1. Acceptance Sampling Terminology
Acceptable Quality Level
LTPD or RQL
Producer’s risk
Consumer’s risk
Factors affecting these risks
Simple single sampling
Rectification based sampling plans
Average out going quality (AOQ)
Average Sample number (ASN)
Average total inspection (ATI)

2. How will you find the consumer’s risk?

3. The general approach N
(Lot) n
Count Number
Conforming
Accept or
Reject Lot
Specify the sampling plan
For a lot size N, determine
the sample size (s) n, and
Select acceptance criteria for good lots
Select rejection criteria bad lots
Accept the lot if acceptance criteria are satisfied
Specify course of action if lot is rejected

4. Sampling plans are based on sample statistics and the theory says that since we inspect only a sample and not the whole lot, there is a chance of making an error.
NOT MEASURING QUALITY, REJECTING OR ACCEPTING A LOT DEPENDING ON CERTAIN CIRCUMSTANCES.

5. We need to consider two types of errors that result in wrong decisions
Reject
Accept
Good lot
Bad lot T R U H
DECISION

6. The Ideal OC Curve
This OC curve represents a sampling plan which has maximum discriminating power.
How can we achieve this ? Pa p
AQL
1.00
0.00

7. This is possible only when we have 100 % inspection
The Ideal OC Curve Pa p
AQL
1.00
0.00
Eventhough this is the most desirable sampling plan, it is not practical to achieve this.
This is possible only when we have 100 % inspection

8. Operating Characteristic Curve
AQL
LTPD
 = 0.10
 = 0.05
Probability of acceptance, Pa {
0.60
0.40
0.20
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.80
Proportion defective p
1.00
OC curve for n and Ac

9. A Typical OC Curve
n1> n2 > n3
Ac = constant
AQL
LTPD
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1 2 3 4 5 6 7 8 9 10 11 12
Percent defective
Probability of acceptance
 = consumer’s risk
= producer’s risk n1 n2 n3  

10. A Typical OC Curve
Percent defective
Ac1< Ac2 < Ac3
n = constant
AQL
LTPD
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1 2 3 4 5 6 7 8 9 10 11 12
Probability of acceptance
 = consumer’s risk
= producer’s risk
Ac1
Ac2
Ac3  

11. = average number of defectives
Poisson Distribution
The probability of obtaining x nonconforming units (defectives) on a single inspection unit, when the average number of defectives is some constant, λ is:
where,
= average number of defectives

12. A process is operating at a nonconformance level of 1%
A process is operating at a nonconformance level of 1%. What is the probability that a sample of size 100 will have 2 defective units ?
p = 0.01, n = 100, x = 2
 = np = 1
= 0.367

13. A process is operating at a nonconformance level of 1%
A process is operating at a nonconformance level of 1%. What is the probability that a sample of size 100 will have 2 or less defective units ?
p = 0.01, n = 100, x = 2
 = np = 1

14. From the Poisson distribution table above, P (x  2 | np = 1) = 0.92
Using standard tables
np = 100 (0.01) = 1
Cumulative Poisson distribution table
From the Poisson distribution table above,
P (x  2 | np = 1) = 0.92

15. From the Poisson distribution table , find
Calculating producer’s risk (a) for a given plan and p
N = 2000, n = 50, Ac = 2, p = AQL= 0.02
np = 50 (0.02) = 1
From the Poisson distribution table , find
Prob (no. of defective units  2, given that np = 1)
= Probability of acceptance = 0.92 = 92 %
Producer’s risk = Probability of rejection =
1 – 0.92 = 0.08 = 8 %

16. From the above Poisson distribution table ,
Calculating consumer’s risk (b) for a given plan and p
N = 2000, n = 50, Ac = 2, p = LTPD = 0.04
np = 50 (0.04) = 2
From the above Poisson distribution table ,
P (x  2 | np = 2) = probability of acceptance = 0.677
Consumer’s risk =
67.7 %

17. We calculated producer’s and consumer’s risk for a given plan.
Example
We calculated producer’s and consumer’s risk for a given plan.
How do we select a sampling plan if we were to have a producer’s risk of 2 % for an AQL of 0.01 ? Use the following table.

18. We calculated producer’s and consumer’s risk for a given plan.
Example
We calculated producer’s and consumer’s risk for a given plan.
How do we select a sampling plan if we were to have a producer’s risk of 2 % for an AQL of 0.01 ? Use the following table.

19. Average Outgoing Quality for rectification based sampling plans
AOQ is the average quality level of a series of lots that leave the inspection station, assuming ‘rectification’, after coming in for inspection at a certain quality level p.

20. What is the AOQ for p = AQL ?
Example
What is the AOQ for p = AQL ?
N = 2000, n = 50, Ac = 2, AQL = 2 % = 0.02
np = 50 x 0.02 = 1
AOQ = [ Pa. p (N-n)] / N
AOQ = [ 0.92 x 0.02 x ( )] / 2000
AOQ = = 1.79 %

21. Average outgoing quality curve

22. Average outgoing quality Limit (AOQL)
It represents the worst average quality that would leave the inspection station, assuming rectification, regardless of incoming quality

23. It is the peak of the AOQ curve.
Average outgoing quality limit
It is the peak of the AOQ curve.
AOQL

24. How much do I need to inspect ?
ATI

25. ATI can be used to calculate the average cost of inspection.
Average Total Inspection (ATI)
It is the average number of items inspected per lot if rectifying inspection is conducted.
ATI can be used to calculate the average cost of inspection.

26. Average Total Inspection Curve
ATI = n + (1- Pa) (N-n)
N=1000
N=25
D=2

27. A manufacturer has selected a supplier to supply the raw material in the form of forged pieces in lots of 2000 units at a price of Rs 200/unit. Due to the nature of the forging process, a variation in the surface hardness is expected in the supplied pieces. The production manager knows that higher values of hardness lead to a poor tool life and hence sees the need to use an acceptance sampling plan to check the hardness of the incoming units. She decides to use a rectification based sampling plan with an acceptable quality level of 1%, a sample size of 20 and an acceptance number of 0. The variable cost of inspection is Rs 10 per unit and the fixed cost is Rs 100 per sample. What is the contribution to cost per piece.?

28. QA