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Unformatted text preview: Slide #1 ECE 4001 L11 2008 Lecture 11B Statistical Models Of Manufacturing Reliability Slide #2 ECE 4001 L11 2008 Normal Distribution ( ) 2 2 2 1 P( ) 2 where is the mean value of the variable and is the standard deviation of the variable Probability density function for a normal distribution is give . y n b y y y y y y y e -- = P( ) y y y - y Slide #3 ECE 4001 L11 2008 Students t-distribution Problems arise in accurately determining the mean and standard deviation when the sample size is small. Students t-distribution can more accurately represent statistics of a process when the sample size is small; however, coverage of this is beyond the scope of ECE4001. William Gosset first published concepts and derivation of the t-distribution in 1908 under the name Student. Slide #4 ECE 4001 L11 2008 Poisson Distribution P(x) the probability of x occurance of defects = mean number of occurances of defects = P(x) is calculated using the Poisson distribution P(x) ! x e x - = The Poisson distribution is derived from random processes that involve occurrences or arrivals It is a discrete random process Slide #5 ECE 4001 L11 2008 Graph Poisson Distribution 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.140 10 20 30 x P(x) 0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 Density Cummulative Slide #6 ECE 4001 L11 2008 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 Slide #7 ECE 4001 L11 2008 System Reliability when Failure Rate is not Constant Weibull Distribution ( ) ( ) 1 / 0 ; ; , ; 1 Failure rate decreases over time 1 Failure constant over time 1 Failure rate increases over time k k x x f x k k x e x k k k k -- < = < = > k < 1 suggests infant mortality k = 1 suggests failures are due to random events k > 1 suggests wear out Slide #8 ECE 4001 L11 2008 Weibull Distribution...
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This note was uploaded on 06/09/2009 for the course ECE 4001 taught by Professor Frazier during the Fall '09 term at Georgia Institute of Technology.
- Fall '09