Operating characteristics curve

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Operating Characteristics Curve (OC Curve) :Chintan H.Trivedi M.Tech Industrial 1 st Sem RCOEM.

description

this presentation gives you an overview of oc curve and will assist you in understanding concept of components in oc curve

Transcript of Operating characteristics curve

Page 1: Operating characteristics curve

Operating Characteristics Curve(OC Curve)

:Chintan H.TrivediM.Tech Industrial1st Sem RCOEM.

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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

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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

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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

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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

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Ideal OC Curve

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Typical Operating Characteristic (OC) Curve.

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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

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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

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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

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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

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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

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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

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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

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PA = The probability of acceptance

p = Proportion defectiveN = Lot sizen = Sample sizec= Acceptance Number α = Producer’s Riskβ= Consumer’s Risk

Definition of Variables

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o Hyper geometric Distributions

o Binomial Distributions

o Poisson’s Distributions

Probability Distributions in OC Curve

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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:

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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:

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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).

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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

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Properties of OC Curves

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

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

Properties of OC Curves

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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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