Analyzing Uncertainty with Probability Plots in Engineering
Explore uncertainty analysis techniques for engineers using probability plots with examples and code snippets. Learn how to formulate CDF, linearize distributions, fit to straight lines, calculate slopes, and more. Enhance your understanding of exponential and Gumbel extreme value distributions through practical demonstrations.
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Presentation Transcript
Probability Plot Examples Jake Blanchard Spring 2008 Uncertainty Analysis for Engineers 1
Making Your Own Prob Plots Sort data Formulate CDF Linearize distribution for CDF Fit to straight line Plot both Uncertainty Analysis for Engineers 2
An Example (7.4 from text) Exponential Distribution ( ) a = 1 exp f x a ( ( x ) ) = exp F 1 x = exp F 1 x a ( ln ) F ( ( ) ) 1 = ln F a ( ) = = x a x a Slope is Uncertainty Analysis for Engineers 3
Code data=[blah blah]; data=sort(data); n=numel(data); for i=1:n plotcdf(i)=-log(1-i/n); end data=data(1:n-1); plotcdf=plotcdf(1:n-1); p=polyfit(data,plotcdf,1); f=polyval(p,data); plot(data,plotcdf,'x',data,f) slope=p(1) invslope=1/slope Uncertainty Analysis for Engineers 4
Plot 4 3.5 3 2.5 2 1.5 1 0.5 0 0 500 1000 1500 2000 2500 3000 Uncertainty Analysis for Engineers 5
Example 7.5 Gumbel Extreme Value ( y ) = = exp exp F ln( y u = ( y ) = ln( ) exp F u ( ) ln ) F u y u Slope= Intercept= u Uncertainty Analysis for Engineers 6
Code data=[blah blah]; n=numel(data); for i=1:n plotcdf(i)=-log(-log(i/n)); end data=data(1:n-1); plotcdf=plotcdf(1:n-1); p=polyfit(data,plotcdf,1); f=polyval(p,data); plot(data,plotcdf,'x',data,f) slope=p(1) Uncertainty Analysis for Engineers 7
Plot 4 3 2 1 0 -1 -2 4.5 5 5.5 6 6.5 7 7.5 Uncertainty Analysis for Engineers 8
