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OC Curves: Construction, Calculation, and Uses

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  1. Presentation Overview • Operation Characteristic (OC) curve Defined • Explanation of OC curves • How to construct an OC curve • An example of an OC curve • Problem solving exercise

  2. OC Curve Defined • What is an Operations Characteristics Curve? • the probability of accepting incoming lots.

  3. OC Curves Uses • Selection of sampling plans • Aids in selection of plans that are effective in reducing risk • Help keep the high cost of inspection down

  4. OC Curves • What can OC curves be used for in an organization?

  5. Types of OC Curves • Type A • Gives the probability of acceptance for an individual lot coming from finite production • Type B • Give the probability of acceptance for lots coming from a continuous process • Type C • Give the long-run percentage of product accepted during the sampling phase

  6. OC Graphs Explained • Y axis • Gives the probability that the lot will be accepted • X axis =p • Fraction Defective • Pf is the probability of rejection, found by 1-PA

  7. OC Curve

  8. Definition of Variables PA = The probability of acceptance p = The fraction or percent defective PF or alpha = The probability of rejection N = Lot size n = The sample size A = The maximum number of defects

  9. OC Curve Calculation • Two Ways of Calculating OC Curves • Binomial Distribution • Poisson formula • P(A) = ( (np)^A * e^-np)/A !

  10. OC Curve Calculation • Binomial Distribution • Cannot use because: • Binomials are based on constant probabilities. • N is not infinite • p changes • But we can use something else.

  11. OC Curve Calculation • A Poisson formula can be used • P(A) = ((np)^A * e^-np) /A ! • Poisson is a limit • Limitations of using Poisson • n<= 1/10 total batch N • Little faith in probability calculation when n is quite small and p quite large. • We will use Poisson charts to make this easier.

  12. Calculation of OC Curve • Find your sample size, n • Find your fraction defect p • Multiply n*p • A = d • From a Poisson table find your PA

  13. N = 1000 n = 60 p = .01 A = 3 Find PA for p = .01, .02, .05, .07, .1, and .12? Calculation of an OC Curve

  14. Properties of OC Curves • Ideal curve would be perfectly perpendicular from 0 to 100% for a given fraction defective.

  15. Properties of OC Curves • The acceptance number and sample size are most important factors. • Decreasing the acceptance number is preferred over increasing sample size. • The larger the sample size the steeper the curve.

  16. Properties of OC Curves

  17. Properties of OC Curves • By changing the acceptance level, the shape of the curve will change. All curves permit the same fraction of sample to be nonconforming.

  18. Example Uses • A company that produces push rods for engines in cars. • A powdered metal company that need to test the strength of the product when the product comes out of the kiln. • The accuracy of the size of bushings.

  19. Problem • MRC is an engine company that builds the engines for GCF cars. They are use a control policy of inspecting 15% of incoming lots and rejects lots with a fraction defect greater than 3%. Find the probability of accepting the following lots:

  20. Problem • A lot size of 300 of which 5 are defective. • A lot size of 1000 of which 4 are defective. • A lot size of 2500 of which 9 are defective. • Use Poisson formula to find the answer to number 2.

  21. Summary • Types of OC curves • Type A, Type B, Type C • Constructing OC curves • Properties of OC Curves • OC Curve Uses • Calculation of an OC Curve

  22. Poisson Table

  23. Poisson Table

  24. Poisson Table

  25. Bibliography Doty, Leonard A. Statistical Process Control. New York, NY: Industrial Press INC, 1996. Grant, Eugene L. and Richard S. Leavenworth. Statistical Quality Control. New York, NY: The McGraw-Hill Companies INC, 1996. Griffith, Gary K. The Quality Technician’s Handbook. Engle Cliffs, NJ: Prentice Hall, 1996. Summers, Donna C. S. Quality. Upper Saddle River, NJ: Prentice Hall, 1997. Vaughn, Richard C. Quality Control. Ames, IA: The Iowa State University, 1974.

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