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CorrectSPC Total Variance Equation

Your process output is not one variance, but a sum of many.

  1. Bob Doering

    Bob Doering Member

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    Bob Doering submitted a new resource:

    Total Variance Equation - Your process output is not one variance, but a sum of many.

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  2. Gejmet

    Gejmet Member

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    Total Variance Equation - Your process output is not one variance, but a sum of many.

    The output of any process is the interaction and summation of many sources of variation, when we determine process capability we usually compare the output of our process in terms of its location and spread with the specifications. The most important thing is that we have homogenous data, in this way we can say something about the future which is indicative of the past.

    If we don't have homogenous data we have unpredictability and therefore there is nothing left to say about the process except to find out why and eliminate it. It's very common for all kinds of indexes to be quoted for data sets which clearly display a lack of homogeneity and its due to a lack of understanding of statistics on the theoretical plane and requirements for data analysis.

    Of course, if the homogenous data computed into an index doesn't give you the elbow room and location you need then you are into understanding the effect of various inputs and how they interact. In the end, teams just brainstorm the possible inputs including some of the ones you have mentioned. Luckily, they don't have to think in detail of how variances interact but select a variable of interest and assess its status as containing either random or special cause variation, then run the study again.

    Ultimately, the output has to be homogenous otherwise the whole experiment has to start again.

    To the vast majority, achieving homogeneity is an achievement to be celebrated and maintained and there is not a distribution or transformation in sight, it's a lot simpler in concept than most people think.

    So, Total Variance Equation, it's nice to be for warned and for armed at the outset with what the general possible inputs are which affect the output but for a lot of processes it's fairly obvious in my experience what the key sources are and what to fix if needed to obtain homogeneity.

    You can of course ignore homogeneity and take a modelling approach to comparing the inputs to the spec, rather like creating uncertainty budgets for measurement. This method might be ok for initial planning in the absence of real data but its a conformance based approach where the only improvement is with your assumptions of the level of the inputs and their associated distributions. You make big assumptions about interactions and ignore generally how natural variation works including the fact that distributions are created by real data.

    Some would say that the empirical approach underestimates the sources of variation, but this ignores how important the achievement is of homogeneity in the data and therefore predictability into the future. In other words, if I can achieve this now, why can't i maintain it into the future?

    The other advantage of the empirical approach is the seemingly endless levels of improvements in the process that can be achieved, I have seen reductions in variation by more than 60% accompanied by an obvious easing of the process, just not possible with the modelling approach which is only concerned with burning and scraping the toast in process terms.
     
  3. Bev D

    Bev D Moderator Staff Member

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