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Math Help - tolerance values

  1. #1
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    tolerance values

    I'd like to add two normal distributions. It's 10 +/- 1 added to 10 +/- 1, with 96% of the cases contained within 9 to 11. Two sigma = sqrt ([1^2] + [1^2]).
    It represents two 10 ohm resistors in series, which give a composite 20 ohm resistor with tolerance +/- 1.41 ohms.

    I did this on a spreadsheet to avoid having to debug a program with nested loops, etc., and each normal curve is approximated by a histogram with 8 bins, with 20 boxes total equaling the area under the curve, which is 1, like so.
    x
    xx
    xxx
    xxxx
    xxxx
    xxx
    xx
    x

    on the left is the value and on the right is how often it occurs.

    9............ 1
    9.285714286 2
    9.571428571 3
    9.857142857 4
    10.14285714 4
    10.42857143 3
    10.71428571 2
    11.......... 1

    The problem is the extremes are off and so is the center value.
    value...#.cdf
    18.000 1 1
    18.286 4 5
    18.571 10 15
    18.857 20 35
    19.143 33 68
    19.429 46 114
    19.714 56 170
    20.000 60 230
    20.286 56 286
    20.571 46 332
    20.857 33 365
    21.143 20 385
    21.429 10 395
    21.714 4 399
    22.000 1 400


    Any clues as to why? I'm most interested in the Z values that contain 50% and 96% of the cases.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ThatGuy View Post
    I'd like to add two normal distributions. It's 10 +/- 1 added to 10 +/- 1, with 96% of the cases contained within 9 to 11. Two sigma = sqrt ([1^2] + [1^2]).
    It represents two 10 ohm resistors in series, which give a composite 20 ohm resistor with tolerance +/- 1.41 ohms.

    I did this on a spreadsheet to avoid having to debug a program with nested loops, etc., and each normal curve is approximated by a histogram with 8 bins, with 20 boxes total equaling the area under the curve, which is 1, like so.
    x
    xx
    xxx
    xxxx
    xxxx
    xxx
    xx
    x

    on the left is the value and on the right is how often it occurs.

    9............ 1
    9.285714286 2
    9.571428571 3
    9.857142857 4
    10.14285714 4
    10.42857143 3
    10.71428571 2
    11.......... 1

    The problem is the extremes are off and so is the center value.
    value...#.cdf
    18.000 1 1
    18.286 4 5
    18.571 10 15
    18.857 20 35
    19.143 33 68
    19.429 46 114
    19.714 56 170
    20.000 60 230
    20.286 56 286
    20.571 46 332
    20.857 33 365
    21.143 20 385
    21.429 10 395
    21.714 4 399
    22.000 1 400


    Any clues as to why? I'm most interested in the Z values that contain 50% and 96% of the cases.
    Why are you doing this this way? You know that the two resistors in series hace a resistance of 20 +/- \sqrt{2} Ohms, so the resistance has a normal distribution with mean 20 and standard deviation \sqrt{2}/2, so now you can use the cumulative normal table to find the resistances which correspond to 50, and 96% (in fact we don't even need to do this as with the normal distribution we know that the 50% point of the cumulative is the mean, and the 96% point is the mean plus 2 sd's.

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Why are you doing this this way? You know that the two resistors in series hace a resistance of 20 +/- \sqrt{2} Ohms, so the resistance has a normal distribution with mean 20 and standard deviation \sqrt{2}/2, so now you can use the cumulative normal table to find the resistances which correspond to 50, and 96% (in fact we don't even need to do this as with the normal distribution we know that the 50% point of the cumulative is the mean, and the 96% point is the mean plus 2 sd's.

    RonL
    I want to get spreadsheets working for adding & subtracting normal distributions because my real purpose is to get spreadsheets working for multiplying & dividing normal distributions, which results are definitely not normally distributed.
    Once I have all these working I can in principle analyze the tolerance for probably any electrical circuit.


    I think I found the problem; my unrealized confusion between the histogram interval widths, end points and center values. That's why the CDF didn't work right although the curve that generated it looked correct.
    My bad!
    Last edited by ThatGuy; October 6th 2008 at 12:17 PM.
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  4. #4
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    MD
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    Another problem

    As above the RSS tolerance on two resistors in series, each of +/- 1 ohm, would be +/- 1.41 ohms.

    But, a capacitor in series with a resistor is modelled by R - jXc. For a tolerance of +/- 1 ohm on each (1 ohm reactive for the capacitor) what would be the RSS tolerance for the series connection?

    The impedance in polar coordinates for this series combination using a 10 ohm resistor and a capacitor of 10 ohms reactance would be Z = 10 -j10 = 14/-45
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