Fundamental Concepts
Types of Sampling Plans
 Single, Double, Multiple and Sequential
Statistical Aspects
Lot-By-Lot Acceptance Sampling Plans for
Acceptance Sampling Plans For :
 Continuous Production
 Variables
Know the advantages and disadvantages of
Understand the types of sampling plans and
selection factors
Determine the Operation Characteristic (OC)
curve for a single sampling plan and the
Lot-by-lot acceptance sampling by attributes is the most
common type of sampling
A predetermined number of units (sample) from each lot
is inspected by attributes
If the number of nonconforming units is less than the
prescribed minimum, the lot is accepted; if not, the lot is
not accepted
Acceptance sampling can be used either for the number
of nonconforming units or for nonconformities per unit
Example :
 Lot size, N = 9000
 Sample size, n = 300
 Acceptance number, c = 2
Acceptance sampling is most likely to be used in one of five
1. When the test is destructive, sampling is necessary;
otherwise, all of the units will be destroyed by testing
2. When the cost of 100% inspection is high in relation to
the cost of passing a nonconforming unit
3. When there are many similar units to be inspected; with
manual inspection, fatigue and boredom cause a higher
percentage of nonconforming material to be passed
than would occur on the average using a sampling plan
4. When information concerning producer’s quality, such
as X-Bar and R, p or c charts and Cpk is not available
5. When automated inspection is not available
More economical (fewer
inspectors and less
Upgrades the inspection
job (piece-by-piece to lotby-lot)
Applies to destructive
Stronger motivation for
improvement (entire lots
are not accepted rather
than the return of a few
nonconforming units)
Certain risks of not
accepting conforming lots
and accepting nonconforming lots
More time and effort is
devoted to planning and
Less information is
provided about the
There is no assurance that
the entire lot conforms to
Lot Formation can influence the effectiveness of the
sampling plan:
Lots should be homogeneous
Lots should be as large as possible
The sample units selected for inspection should be
representative of the entire lot – random sampling
There are a number of courses of action that can be taken
on the non-accepted lots:
Passed to the production facilities and the nonconforming units sorted by production personnel
b. Rectified at the consumer’s plant by personnel from
either the producer’s or the consumer’s plant
c. Returned to the producer for rectification
Single – one sample is taken from the lot and a decision
to accept or not accept the lot is made based on the
inspection results of that sample
Double – on the initial sample, a decision, based on the
inspection results, is made whether:
To accept the lot
 Not to accept the lot
 To take another sample
If the quality is very good, the lot is accepted on the first sample
and a second sample is not taken; if the quality is very poor, the
lot is not accepted on the first sample and a second sample is not
Only when the quality level is neither very good nor very bad is a
second sample taken
Multiple – is a continuation of double sampling in that
three, four, five or as many samples as desired can be
established. Sample sizes are much smaller
Sequential – items are sampled and inspected one after
another. A cumulative record is maintained and a
decision is made to accept or not accept the lot as soon
as there is sufficient cumulative evidence
 All four types of sampling plans can give the same results. Thus, the
type of plan for a particular unit is based on factors other than
 These factor are simplicity, administrative costs, quality information,
number of units inspected and psychological impact
Operation Characteristic (OC) Curve for Single Sampling
 In judging a particular sampling plan, it is desirable to
know the probability that a lot submitted with a
certain percent nonconforming, 100po , will be
accepted – the OC curve will provide this information
 When the percent nonconforming is low, the
probability of the lot being accepted is large and
decreases as the percent nonconforming increases
 In graphing the curve with the variables 100Pa (percent
of lots accepted) and 100po (percent nonconforming),
one value, 100po , will be assumed and the other
Construction of an OC Curve
Assume po value
Calculate npo value
Attain Pa values from the
Poisson table using the
applicable c and npo
Plot point (100po , 100Pa)
Repeat 1,2,3 and 4 until
a smooth curve is
OC Curve for the Single Sampling Plan
OC Curve Properties
Acceptance sampling plans with similar properties can give
different Operation Characteristic (OC) curve:
Sample size as a fixed
percentage of lot size
Fixed sample size
OC Curve Properties (cont.)
As sample size increase, the curve
becomes steeper
As the acceptance number decrease,
the curve becomes steeper
Consumer-Producer Relationship
 There is a conflicting interest between the consumer
and the producer when using acceptance sampling
 Ideal OC curve that is a vertical line can satisfy both –
can be achieved only with 100% inspection
 Sampling carries risks of not accepting lots that are
acceptable and of accepting lots that are unacceptable
 Acceptance Quality Limit (AQL)
“Is the quality level that is the worst tolerable process average
when a continuing series of lots is submitted for acceptance
sampling. It is a reference point on the OC curve and is not meant
to convey to the producer that any percent nonconforming is
acceptable. It is a statistical term and is not meant to be used by
the general public”
Consumer-Producer Relationship (cont.)
1. Producer’s Risk
 Represented by the symbol α, is the probability of
non acceptance of a conforming lot
 This risk is frequently given as 0.05, but it can range
from 0.001 to 0.10 or more
 It cannot be located on an OC curve unless specified
in terms of the probability of acceptance
 This conversion is accomplished by subtracting from 1
 Thus, Pa = 1 – α and for α = 0.05, Pa = 0.95
Consumer-Producer Relationship (cont.)
 Limiting Quality (LQ)
“Is the percent nonconforming in a lot or batch for which, for
acceptance sampling purposes, the consumer wishes the
probability of acceptance to be low”
Consumer’s Risk
 Represented by the symbol β, is the probability of
acceptance of a nonconforming lot
 This risk is frequently given as 0.10
Consumer-Producer Relationship (cont.)
AQL = 0.7%
There are 0.7% nonconforming will
have a non-acceptance probability of
5% or in other words; 1 out of 20 lots
that are 0.7% nonconforming will not
be accepted by the sampling plan
LQ = 2.6%
There are 2.6% nonconforming will
have a 10% chance of being accepted
or in other words; 1 out of 10 lots that
are 2.6% nonconforming will be
accepted by this sampling plan
Was first devised in 1942 by a group of engineers at Bell Telephone
Laboratories for use by the US government
It was designated JAN-STD-105 and adopted by the ISO and designated
Have been revised 5 times (MIL-STD-105E) and modified by American
Society for Quality (ASQ) under the designation ANSI/ASQ Z1.4 – all
tables and procedures remain unchanged
Attributes (cont.)
Continuous Production

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