Post on 23-Jun-2015
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Operating Characteristics Curve(OC Curve)
:Chintan H.TrivediM.Tech Industrial1st Sem RCOEM.
o OC Curve?o Shape of OC curveo Types of OC curveo Specific Points On OC Curveo Probability Distributions used in OC Curve o OC Curve Useso OC Curve Properties
Seminar Overview
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.
OC Curve
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
Shape Of OC Curve
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.
Shape Of OC Curve
Ideal OC Curve
Typical Operating Characteristic (OC) Curve.
o Type AoGives the probability of acceptance for an individual lot
coming from finite productionoThis Curves are discontinuous.
o Type BoGive the probability of acceptance for lots coming from
a continuous processoThis Curves are correctly viewed as Continuous.
Types of OC Curves
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Type A OC Curve
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
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.
Type B OC Curve
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%.
Specific Points On OC Curve
o Consumer’s Risks (β):
o Risk associated with Consumer.
o Probability of accepting a non-conforming lot.
o Usually it is 10%.
Specific Points On OC Curve
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”.
Specific Points On OC Curve
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.
Specific Points On OC Curve
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.
OC Graphs Explanation
PA = The probability of acceptance
p = Proportion defectiveN = Lot sizen = Sample sizec= Acceptance Number α = Producer’s Riskβ= Consumer’s Risk
Definition of Variables
o Hyper geometric Distributions
o Binomial Distributions
o Poisson’s Distributions
Probability Distributions in OC Curve
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.
Hyper Geometric Distributions
The probability of exactly x defective parts in a sample n:
Binomial Distributions
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:
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).
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
OC Curves Uses
Properties of OC Curves
o Ideal curve would be perfectly perpendicular from 0 to 100% for a given fraction defective.
o Sampling Plans with Same Percent samples give very different quality protection.
Properties of OC Curves
Properties of OC Curves
o Larger the sample size steeper is the slope of OC curve.
o Larger sample size gives protection to consumer and producer.
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