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Lecture11_Testing _ Inspection

# Lecture11_Testing _ Inspection - Lecture 11 Statistical...

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Lecture 11 Statistical Models Of Manufacturing Reliability

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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!

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* * What is the probability , where is some specific value of ? y y y y * * Pr( ) Pr( ) y y z z =
Tail-End-Z-Table (Posted on WebCT)

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Standard Normal Cumulative Probability Table – Page 1
Standard Normal Cumulative Probability Table – Page 2

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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 t-distribution Problems arise in accurately determining the mean and standard deviation when the sample size is small. Student’s 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.”

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Poisson Distribution P(x) the probability of x occurance of defects =
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