acceptance sampling plan

1. Operating Characteristic Curves
(Advance Sampling Plan)
SANYOGITA
BE+MBA
4th YEAR
CM14226

2. Operating Characteristic Curve
• It is a graph used in quality control to determine
the probability of accepting production lot.
• The operating characteristic (OC) curve depicts
the discriminatory power of an acceptance
sampling plan.
• The OC curve plots the probabilities of accepting
a lot versus the fraction defective.
• When the OC curve is plotted, the sampling risks
are obvious.

3. Shape of OC Curve
• Ideal OC curve
• When percentage of Non-Conforming items
are Below prescribed level Pa is 100%. And
more than it makes Pa 0%.
• Ideal OC Curve Can be Obtained By 100%
Inspection.
• Dividing line of Probability of acceptance
Between 0 to 100% is AQL
• No sampling plan give such a ideal OC Curve.

4. • Typical OC Curve:
• This is Curve Roughly “S” Shaped.
• Obtained by joining points between
Probability of acceptance & Percentage non
conforming items.
• Obtained by Performing Sampling Inspection.

6. Specific Points in OC Curve
• Producer’s Risks (α):
• Probability of Rejection of a conforming lot.
• To Reduce Producers Risk Produce Product at
a better Quality Level Than AQL.
• Value of Producer’s Risks is Commonly 5%.
• =1-PA(at AQL)

7. • Consumer’s Risks (β):
• Risk associated with Consumer.
• Probability of accepting a non-conforming lot.
• Usually it is 10%.
• =PA(at LTPD)

8. • AQL(Acceptable Quality Level):
• Maximum Percent of defectives that will make
lot easily acceptable.
• Fraction of Defectives accepted without any
serious effect on quality and customer
relations.
• PA for an AQL lot should be high.
• AQL is also Termed as Producer’s “safe point”.

9. • Rejectable Quality Level(RQL):
• Quality Level Unacceptable to the Customer.
• Definition Of Unsatisfactory Quality.
• Characterised by low probability of
acceptance.
• PA of lot at RQL represents Consumer’s Risk.

11. DEFINATION OF VARIABLES
• PA = The probability of acceptance
• p = Proportion defective
• N = Lot size
• n = Sample size
• c= Acceptance Number
• α = Producer’s Risk
• β= Consumer’s Risk

12. Steps for drawing OC Curve
• Multiply proportion defective(p) with sample
size (n)
• Record the value for Probability of acceptance
,Pa from poisson probability distribution table
• Then plot OC Curve i.e. proportion defective
vs probability of acceptance.
Given
data
Lot size N
sample size n
Acceptance size c
AQL
LTPD

13. EXAMPLE
QUESTION
• The Noise King Muffler Shop, a high-volume installer of
replacement exhaust muffler systems, just received a
shipment of 1,000 mufflers. The sampling plan for
inspecting these mufflers calls for a sample size and an
acceptance number . The contract with the muffler
manufacturer calls for an AQL of 1 defective muffler
per 100 and an LTPD of 6 defective mufflers per 100.
Calculate the OC curve for this plan, and determine the
producer’s risk and the consumer’s risk for the plan.

14. SOLUTION
GIVEN
N=1000
N=60
C=1
AQL=.01
LTPD=.06
• Let p=.01

15. • Here =12.2% & =12.6%
• Both the values are higher
than the values usually
acceptable .
• We can adjust the risk by
changing the sampling
size.

16. Changes in OC Curve
• Sample size effect:
• Increasing n while holding c constant increase
producer risk () and reduces consumer risk
()
• c =1
n Producer’s risk() Consumer’s risk ()
60 0.122 0.126
80 0.191 0.048
100 0.264 0.017
120 0.332 0.006

18. • Acceptance level effect:
• Increasing c while holding n constant
decreases the producer’s risk and increases
the consumer’s risk.
• n=60
c Producer’s risk Consumer’s risk
1 0.122 0.126
2 0.023 0.303
3 .003 0.515
4 0.000 0.706

20. • We should increase the sample size, which
reduces the consumer’s risk, and increase the
acceptance number, which reduces the
producer’s risk .
• A improved combination can be found by trail
and error.

21. THANK YOU