1. TM 720: Statistical Process Control Acceptance Sampling Plans
TM Lecture 11
Acceptance Sampling Plans
4/17/2017
TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

2. TM 720: Statistical Process Control
Assignment:
Reading:
Finish Chapter 14
Sections 14.1 – 14.2
Sections 14.4
Start Chapter 12
Assignment:
Download and complete Assign 08: Acceptance Sampling
Requires MS Word for Nomograph
Requires MS Excel for AOQ
Solutions for 8 will post on Thursday
4/17/2017
TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

3. TM 720: Statistical Process Control
Acceptance Sampling
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TM 720: Statistical Process Control
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4. Three Important Aspects of Acceptance Sampling
TM 720: Statistical Process Control
Three Important Aspects of Acceptance Sampling
Purpose is to sentence lots, not to estimate lot quality
Acceptance sampling does not provide any direct form of quality control. It simply rejects or accepts lots. Process controls are used to control and systematically improve quality, but acceptance sampling is not.
Most effective use of acceptance sampling is not to “inspect quality into the product,” but rather as audit tool to insure that output of process conforms to requirements.
4/17/2017
TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

5. Three Approaches to Lot Sentencing
TM 720: Statistical Process Control
Three Approaches to Lot Sentencing
Accept with no inspection
100% inspection – inspect every item in the lot, remove all defectives Defectives – returned to vendor, reworked, replaced or discarded
Acceptance sampling – sample is taken from lot, a quality characteristic is inspected; then on the basis of information in sample, a decision is made regarding lot disposition.
4/17/2017
TM 720: Statistical Process Control
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6. Acceptance Sampling Used When:
TM 720: Statistical Process Control
Acceptance Sampling Used When:
Testing is destructive
100% inspection is not technologically feasible
100% inspection error rate results in higher percentage of defectives being passed than is inherent to product
Cost of 100% inspection extremely high
Vender has excellent quality history so reduction from 100% is desired but not high enough to eliminate inspection altogether
Potential for serious product liability risks; program for continuously monitoring product required
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TM 720: Statistical Process Control
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7. Advantages of Acceptance Sampling over 100% Inspection
TM 720: Statistical Process Control
Advantages of Acceptance Sampling over 100% Inspection
Less expensive because there is less sampling
Less handling of product hence reduced damage
Applicable to destructive testing
Fewer personnel are involved in inspection activities
Greatly reduces amount of inspection error
Rejection of entire lots as opposed to return of defectives provides stronger motivation to vendor for quality improvements
4/17/2017
TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

8. Disadvantages of Acceptance Sampling (vs 100% Inspection)
TM 720: Statistical Process Control
Disadvantages of Acceptance Sampling (vs 100% Inspection)
Always a risk of accepting “bad” lots and rejecting “good” lots
Producer’s Risk: chance of rejecting a “good” lot – 
Consumer’s Risk: chance of accepting a “bad” lot – 
Less information is generated about the product or the process that manufactured the product
Requires planning and documentation of the procedure – 100% inspection does not
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TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

9. TM 720: Statistical Process Control
Lot Formation
Lots should be homogeneous
Units in a lot should be produced by the same:
machines,
operators,
from common raw materials,
approximately same time
If lots are not homogeneous – acceptance-sampling scheme may not function effectively and make it difficult to eliminate the source of defective products.
Larger lots preferred to smaller ones – more economically efficient
Lots should conform to the materials-handling systems in both the vendor and consumer facilities
Lots should be packaged to minimized shipping risks and make selection of sample units easy
4/17/2017
TM 720: Statistical Process Control
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10. TM 720: Statistical Process Control
Random Sampling
IMPORTANT:
Units selected for inspection from lot must be chosen at random
Should be representative of all units in a lot
Watch for Salting:
Vendor may put “good” units on top layer of lot knowing a lax inspector might only sample from the top layer
Suggested technique:
Assign a number to each unit, or use location of unit in lot
Generate/pick a random number for each unit/location in lot
Sort on the random number – reordering the lot/location pairs
Select first (or last) n items to make sample
4/17/2017
TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

11. Single Sampling Plans for Attributes
TM 720: Statistical Process Control
Single Sampling Plans for Attributes
Quality characteristic is an attribute, i.e., conforming or nonconforming
N - Lot size
n - sample size
c - acceptance number
Ex. Consider N = 10,000 with sampling plan n = 89 and c = 2
From lot of size N = 10,000
Draw sample of size n = 89
If # of defectives  c = 2
Accept lot
If # of defectives > c = 2
Reject lot
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TM 720: Statistical Process Control
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12. How to Compute the OC Curve Probabilities
TM 720: Statistical Process Control
How to Compute the OC Curve Probabilities
Assume that the lot size N is large (infinite)
d - # defectives ~ Binomial() where
p - fraction defective items in lot
n - sample size
Probability of acceptance:
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TM 720: Statistical Process Control
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13. TM 720: Statistical Process Control
Example
Lot fraction defective is p = 0.01, n = 89 and c = 2. Find probability of accepting lot.
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TM 720: Statistical Process Control
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14. TM 720: Statistical Process Control
OC Curve
Performance measure of acceptance-sampling plan
displays discriminatory power of sampling plan
Plot of: Pa vs. p
Pa = P[Accepting Lot]
p = lot fraction defective
p = fraction defective in lot
Pa = P[Accepting Lot]
0.005
0.9897
0.010
0.9397
0.015
0.8502
0.020
0.7366
0.025
0.6153
0.030
0.4985
0.035
0.3936
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TM 720: Statistical Process Control
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15. TM 720: Statistical Process Control
OC Curve
OC curve displays the probability that a lot submitted with a certain fraction defective will be either accepted or rejected given the current sampling plan
4/17/2017
TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

16. TM 720: Statistical Process Control
Ideal OC Curve
Suppose the lot quality is considered bad if p = 0.01 or more
A sampling plan that discriminated perfectly between good and bad lots would have an OC curve like:
4/17/2017
TM 720: Statistical Process Control
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17. TM 720: Statistical Process Control
Ideal OC Curve
In theory it is obtainable by 100% inspection IF inspection were error free.
Obviously, ideal OC curve is unobtainable in practice
But, ideal OC curve can be approached by increasing sample size, n.
4/17/2017
TM 720: Statistical Process Control
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18. TM 720: Statistical Process Control
Effect of n on OC Curve
The precision with which a sampling plan differentiates between good and bad lots increases as the sample size increases
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TM 720: Statistical Process Control
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19. TM 720: Statistical Process Control
Effect of c on OC Curve
Changing acceptance number, c, does not dramatically change slope of OC curve.
Plans with smaller values of c provide discrimination at lower levels of lot fraction defective
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TM 720: Statistical Process Control
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20. Producer and Consumer Risks in Acceptance Sampling
TM 720: Statistical Process Control
Producer and Consumer Risks in Acceptance Sampling
Because we take only a sub-sample from a lot, there is a risk that:
a good lot will be rejected (Producer’s Risk – a )
and
a bad lot will be accepted (Consumer’s Risk – b )
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TM 720: Statistical Process Control
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21. TM 720: Statistical Process Control
Producer’s Risk - a
Producer wants as many lots accepted by consumer as possible so
Producer “makes sure” the process produces a level of fraction defective equal to or less than: p1 = AQL = Acceptable Quality Level a is the probability that a good lot will be rejected by the consumer even though the lot really has a fraction defective  p1
That is,
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TM 720: Statistical Process Control
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22. TM 720: Statistical Process Control
Consumer’s Risk - b
Consumer wants to make sure that no bad lots are accepted
Consumer says, “I will not accept a lot if percent defective is greater than or equal to p2”
p2 = LPTD = Lot Tolerance Percent Defective
b probability bad lot is accepted by the consumer when lot really has a fraction defective  p2
That is,  
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TM 720: Statistical Process Control
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23. Designing a Single-Sampling Plan with a Specified OC Curve
TM 720: Statistical Process Control
Designing a Single-Sampling Plan with a Specified OC Curve
Use a chart called a Binomial Nomograph to design plan
Specify:
p1 = AQL (Acceptable Quality Level)
p2 = LTPD (Lot Tolerance Percent Defective)
1 – a = P[Lot is accepted | p = AQL]
β = P[Lot is accepted | p = LTPD]
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TM 720: Statistical Process Control
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24. Use a Binomial Nomograph to Find Sampling Plan (Figure 14-9, p. 658)
TM 720: Statistical Process Control
Use a Binomial Nomograph to Find Sampling Plan (Figure 14-9, p. 658)
Draw two lines on nomograph
Line 1 connects p1 = AQL to (1- a)
Line 2 connects p2 = LTPD to b
Pick n and c from intersection of lines
Example: Suppose
p1 = 0.01,
α = 0.05,
p2 = 0.06,
β = 0.10.
Find the acceptance sampling plan.
4/17/2017
TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

25. Rectifying Inspection Programs
TM 720: Statistical Process Control
Rectifying Inspection Programs
Acceptance sampling programs usually require corrective action when lots are rejected, that is,
Screening rejected lots
Screening means doing 100% inspection on lot
In screening, defective items are
Removed or
Reworked or
Returned to vendor or
Replaced with known good items
4/17/2017
TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

26. Rectifying Inspection Programs
TM 720: Statistical Process Control
Rectifying Inspection Programs
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TM 720: Statistical Process Control
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27. Where to Use Rectifying Inspection
TM 720: Statistical Process Control
Where to Use Rectifying Inspection
Used when manufacturer wishes to know average level of quality that is likely to result at given stage of manufacturing
Example stages:
Receiving inspection
In-process inspection of semi-finished goods
Final inspection of finished goods
Objective: give assurance regarding average quality of material used in next stage of manufacturing operations
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TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

28. Average Outgoing Quality: AOQ
TM 720: Statistical Process Control
Average Outgoing Quality: AOQ
Quality that results from application of rectifying inspection
Average value obtained over long sequence of lots from process with fraction defective p
N - Lot size, n = # units in sample
Assumes all known defective units replaced with good ones, that is,
If lot rejected, replace all bad units in lot
If lot accepted, just replace the bad units in sample
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TM 720: Statistical Process Control
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29. TM 720: Statistical Process Control
Development of AOQ
If lot accepted: Number defective units in lot:
Expected number of defective units:
Average fraction defective, Average Outgoing Quality, AOQ:
4/17/2017
TM 720: Statistical Process Control
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30. TM 720: Statistical Process Control
Example for AOQ
Suppose N = 10,000, n = 89, c = 2, and incoming lot quality is p = Find the average outgoing lot quality.
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TM 720: Statistical Process Control
(c) D.H. Jensen & R.C. Wurl

31. Military Standard 105E (MIL STD 105E) (ANSI/ASQC Z1.4, ISO 2859)
TM 720: Statistical Process Control
Military Standard 105E (MIL STD 105E) (ANSI/ASQC Z1.4, ISO 2859)
Most widely used acceptance sampling system for attributes
MIL STD 105E is Acceptance Sampling System
collection of sampling schemes
Can be used with single, double or multiple sampling plans
We will consider single sampling plans for this course
4/17/2017
TM 720: Statistical Process Control
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32. TM 720: Statistical Process Control
Inspection Types
Normal Inspection
Used at start of inspection activity
Tightened Inspection
Instituted when vendor’s recent quality history has deteriorated
Acceptance requirements for lots are more stringent
Reduced Inspection
Instituted when vendor’s recent quality history has been exceptionally good
Sample size is usually smaller than under normal inspection
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TM 720: Statistical Process Control
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33. TM 720: Statistical Process Control
Switching Rules
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TM 720: Statistical Process Control
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34. TM 720: Statistical Process Control
Procedure for MIL STD 105E
STEP 1: Choose AQL
MIL STD 105E designed around Acceptable Quality Level, AQL
Recall that the Acceptable Quality Level, AQL, is producer's largest acceptable fraction defective in process
Typical AQL range:
0.01%  AQL  10%
Specified by contract or authority responsible for sampling
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TM 720: Statistical Process Control
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35. TM 720: Statistical Process Control
Procedure for MIL STD 105E
STEP 2: Choose inspection level
Level II
Designated as normal
Level I
Requires about one-half the amount of inspection as Level II
Use when less discrimination needed
Level III
Requires about twice as much
Use when more discrimination needed
Four special inspection levels used if very small samples necessary
S-1, S-2, S-3, S-4
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TM 720: Statistical Process Control
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36. TM 720: Statistical Process Control
Procedure for MIL STD 105E
STEP 3–Determine lot size, N
Lot size most likely dictated by vendor
STEP 4: Find sample size code letter
From Table 14-4, p 675
Given lot size, N, and Inspection Level, use table to determine sample size code letters
STEP 5: Determine appropriate type sampling plan
Decide if Single, Double or Multiple sampling plan is to be used
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TM 720: Statistical Process Control
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37. TM 720: Statistical Process Control
Procedure for MIL STD 105E
STEP 6: Find Sample Size, n, and Acceptance Level, c
Given sample size letter code, use Master Tables: 14-5, 14-6, and 14-7 on pp
Find n and c for all three inspection types:
Normal Inspection
Tightened Inspection
Reduced Inspection
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TM 720: Statistical Process Control
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38. TM 720: Statistical Process Control
Example
Suppose product comes from vendor in lots of size 2000 units. The acceptable quality level is 0.65%. Determine the MIL STD 105E acceptance-sampling system.
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TM 720: Statistical Process Control
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39. TM 720: Statistical Process Control
Questions & Issues
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TM 720: Statistical Process Control