. Have a documented system for controlling
product quality and design changes
2. Have instituted a system that is capable of
detecting and correcting changes that might
adversely affect quality.
3. Not have experienced an organizational
change that might adversely affect quality
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ANSI/ASQ S1
 Additional requirements of the product:
 Be of stable design
 Have been manufactured on a continuous basis
for at least 6 months unless agreed to a longer
period.
 Have been on normal and reduced inspection
during the qualification period.
 Have maintained a quality level at or less than
the AQL for at least 6 months.
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ANSI/ASQ S1
Other:
The previous 10 or more consecutive lots
have been accepted
The min cumulative sample size for the last
10 or more consecutive lots have been met.
The acceptance numbers for the last 2 lots
have been met
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Sampling for Continuous Production
 Acceptance sampling for continuous
production implies that manufacturing
operations do not create lots as part of the
normal part of the production process.
Parts are produced by a continuous
process on a conveyor or similar
system.
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Sampling for Continuous Production
 Plans for continuous production consist of
alternating sequences of sampling inspection
and screening (100%) inspection.
 Plans begin with 100% inspection and
convert to sampling after a stated number
of items are free of nonconformities.
 Sampling continues until a stated number of
nonconforming units are found, at which
time 100% inspection in reinstated.
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Sampling for Continuous Production
 Applicable to attribute, nondestructive
inspection of moving product.
 Inspection should be easy and rapid
 Process must be capable of
manufacturing homogeneous product
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Sampling for Continuous Production
 Developed by Dodge
CSP-1, CSP-2, CSP-3
Later, MIL-STD-1235B
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Sampling for Continuous Production
 CSP-1
Begins with 100% inspection of the
product in the order of production until
a certain number of successive units
are free of nonconformities.
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Sampling for Continuous Production
 CSP-1
Sampling inspection is then instituted
Samples are selected in such a
manner as to minimize any bias
If a nonconformity occurs, sampling is
discontinued and 100% inspection
begins.
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CSP-1 and CSP-F Plans
Start
The Screening Crew Inspects 100% of the Units
When i Consecutive Units Are Found Free of
Nonconformities Concerned,
The Screening Crew is Released from 100% Inspection
and the Sampling Inspector Inspects a Fraction, f, of
the Units, Where the Sample Units are Selected in a
Random Manner.
When the Sampling Inspector Finds One of the
Nonconformities Concerned,
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MIL-STD-1235B
 Standard is composed of five different
continuous sampling plans.
Designated by code letters
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MIL-STD-1235B
 Inspection is by attributes for nonconforming
units using three classes of severity:
Critical
Major
Minor
 Each of the plans incorporates a provision for
discontinuance of inspection
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Acceptance Sampling Plans for
Variables
 Shainin Lot Plot
 ANSI/ASQ Z1.9-2003
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Acceptance Sampling Plans for
Variables
 Shainin Lot Plot
 Random sample of 10 subgroups of 5 each
 Find average and range
 Construct a histogram
 Calculate Xdouble bar, R bar
 Calculate ULL and LLL
 Compare to lot plots in Figure 10-15
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Acceptance Sampling Plans for
Variables
ANSI/ASQ Z1.9-2003 Sampling
Procedures and Tables for Inspection by
Variables for Percent Nonconforming is
an acceptance sampling system to be
used on a continuing stream of lots for
Acceptance Quality Limit (AQL) specified.
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Acceptance Sampling Plans for
Variables
ANSI/ASQ Z1.9-2003 provides tightened,
normal, and reduced plans to be used on
measurements which are normally
distributed. Variation may be measured
by sample standard deviation, sample
range, or known standard deviation. It is
applicable only when the normality of the
measurements is assured.
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