L11_ECE4001_Spring_2010

# L11_ECE4001_Spring_2010 - Lecture 11 Statistical Models Of...

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J. Stevenson Kenney © 2010 1 Lecture 11 Statistical Models Of Manufacturing Reliability February 17, 2010

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J. Stevenson Kenney © 2010 2 Poisson Distribution P(x) the probability of x occurance of defects = mean number of occurances of defects λ= P(x) is calculated using the Poisson distribution P(x) ! x e x λ = • The Poisson distribution is derived from random processes that involve “occurrences” or “arrivals” • It is a discrete random process
J. Stevenson Kenney © 2010 3 Graph Poisson Distribution 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 01 0 2 0 3 0 x P(x) 0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 Density Cummulative

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J. Stevenson Kenney © 2010 4 Properties of Poisson Distribution Poisson distribution: P(x) ! Mean: Standard Deviation: 1 Skewness: 1 Kurtosis: 3 x e x λ = +
J. Stevenson Kenney © 2010 5 Relationship to the Normal Distribution and Use in DFM • For large numbers, the Normal distribution may be used to approximate the Poisson distribution http://www.stattucino.com/berrie/dsl/poissonclt.html • We use Poisson when we are concerned about a small number of defects

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J. Stevenson Kenney © 2010 6 Probability of defects in a device Consider a unit taken at random from after a manufacturing process where number of defects per unit dpu. The probability that the unit will have defects is determined by the Poisson distributio k λ == n () P( defects) ! dpu k e dpu k k = 0 and the probability of having zero defects is P(0 defects) 0! dpu dpu ed p u e and first time yield for a testing or inspection process dpu e =
J. Stevenson Kenney © 2010 7 Example What is the probability of a unit having exactly 4 defects when the mean number of defects is dpu = 3?

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## L11_ECE4001_Spring_2010 - Lecture 11 Statistical Models Of...

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