This document discusses acceptance sampling and key concepts related to statistical quality control sampling plans. It covers: - The advantages of statistical sampling plans over traditional fixed-percentage sampling or 100% inspection in providing uniform protection against poor quality lots. - Key aspects of different types of sampling plans including attributes vs variables, single vs double sampling, and published sampling plan standards. - Important sampling plan definitions like AQL, LTPD, producer's and consumer's risk levels. - Steps for designing your own sampling plan or selecting from published standards like ISO or Indian standards. - Requirements for effective sampling like ensuring lots are homogeneous, samples are drawn randomly, and using operating characteristic curves to validate sampling plan

1. ACCEPTANCE SAMPLING
A presentation by
THE SOCIETY
OF
STATISTICAL QUALITY CONTROL ENGINEERS
BHOPAL

2. SAMPLE INSPECTION Vs 100% INSPECTION
SAMPLING INSPECTION 100% INSPECTION
Cost of inspection low Cost of inspection very high and at times
prohibitive
Subject to sampling error but the magnitude
of sampling error can be estimated
Subject to errors arising out of fatigue and
boredome of inspectors, particularly if the
lot size is large and inspection is manual
Only recourse for inspection in case of
destructive tests.
Not feasible when inspection involves
destructive tests

3. DRAWBACKS OF TRADITIONAL
SAMPLING PLANS:
 These plans have no scientific basis. Generally they are
hunch based e.g. “take a sample of 5%” or “take a sample
of 10%”
 Traditional sampling plans are generally fixed percentage
sampling plans. This suffers from a major drawback. It can be
proved by statistical methods that taking a fixed percentage of
sample will not provide uniform protection against bad lots if the
lot size is varying.
 The risks involved in traditional sampling plan are not quantified.
There is no knowledge about the quality level of lots accepted.

4. ADVANTAGES OF STATISTICAL
SAMPLING PLANS
 These plans are based on a firm scientific footing. The plans are
so designed that a uniform protection against bad lots is
achieved even though lot sizes are varying.
 Effectiveness of sampling plan is verified by plotting “operating
characteristics” which is based purely on probability theory and
hence there is no subjectivity.
 Good lots and bad lots are defined in terms of percent
defectives. Thus the quality level of accepted lots is known.

5. SAMPLING PLAN FALLACIES
(Appear to be true, but false!)
(1) As lot size increases, sample size should increase
in the same proportion.
(2) Permissible number of defectives in a sample
should always be zero
(3) In a double sampling plan, the size of second sample
shall always be double the size of first sample. Also, the results
of first sample should be discarded
(4) Rejection of a lot during sampling inspection implies
that all items in the lot are defective.
(5) Sampling inspection involves high risks whereas 100%
inspection is 100% risk-free.

6. TYPES OF SAMPLING PLANS
 Acceptance sampling by attributes
 Acceptance sampling by variables

7. TYPES OF SAMPLING PLANS
(Contd.)
(1) Single sampling plan
(2) Double sampling plans
(3) Multiple sampling plans
(4) Sequential sampling plans
(5) Continuous sampling plans

8. SINGLE SAMPLING PLAN Vs DOUBLE SAMPLING PLAN
SINGLE SAMPLING PLAN DOUBLE SAMPLING PLAN
Simple to operate Complex to operate
Overall inspection load is relatively
higher due to larger samples sizes
Overall inspection load is relatively less
due to smaller sample sizes

10. ATTRIBUTE SAMPLING PLAN Vs VARIABLE SAMPLING PLAN
SAMPLING PLAN FOR
ATTRIBUTES
SAMPLING PLAN FOR VARIABLES
Simple to operate. Decision taken merely
by gauging and counting defectives
Complex to operate, involves calculation of
averages and “factors” related to acceptability
criteria for taking decision
No attention to individual quality
characteristic. Normally, defects of various
kinds are clubbed to decide on whether an
item is defective or OK.
Each quality characteristic is dealt with
separately. More scientific and informative
and particularly suited to critical quality
characteristic.
Certain quality characteristics are attribute
by nature and in such cases attribute
sampling plan is the obvious choice
Can not be applied for those quality
characteristics which are attribute by nature
For the same risk, attribute sampling plan
calls for larger sample size, hence more
amount of inspection.
For the same risk, variable sampling plan
calls for smaller sample size hence more
suited to destructive tests.

11. TYPICAL SAMPLING PLAN
(FIXED LOT SIZE)
Lot Size (N) = 400
Sample Size (n) = 50
Acceptance Number (c) = 2
AQL = 1.5 %

12. TYPICAL SAMPLING PLAN
(VARIABLE LOT SIZE)
Lot Size
(N)
Sample Size
(n)
Permissible number
of defectives
(c)
Up to 50
51 to 100
101 to 300
301 to 500
501 to 1000
1001 and above
5
8
13
20
32
50
0
0
1
1
2
3

13. SAMPLING PLAN
Key Definitions
PRODUCER’S RISK (α)
Probability that a good lot will be rejected
CONSUMER’S RISK (ß)
Probability that a bad lot will be accepted
ACCEPTABLE QUALITY LEVEL ( AQL)
There is a level of quality such that the customer would like to accept most of
the time lots superior to this level. This is known as the Acceptable Quality Level (AQL)
LOT TOLERANCE PERCENT DEFECTIVE (LTPD)
There is a level of quality such that the customer would like to reject all the
time lots inferior to this level. This is known as Lot Tolerance Percent Defective (LTPD)
AVERAGE OUT GOING QUALITY LIMIT (AOQL )
Applicable when rejected lots are screened and defective items are replaced by
good items. With this system, the average quality of received lots can never go
worse than AOQL.

14. SELECTING A SAMPLING PLAN:
TWO ALTERNATIVES
(i) Design of your own sampling plan
(ii) Refer to published sampling plans

15. DESIGNING A SAMPLING PLAN
STEP 1:SELECT THE BASIS OF SAMPLING PLAN
(i) AQL (Acceptable Quality Level )
(ii) LTPD (Lot Tolerance Percent defective)
(iii) AOQL (Average out going quality limit)
STEP 2:SPECIFY RISKS
(i) Producer’s risk (α)
(Probability that a good lot will be rejected)
(ii) Consumer’s risk (ß)
(Probability that a bad lot will be accepted)
STEP 3:SELECT THE TYPE OF SAMPLING PLAN
e.g. Single/Double, Attribute/Variable, etc.
STEP 4: DESIGN THE SAMPLING PLAN
Design the plan using poisson probabilities for attributes
Design the plan using Normal probabilities for variables

16. PUBLISHED SAMPLING PLANS
(1) Dodge – Romig sampling plans
(2) Military standard 105D (Attributes)
(3) Military standard 414 (Variables)
(4) ISO 2859 sampling plans
(3) IS: 2500 sampling plans
(4) Product specific sampling plans

17. IMPORTANT FEATURES OF IS-2500 (Part-I)
(Sampling procedure for inspection by attributes)
 These sampling plan are AQL based plans, hence they protect the supplier against
rejection of good lots i.e. lots of AQL quality or better.
 AQLs very from 0.010% to 100%, but for all practical purposes AQL beyond
10% is not taken.
 AQLs above 100% indicate number of defects per 100 items.
 There is provision for seven inspection levels related to varying amount of
inspection. A higher inspection level implies larger sample size, more amount of
inspection, but lesser risk. Normally inspection level II is used.
 There is provision of Normal inspection, Reduced inspection and Tightened
inspection. To start with, Normal inspection is implemented. Depending upon
the quality of lots received, we can switch over to reduced inspection or
tightened inspection as per switching rules.
 The sampling tables contained in IS 2500 (Part I) are aligned with sampling
tables of International Standard ISO-2859 on sampling inspection by attributes.

18. PRE-REQUISITES FOR SUCCESS OF SAMPLING INSPECTION
(1) Lot should be homogeneous
(2) Lot should be “process based”
rather than “shipment based”
(3) Sample should be taken randomly

19. WHY TAKE RANDOM SAMPLE
Even the best designed sampling plan will not provide
protection against bad lots if the sample in NOT random.
Therefore, taking random sample is very important for
effectiveness of any sampling plan.
HOW TO TAKE RANDOM SAMPLE
(1) Mix the lot thoroughly to make it homogeneous and take
sample from random locations.
(2) If there are practical difficulties in mixing the lot, assign running
serial number to each component/piece (1,2…….. N). Thereafter,
select random samples by referring to TABLE OF RANDOM NUMBERS.
(Random number tables are available in IS-4905 or other statistical
publications)

20. OPERATING CHARACTERISTIC CURVES
(OC CURVES) OF SAMPLING PLANS