This document discusses operational characteristic (OC) curves, which are graphs used in quality control to determine the probability that a production lot will be accepted based on the percentage of non-conforming items found during sampling inspections. The key points covered include: - The components of an OC curve including probability of acceptance (Pa) on the y-axis and percentage of defective items (p) on the x-axis. - The different types of OC curves (A and B) which depend on whether the lot size is finite or infinite. - Important points on the curve including the acceptable quality level (AQL) and rejectable quality level (RQL). - The probability distributions used to model different sampling plans

1. :Chintan H.Trivedi
M.Tech Industrial
1st Sem RCOEM.

2. o OC Curve?
o Shape of OC curve
o Types of OC curve
o Specific Points On OC Curve
o Probability Distributions used in OC Curve
o OC Curve Uses
o OC Curve Properties

3. o OC Curve was Developed along with SQC in 1930’s and
40’s.
o Graph used in quality control to determine the probability
of accepting production lots.
o Used in Discrimination of Sampling Plan Between Good
And Bad Lots.
o Measures Performance of Acceptance Sampling Plans.

4. o Ideal OC Curve:
o When percentage of Non-Conforming items are Below
prescribed level Pa is 100%. And more than it makes
Pa 0%.
o Ideal OC Curve Can be Obtained By 100% Inspection.
o Dividing line of Probability of acceptance Between 0 to
100% is AQL

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

8. o Type A
oGives the probability of acceptance for an individual lot
coming from finite production
oThis Curves are discontinuous.
o Type B
oGive the probability of acceptance for lots coming from
a continuous process
oThis Curves are correctly viewed as Continuous.

9. 9
o Assumes a finite lot.
o Hypergeometric distribution is used for this type
of curve.
o Binomial or Poisson distribution often provides a
good approximation.
o View point of Type A curve is to evaluate
consumer’s risk

10. o Assumes an infinite lot.
o Binomial distribution is the correct one.
o Poisson distribution often provides a good
approximation.
o View Point Type B OC curve is to evaluate
producers risks.

11. o Producer’s Risks (α):
o Probability of Rejection of a conforming lot.
o To Reduce Producers Risk Produce Product at a better
Quality Level Than AQL.
o Value of Producer’s Risks is Commonly 5%.

12. o Consumer’s Risks (β):
o Risk associated with Consumer.
o Probability of accepting a non-conforming lot.
o Usually it is 10%.

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

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

16. o Y axis
Gives the probability that the lot will be accepted (Pa).
o X axis = p
Percentage Defective.
o Shows percentage-defectives along the horizontal ('X'),
axis and probability of acceptance along the vertical ('Y')
axis.

17. 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

18. o Hyper geometric Distributions
o Binomial Distributions
o Poisson’s Distributions

19. o The hyper geometric
distribution is used to
calculate the probability
of acceptance of a
sampling plan when the
lot is relatively small.
o Calculations Becomes
Cumbersome for large
lot sizes.
The probability of exactly x
defective parts in a sample n:

20. o The binomial assumes that
the probabilities associated
with all samples are equal.
o This is referred to as
sampling with replacement.
The probability of exactly x
defective parts in a sample n:

21. Poisson Distributions
o Used for sampling plans
involving the number of
defects or defects per unit
rather than the number of
defective parts.
o When n is large and p is
small, the Poisson
distribution formula may be
used.
o The probability of exactly x
defects or defective parts in
a sample n:
o The letter e represents the
value of the base of the natural
logarithm system. It is a
constant value (e = 2.71828).

22. o Selection of sampling plans
o Aids in selection of plans that are effective in reducing
risk
o keeps the high cost of inspection down

23. o Ideal curve would be
perfectly perpendicular
from 0 to 100% for a
given fraction defective.

24. o Sampling Plans with Same Percent samples give very
different quality protection.

25. o Larger the sample size
steeper is the slope of
OC curve.
o Larger sample size
gives protection to
consumer and producer.