1. ## 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.

2. Originally Posted by ThatGuy
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

3. Originally Posted by CaptainBlack
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.