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April 17th, 2009, 04:01 AM   #1
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Variance and covariance

I am hoping this is a simple question and that I am getting forgetful in my old age.

I am taking measurements of color distance, and the dimensions are L (lightness/darkness), A(red/green), and B(Blue/Yellow).

I want to calculate the percent overlap between two processes each of which produces a normal distubition in L, A, & B.

I orginally calculated it simply as a distance between two means in L, A, & B with the variance of the two processes being the sum of the variances for each of the individual processes. I then calculated the proability density between the upper and lower specifications for each of the three dimensions and multiplied the proabilites to get the proability of all three of them being in spec.

The problem is that covariance exists, a part that is yellow will also tend to be red for example as the metallic in the paint tends to cause a perdictable movement. As a result the part will never be yellow and green from the standard so multipling the proability densities doesn't work.

At this point I am getting out of my depth, any suggestions greatly appreciated.

Mike
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