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Unformatted text preview: Lecture 11 Statistical Models Of Manufacturing Reliability Normal Distribution ( 29 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 μ σ σ π μ σ  = P( ) y y y σ y σ μ Transformation From The Normal Distribution To The Standard Normal Distribution Assume we have a of the variable with: mean value of standard de Normal Distribution Standard Normal Distr viation of The is the transformation from to via: ibution Th e y y y y y y y y z y z μ σ μ σ = = = Standard Normal Distribution has a mean of zero and a standard deviation of 1! * * What is the probability , where is some specific value of ? y y y y * * Pr( ) Pr( ) y y z z = TailEndZTable (Posted on WebCT) Standard Normal Cumulative Probability Table – Page 1 Standard Normal Cumulative Probability Table – Page 2 Sampling a Normally Distributed Process Suppose a process is normally distributed with a mean of µ and a standard deviation of σ. Further, suppose that you do not know the values for µ and σ, but want to determine these values by measuring n samples. Provided that the sampled distribution is symmetric, unimodal and without outliers, and the number of samples is > 40, then use the equations below to compute µ and σ. 1 mean N i i x x N = = = ∑ 2 1 ( ) standard deviation 1 N i i x x x N σ = = = ∑ Student’s tdistribution Problems arise in accurately determining the mean and standard deviation when the sample size is small. Student’s tdistribution 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 tdistribution in 1908 under the name “Student.” Poisson Distribution P(x) the probability of x occurance of defects = mean number of occurances of defects...
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This note was uploaded on 04/09/2009 for the course ECE 4001 taught by Professor Frazier during the Spring '09 term at Georgia Institute of Technology.
 Spring '09
 FRAZIER

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