Vectors and distributions

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    Mark F.

    I am a statistical novice, but I have been wondering how to determine measurement error on a balancing machine that we have. 
    I was trying to do some sort of repeatability study, but the results of a balancing run is both a magnitude of imbalance and an angle.  I though about converting these values into x and y compents and calculating the stdev of each component, but I am not sure how to add the components back together to get a confidence interval or in this case confidence circle.


    D. Meckley

    If I understand your measurement concern, you have two error components that contribute error to the same measurement simultaneously.
    Try using a Root Sum Square method for the components involved.  Take the standard deviation for each error component (magnitude, and imbalance) and square them.  Add the two squares, and calculate the square root of the sum.
    Multiply by some coverage factor for confidence level (typically k = 2), and you should have the most likely measurement uncertainty level for the combination of the two factors. 
    This is simplistic method for measurement uncertainty, but it will get you a good approximation.  Note that you can add as many error components as necessary.  Just sum up the total of all the squares, and calculate the square root.
    Hope this helps.



    When we perform measurment error on a balancer we only use the imbalance reading.  The purpose for angle (in our case) is to know the location of where material needs to be removed from the part for balance correction.  The angle reading becomes increasingly inaccurate the closer to the center point the imbalance is.  An important measure to include along with a balancer R&R is linearity, to be sure various amounts of imbalance on the part is indeed linear. 
    Good luck!


    Mike Carnell

    Mark F,
    Our experience with balancing was much the same as ahardy’s. For the most part it is a pretty bad measurement. We were balancing individual components, subassemblies and assemblies. Ultimately every level needed to be rebalanced. We were reworking the rework.
    At the end of the day balancing is rework. The only way out of it is to build components that are balanced to begin with. We made a lot more progress attacking it from that direction.
    The down side is people with long histories in this type of business will fight you constantly because they have novision of not balancing. Whatever you do (except just living with it like it is) your job will be a difficult one.
    Just my opinion.
    Good luck.



    This is a very similar problem to determining the capability of the position of the centre of a drilled hole.  At its best it is spot on and hence have a 0 deviation (it can never be less than this).
    If you convert the polar coordinates given by angle and magnitude into cartesian x,y, it is probable that individually they will appear normally distributed, but as a polar set, the distribution is a Weibull one (Rayleigh’s to be precise). If you keep the set as x and y you will end up with a confidence square rather than the circle which you rightly propose. So it must be converted to a polar type of capability.
    There are several proposed ways of doing this, but the most concise that I have seen is at
    See the article about SPC for true position



    I tried to search first, so that is why I am digging up an old thread. 
    Mine is a very similar issue to the above.  I am trying to do an MSA on the balancers, though.  We do not correct the imbalance, but are simply measuring it. 
    We can easily quantify the bias of a given balancer by using cartesian coordinates, but R&R seems to have me a bit stymied.  I can do an MSA on either magnitude OR angle (though I am not sure angle works very well) OR catesian X OR cartisian Y.  Should I do two and marry them back together?  How? 
    Thanks for any feedback!

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