1. ACCEPTANCE SAMPLING FOR ATTRIBUTES
Types Of Sampling Plans
Mistakes To Avoid, And Their Statistical Equivalents
AQL & LTPD
Single-sampling Plans
 Average Outgoing Quality
ISO 2859 & Dodge-Romig Plans
OPS Qual Mgmt

2. IS THIS SHIPMENT ANY GOOD?
Can you trust your vendor's quality?
If so, great!
If not, inspect each shipment that arrives
Sorting out good from bad shipments
OPS Qual Mgmt

3. OPTIONS FOR VENDOR QUALITY
Objective: ensure vendor delivers quality supplies
Two ways to reach objective
Inspect vendor's shipments
“Acceptance" sampling:
Have vendor performing QM
Vendor supplies customer with relevant control charts
Customer certifies vendor in QM
The first approach is traditional, but the second is preferable in general and necessary for lean operations
OPS Qual Mgmt

4. "ACCEPTANCE" SAMPLING Basic idea: Inspect a random sample of each lot
Classify each item as ok/not ok
Conclude entire lot is either
Ok -- accept it
Not ok -- reject it and/or sort it
OPS Qual Mgmt

5. ATTRIBUTE VS. VARIABLE SAMPLING PLANS
Simplest sampling plans are attribute
Based on binomial (or hypergeometric) distribution
May lose variable data on several QC'S
Requires large sample size
Plans based on variable data
Based on normal distribution
Provide more information on source of quality problems
Require smaller samples for same a, b
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6. SINGLE, DOUBLE, & MULTIPLE SAMPLING PLANS
Single sampling plans:
Make accept/reject decision based on one sample
Double sampling plans:
Make accept/reject/take-another- sample decision based on first sample
Make accept/reject decision based on second sample (if taken)
Can have "triple", "quadruple", or any other multiple sampling plan
Multiple sampling plans require more but smaller samples for same a, b
OPS Qual Mgmt

7. SINGLE (ATTRIBUTE-BASED) SAMPLING PLANS
Define:
N -- number of parts in shipment
n -- number of parts in a sample from shipment
c -- acceptance number
Acceptance sampling has 3 easy steps:
For each shipment of N parts, a sample of size n is taken
Inspect each of the n parts
Reject the shipment if the number of defects exceeds c units. Otherwise, accept the shipment
OPS Qual Mgmt

8. MISTAKES TO AVOID, & THEIR STATISTICAL EQUIVALENTS
As with product quality control, there are two types of mistakes to avoid:
Type I -- Conclude the shipment is bad when in fact it is good (false alarm)
Type II -- Conclude the shipment is good when in fact it is bad (overlooked problem)
Probability of each type of mistake:
Type I -- a Type II -- b
This is standard hypothesis testing with the following null hypothesis:
H0: the shipment is good
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9. DOUBLE SAMPLING PLANS Define: Take sample of size n1
n1 -- sample size on first sample
c1 -- acceptance number for first sample
d1 -- defectives in first sample
n2 -- sample size on second sample
c2 -- acceptance number for both samples
d2 -- defectives in second sample
Take sample of size n1
Accept if d1 £ c1; reject if d1 > c2;
Take second sample of size n2 if c1 < d1 £ c2
Accept if d1+d2 £ c2; reject if d1+d2 > c2
OPS Qual Mgmt

10. DEFINING GOOD AND BAD SHIPMENTS: AQL VERSUS LTPD
Instead of simply "good" versus "bad", we will define "really good", "really bad", and "ok, but not great" shipments
p -- True (unknown) percent defective in shipment
AQL -- Acceptable quality level
LTPD -- lot tolerance percent defective
Then:
A really good shipment has p <= AQL
A really bad shipment has p >= LTPD
Anything in between (AQL < p < LTPD) is ok, but not great
OPS Qual Mgmt

11. THE OPERATING-CHARACTERISTIC (OC) CURVE
For a given a sampling plan and a specified true fraction defective p, we can calculate
Pa -- Probability of accepting lot
If lot is truly good, 1 - Pa = a
If lot is truly bad, Pa = b
A plot of Pa as a function of p is called the OC curve for a given sampling plan
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12. THE OPERATING-CHARACTERISTIC (OC) CURVE
The ideal sampling plan discriminates perfectly between good and bad shipments
Both a and b are zero in this example!
This requires a sample size equal to the population -- not feasible
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13. CONSTRUCTING AN (OC) CURVE
For a specified single sampling plan, the OC curve may be constructed using a binomial distribution if n is small relative to the lot size
p -- true fraction nonconforming
n -- sample size
c -- acceptance number
We know that
Excel
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14. CONSTRUCTING AN (OC) CURVE
Suppose we have a sampling plan defined by the following parameters:
n = 100
c = 2
What is the probability of accepting a lot with 0.5% defectives?
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15. CONSTRUCTING AN (OC) CURVE
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16. USING AN (OC) CURVE How do we find a and b using an OC curve?
AQL = 0.01
LTPD = 0.05
Then a = 1 – Pa(p=0.01) = =
And b = Pa(p=0.05) =
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17. AVERAGE OUTGOING QUALITY
Consider a part with a long-term fraction nonconforming of p
Samples of size n are taken from a lot of size N and inspected
Any defectives in the sample of size n are replaced, accept or reject
When a lot of is accepted, we expect p(N-n) defectives in the remainder of the lot
When a lot is rejected, it will be sorted and defective units replaced, leaving N-n good units in the remainder
This is referred to as "rectifying" inspection
OPS Qual Mgmt

18. AVERAGE OUTGOING QUALITY
If Pa is the probability of accepting a lot, then the average outgoing quality is:
The worst possible AOQ is the AOQ Limit or AOQL
Excel
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19. AVERAGE TOTAL INSPECTION
Rectifying plans have greater inspection requirements
The Average Total Inspections:
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20. ISO 2859 (ANSI/ASQC Z1.4) One of oldest sampling systems
Covers single, double, & multiple sampling
AQL-based: Type I error ranges 9%-1% as sample size increases
Minimal control over Type II error
Type II error decreases as general inspection level (I, II, III) increases
“Special” inspection levels when small samples needed (and high Type II error probability tolerated)
Mechanism for reduced or tightened inspection depending on recent vendor performance
Tightened -- more inspection
Reduced -- less inspection
OPS Qual Mgmt

21. ISO 2859 (ANSI/ASQC Z1.4)
A vendor begins at a "normal" inspection level
Normal to tightened: 2/5 lots rejected
Normal to reduced:
Previous 10 lots accepted (NOT ISO 2859)
Total defectives from 10 lots ok (NOT ISO 2859)
If a vendor is at a tightened level:
Tightened to normal: 5 previous lots accepted
If a vendor is at a reduced level:
Reduced to normal: a lot is rejected
OPS Qual Mgmt

22. ISO 2859 A vendor begins at a "normal" inspection level
Normal to reduced:
“Switching score” set to zero
If acceptance number is 0 or 1:
Add 3 to the score if the lot would still have been accepted with an AQL one step tighter; else reset score to 0
If acceptance number is 2 or more:
Add 3 to the score if the lot is accepted; else reset score to 0
If score hits 30, switch to reduced inspection
OPS Qual Mgmt

23. USING ISO 2859 Choose the AQL Choose the general inspection level
Determine lot size
Find sample size code
Choose type of sampling plan
Select appropriate plan from table
Switch to reduced/tightened inspection as required
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24. USING ISO 2859
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25. USING ISO 2859
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26. USING ISO 2859
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27. USING ISO 2859
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28. DODGE-ROMIG PLANS Developed in the 1920's Rectifying plans
Requires knowledge of vendor's long-term process average (fraction non-conforming)
Choice of LTPD or AOQL orientation
Both minimize ATI for specified process average
Type II error = 10%,
OPS Qual Mgmt

29. DODGE-ROMIG PLANS AOQL plans: LTPD plans: 1) Determine N, p, and AOQL
2) Use table to find n and c
Finds plan with specified AOQL which minimizes ATI
Calculate resulting LTPD with Type II error = 10%
LTPD plans:
1) Determine N, p, and LTPD
Finds plan with specified LTPD which minimizes ATI
Calculate resulting AOQL
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30. DODGE-ROMIG PLANS
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31. DODGE-ROMIG PLANS
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