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Math Help - Error Analysis

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    Error Analysis

    So im doing a little project, and I have various tolerances for various parts. All these tolerances add up, and if the values are too large, what my machine is trying to do won't work.

    I know one way to analyze this is simple to take the greatest error and add it, but the chances that each error will contribute is maximum amount to the total error is unlikely.

    Is there any way to add this up and do some standard deviation stuff or anything so that I get a distribution of how likely the sum of all these errors is going to get?

    I can easily just take the standard deviation of all the individual errors, but I'm not sure what that tells me in this case, My experiance with statics is rather limited, and consists mostly of my knowledge from grading curves, so sorry if this post makes no sense at all. I'd appreciate any help or links to any wikipedia articles or whatnot that may be able to help me.
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    Grand Panjandrum
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    Quote Originally Posted by modain View Post
    So im doing a little project, and I have various tolerances for various parts. All these tolerances add up, and if the values are too large, what my machine is trying to do won't work.

    I know one way to analyze this is simple to take the greatest error and add it, but the chances that each error will contribute is maximum amount to the total error is unlikely.

    Is there any way to add this up and do some standard deviation stuff or anything so that I get a distribution of how likely the sum of all these errors is going to get?

    I can easily just take the standard deviation of all the individual errors, but I'm not sure what that tells me in this case, My experiance with statics is rather limited, and consists mostly of my knowledge from grading curves, so sorry if this post makes no sense at all. I'd appreciate any help or links to any wikipedia articles or whatnot that may be able to help me.
    If you have a sum of errors \epsilon_i,\ i=1, .., n each with standard deviation \sigma_i,\ i=1, .., n and assuming they are independent the sd of the sum is \sqrt{\sum_{i=1}^n \sigma_i^2}.

    RonL
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    Quote Originally Posted by modain View Post
    So im doing a little project, and I have various tolerances for various parts. All these tolerances add up, and if the values are too large, what my machine is trying to do won't work.

    I know one way to analyze this is simple to take the greatest error and add it, but the chances that each error will contribute is maximum amount to the total error is unlikely.

    Is there any way to add this up and do some standard deviation stuff or anything so that I get a distribution of how likely the sum of all these errors is going to get?

    I can easily just take the standard deviation of all the individual errors, but I'm not sure what that tells me in this case, My experiance with statics is rather limited, and consists mostly of my knowledge from grading curves, so sorry if this post makes no sense at all. I'd appreciate any help or links to any wikipedia articles or whatnot that may be able to help me.
    Perhaps you mean the technique of Propagation of Errors. I didn't find any great articles on the web, but here's one that at least gives the general derivation.

    -Dan
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    Quote Originally Posted by CaptainBlack View Post
    If you have a sum of errors \epsilon_i,\ i=1, .., n each with standard deviation \sigma_i,\ i=1, .., n and assuming they are independent the sd of the sum is \sqrt{\sum_{i=1}^n \sigma_i^2}.

    RonL
    Hmm this is probably what I'm looking for. The thing is though, that don't know the standard deviation of each individual error. Is there any good guesses I can make, or is that something that is really dependant on what the piece of machinery is?
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    Quote Originally Posted by topsquark View Post
    Perhaps you mean the technique of Propagation of Errors. I didn't find any great articles on the web, but here's one that at least gives the general derivation.

    -Dan
    I read over that as well, and it doesn't make that much sense to me. Why would the total error be the square root of the sum of the squares of the individual errors? It seem like when taking a worst case scenario situation, the error can be more than just that square root sum of the squares.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by modain View Post
    I read over that as well, and it doesn't make that much sense to me. Why would the total error be the square root of the sum of the squares of the individual errors? It seem like when taking a worst case scenario situation, the error can be more than just that square root sum of the squares.
    It's simply one way to put together a set of errors in measurements of a calculated value to get the error in the calculated value. Stats isn't my forte, so I don't know if there are better ways to do this or not.

    -Dan
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    Grand Panjandrum
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    Quote Originally Posted by modain View Post
    Hmm this is probably what I'm looking for. The thing is though, that don't know the standard deviation of each individual error. Is there any good guesses I can make, or is that something that is really dependant on what the piece of machinery is?
    It does depend on the machinery, so there is nothing we can tell you.
    However if you know what the machinery is and the nature of the errors
    in what it does you should be able to estimate the standard deviations.

    In fact in your original post you talk about adding the greatest errors,
    if you have these you may be in luck. It is often the case that you can
    treat the SD as 1/3 of the maximum error (at least for a first guess)

    RonL
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    Thanks a lot to both of you.

    I think I figured out the stuff from that article, and it makes more sense now, especially when I assume that the error is 3 times the STD. I've found various sources saying that the min/max error is usually a multiple of the STD, but they say anything from 1/3 to 1/1. I've been playing around with the STD being different fractions of the min/max errors and although the results vary, I now understand the concept and with a little more research, I should be well on my way. Thanks.
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