uncertainty of constants

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Peter 2011-10-3

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hi.

Im having problems with a simple calculation. I have 2 constants, R and C and I need to multiply them. However R has got an uncertainty of +- 10% and C of +-1%. How do I get a result witch takes this into account?

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Answer 1

Walter Roberson 2011-10-3

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The only possible answer in a simple calculation such as that is a range,

R * C * [9/10 * 99/100, 11/10 * 101/100]

With more complex expressions, determining the effect of a change in the inputs can be very difficult. Chaos Theory suggests that, indeed, there are many expressions for which the smallest possible change in the inputs can have results that are essentially unpredictable.

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John D'Errico 2011-10-6

This is NOT the only possible answer!!!!!! In fact, statistical tolerancing theory provides tools to measure the uncertainty in the result. If R and C are assumed uniform, then the distribution can be computed, although that distribution may often not be a simple one.

Walter Roberson 2011-10-6

"Assumed uniform" is the key there, John. The original question gives no distribution information or hints, so the best we can do is define the output range.

testing with

[R,C] = ndgrid(linspace(0.9,1.1,100),linspace(0.99,1.01,100));

and plotting R.*C in various forms, I see no indication of anything other than a strictly uniform distribution over the expected trapezoid.

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