sampling oc
TRANSCRIPT
SAFM CONSULTING SERVICES
Sampling ProceduresInspection by
Attributes
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LEARNING OBJECTIVES
Explain the purpose of acceptance sampling
Contrast acceptance sampling and process control
Compare and contrast single and multiple sampling plans
Determine the average outgoing quality of inspected lots
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SAMPLING PLANS
Acceptance sampling: Form of inspection applied to lots or batches of items before or after a process, to judge conformance with predetermined standards
Sampling plans: Plans that specify lot size, sample size, number of samples, and acceptance/rejection criteria Single-sampling Double-sampling Multiple-sampling
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ACCEPTANCE SAMPLING
Acceptance Sampling most useful when A large number of items must be
processed in a short time The cost consequences of passing defects
are low Destructive testing is required Fatigue or boredom leads to inspection
errors
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INTRODUCTION BS 6001-1 1999 (ISO 2859-1:1999) Sampling procedures for inspection by attributes. Part 1:
Sampling schemes indexed by acceptance qualitylimit (AQL) for lot-by-lot inspection.
ISO 2859-2:1985 Sampling procedures forinspection by attributes. Sampling plans indexedby limiting quality (LQ) for isolated lot inspection.
ISO 2859-0:1995 - Part 0: Introduction to theISO 2859 attribute sampling system.
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ISO 2859 PART 1
Acceptance sampling system for inspection by attributes.
It is indexed in terms of acceptance quality level (AQL)
Aim - to induce a supplier to maintain a process average at least as good as the specified acceptance AQL, whilst at the same time providing an upper limit for the risk to the consumer of accepting the occasional poor lot.
Applicable to end products, raw materials, operations, maintenance operations, administrative procedures.
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USAGE OF THE PART 1 SCHEME.
Intended to be used for a continuing series of lots, which will allow the application of switchingrules. The rules provide:
- protection to the consumer should a deterioration in quality be detected.
- an incentive to the supplier to reduceinspection costs should consistently goodquality be achieved.
Can also be used for inspection of lots inisolation
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TERMINOLOGY Inspection by attributes: inspection where an
item is classified as conforming or nonconforming with respect to a specified requirement or set of requirements.
Nonconformity: Non fulfillment of a specifiedrequirement. Usually classified according to thedegree of seriousness. More seriousnonconformities will usually be assigned a verysmall AQL, whilst less serious nonconformitieswill be assigned higher AQL values.
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TERMINOLOGY (CONT) Normal inspection: Use of a sampling plan with
acceptance criteria devised to secure the producer a high probability of acceptance when the process average of the lot is better than the AQL. Used when there is no reason to suspect the process average differs from an acceptable level.
Tightened inspection: Use of a sampling planwith an acceptance criteria that is tighter than that for the corresponding plan for normal inspection. Invoked when the inspection results of consecutive lots indicate that the process average might be poorer than the AQL.
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TERMINOLOGY (CONT) Acceptable Quality Limit (AQL): Quality level
that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling. AQL does not mean ’desirable level’. ISO 2859 is designed to encourage suppliers to have process averages consistently better than the AQL, otherwise there is a risk of switching to tighter inspection.
The designation of an AQL does not imply that the supplier has the right knowingly to supply anynonconforming items.
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TERMINOLOGY (CONT) AQL values shall not exceed 10%
nonconforming. When the quality level is expressed as number of
nonconformities per 100 items, AQL values up to1000 nonconformities per 100 items may be used.Sampling:
Sample selection must be drawn from the lot by simple random sampling.
When double or random sampling is to be used, each subsequent sample shall be selected from the remainder of the same lot.
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INSPECTION LEVELS 4 special inspection levels - S1, S2, S3, S4. 3 general inspection levels - I, II, III. Special inspection levels used when sample size
must be kept small and larger sampling risks canbe tolerated.
Level II will be used unless another inspection level is specified.
Level I is used when less discrimination is required, Level III when greater discrimination isrequired.
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STEPS IN THE USE OF THE STANDARD
be summarized as follows: Decide on the AQL. Decide on the inspection level. Determine the lot size. Enter the table to find sample size code letter. Decide on type of sampling to be used. Enter proper table to find the plan to be used. Begin with normal inspection, follow the
switching rules and the rule for stopping the inspection (if needed).
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SAMPLE SIZE CODE LETTERS
Lot Size Special Inspection Levels General Insp. LevelsS1 S2 S3 S4 I II III
2 - 8 A A A A A A B
9-15 A A A A A B C
16-25 A A B B B C D
26-50 A B B C C D E
51-90 B B C C C E F
91-150 B B C D D F G
151-280 B C D E E G H
281-500 B C D E F H J
501-1200
C C E F G J K
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SAMPLE SIZE CODE LETTERS (CONT.)
Lot Size Special Inspection Levels General Insp. LevelsS1 S2 S3 S4 I II III
1201-3200 C D E G H K L3201-10000
C D F G J L M
10001-35000
C D F H K M N
35001-150000
D E G J L N P
150000-500000
D E G J M P Q
>=500000
D E H K N Q R
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SINGLE SAMPLING PLANSSELECTED SEGMENT OF NORMAL INSPECTION TABLE
Code Letter
Sample Size
AQL
0.010
0.015 0.025 0.040 0.065 0.10 0.15
Ac Re
AC Re AC Re AC Re AC Re AC Re AC Re
G 32 ↓ ↓ ↓ ↓ ↓ ↓ ↓
H 50 ↓ ↓ ↓ ↓ ↓ ↓ ↓
J 80 ↓ ↓ ↓ ↓ ↓ ↓ 01
K 125 ↓ ↓ ↓ ↓ ↓ 01 ↑
L 200 ↓ ↓ ↓ ↓ 01 ↑ ↓
M 315 ↓ ↓ ↓ 01 ↑ ↓ 12
N 500 ↓ ↓ 01 ↑ ↓ 12 23
P 800 ↓ 01 ↑ ↓ 12 23 34
Q 1250 01 ↑ ↓ 12 23 34 56
R 2000 ↑ ↑ 12 23 34 56 78
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DOUBLE SAMPLING PLANS NORMAL INSPECTION
Code Letter
Sample Sample Size
CumulativeSamples
AQL
1.5 2.5 4.5 6.5 10
Ac Re
AC Re
AC Re
AC Re AC Re
G FIRST 20 20 02 03 13 25 36
G SECOND 20 40 12 34 45 67 910
H FIRST 32 32 03 13 25 36 59
H SECOND 32 64 34 45 67 910 1213
J FIRST 50 50 13 25 36 59 711
J SECOND 50 100 45 67 910 1213 1819
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OC CURVESOperating Characteristic Curves OC curve is a graph showing what any particular
sampling plan can be expected to do in terms of accepting and rejecting batches.
An understanding of the implications of an OC curve helps understand the risks to the manufacturer, consumer, and in deciding inspection levels and batch sizes.
Each possible plan has its own OC curve. Horizontal scale - shows the percentage defective. Vertical scale - shows the percentage of batches that
may be expected to be accepted if batches are produced with that percentage of defects.
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OC CURVE Operating Characteristic (OC) Curve:
Probability curve that shows the probabilities of accepting lots with various fractions defective.
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TYPICAL OC CURVE
00.10.20.30.40.50.60.70.80.9
1
0 .05 .10 .15 .20 .25
Pro
bab
ilit
y of
acc
epti
ng
lot
Lot quality (fraction defective)
3%
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DECISION CRITERIA
0
1.00P
rob
abil
ity
of a
ccep
tin
g lo
t
Lot quality (fraction defective)
“Good” “Bad”
Ideal
Not verydiscriminating
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SAMPLING TERMS
Acceptance quality level (AQL): the percentage of defects at which consumers are willing to accept lots as “good”
Lot tolerance percent defective (LTPD): the upper limit on the percentage of defects that a consumer is willing to accept
Consumer’s risk: the probability that a lot contained defectives exceeding the LTPD will be accepted
Producer’s risk: the probability that a lot containing the acceptable quality level will be rejected
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CONSUMER’S AND PRODUCER’S RISK
00.10.20.30.40.50.60.70.80.9
1
0 .05 .10 .15 .20 .25
Pro
bab
ilit
y of
acc
epti
ng
lot
Lot quality (fraction defective)
= .10
= .10
“Good”
AQL
“Bad”Indifferent
LTPD
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OC Curve e.g. (n = 10, c = 1)
00.10.20.30.40.50.60.70.80.9
1
0 .10 .20 .30 .40 .50
Pro
bab
ilit
y of
acc
epta
nce
Fraction defective in lot
.9139
.7361
.5443
.3758
.2440.1493
.0860
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AVERAGE QUALITY
Average outgoing quality (AOQ): Average of inspected lots (100%) and uninspected lots
AOQ Pac pN n
N
Pac = Probability of accepting lotp = Fraction defectiveN = Lot sizen = Sample size
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EXAMPLE : AOQ
0 00.05 0.0460.1 0.0740.15 0.0820.2 0.0750.25 0.0610.3 0.0450.35 0.030.4 0.019
00.010.020.030.040.050.060.070.080.09
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Approximate AOQL = .082
AO
Q (
Fra
cti
on
defe
cti
ve o
ut)
Incoming fraction defective
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OC CURVE
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OC CURVE EXAMPLE Code Letter M AQL 1.5 Sample size - 315 Accept: 10, Reject: 11 What happens if a batch with 3% defectives is
submitted ? Find 3% on the X axis, and follow a vertical line up
until it meets the 1.5% curve. Take a horizontal line across to the Y axis, and read
off the value of 65%. I.e., 65% of batches would be accepted and 35%
rejected.
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MORE OC CURVE EXAMPLES
PaAQL for Sample Plan M AQL for Sample Plan J
1.0 1.5 2.5 4.0 1.0 1.5 2.5 4.0
99 0.929 1.53 2.40 4.05 0.55 1.04 2.28 3.73
95 1.27 1.97 2.96 4.78 1.03 1.73 3.32 5.07
90 1.48 2.24 3.29 5.20 1.39 2.20 3.99 5.91
75 1.89 2.74 3.90 5.95 2.16 3.18 5.30 7.50
50 2.43 3.38 4.65 6.87 3.33 4.57 7.06 9.55
25 3.06 4.11 5.49 7.87 4.84 6.30 9.14 11.9
10 3.71 4.85 6.33 8.84 6.52 8.16 11.3 14.3
5 4.13 5.33 6.86 9.46 7.66 9.41 12.7 15.8
1 5.01 6.29 7.93 10.7 10.1 12.0 15.6 18.9
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MORE EXAMPLES
Pinholes General inspection level 1, AQL 1.5%. Minimum Sample size code lettre L (200 Sample) If a batch with 3% pinholes is submitted, there is
a 75% chance of them being accepted. Container
Agreed AQL of 0.65%, general Inspection level I. Sample code L (200 Sample). If a batch with 5% leakers is submitted, there is a
99% chance of them being rejected.
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SETTING AN INSPECTION LEVEL
Select the required AQL (as an average).
Decide what quality should have a high chance of rejection.
Choose the appropriate sampling plan by inspecting the OC curves.
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SETTING AN INSPECTION LEVEL
Example An AQL of 1.5% defective items has been chosen. It is desired to have at least an 80% chance of rejecting a
6%defective batch under normal inspection.
Code letters A->J fail to meet the requirement. Code letter K almost meets it, codes L-P more than meet it. Decide the batch size. If batch size is 1000, check sample
size code letters table - we can use general inspection level III.
The sampling plan would therefore be AQL=1.5%, GeneralInspection Level=III.
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SWITCHING RULES
Normal to tightened: Shall be implemented as soon as two outof five (or fewer than five) consecutive lots have beennon-acceptable on original inspection.
Tightened to normal: Shall be reinstated when five consecutivelots have been considered acceptable on original inspection.
Normal to reduced: implemented when the switching score is atleast 30, production is at a steady state, and reduced inspection isconsidered desirable by the responsible authority.
Discontinuation of inspection: is implemented when thenumber of lots not accepted in a sequence of consecutive lots onoriginal tightened inspection reaches 5.
Reduced to normal: if a lot is not accepted or irregular/delayedproduction.
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SWITCHING SCORES
Single Sampling Plans Used when deciding whether to switch to reduced inspection. Set switching score to 0 at start of normal inspection. Score updated following the inspection of each lot. When the acceptance number is >= 2, add 3 to the switching
score if the lot would have been accepted if the AQL had beenone step tighter; otherwise reset score to 0.
When the acceptance number is 0 or 1, add 2 to the switchingscore if the lot is accepted; otherwise reset score to 0.
As in the previous slide, when the switching score is at least 30and production is at a steady state, switch to reduced inspection ifconsidered desirable by the responsible authority.
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IMPORTANT POINTS Setting an AQL does not guarantee to the customer
that batches of a worse quality will not be accepted. If the average quality of batches being submitted are
a little worse than the AQL, a number of batches will probably be accepted before a switch to tightened inspection is called for.
In general, the customer gets a quality which is, on average, better than the AQL, since the tables are arranged to provide an economic incentive -the manufacturer cannot afford to have more than a small proportion of batches rejected, and so will improve the quality if this proportion is exceeded.