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Control Limits : Uniform Distribution

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  • #37675

    Tom Dyer
    Member

    We run a process which follows a uniform distribution . How do we calculate the control limits for if we were to use a control charting to operate the process.
    Tom.

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    #111360

    Lala
    Member

    Tom,
    I wonder whether there exists any Xbar-R chart for uniform Distribution. However, I do not believe that a uniform distribution exists in reality. Even if it exists, use central limit theorem to use conventional Xbar-R chart.
    Hope this help you to think.
    Sunil.

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    #111362

    Tim F
    Member

    Tom,At the simplest level, the control limits are independent of the distribution. They are simply an empirical rule that says anything more that 3 sigma from the center is worth taking a look at. So the control limts are 3 sigma to either side of the center line. If you want to calculate odds, then the normal distribution is handy and it is want most calculation assume – e.g. 0.3% outside 3 sigma is true for a normal distribution, but not true for most other distributions. But it is not a requirement for control charting.For those who are interested, it isn’t too hard to look at the behavior of a uniform distrubion. For a truly uniform distribution, it turns out that if you look at subgroups of 1,2, or 3, it is mathematically impossible to have any points outside the 3 sigma limits. This is a good thing since you can never get a “false positive” reading which would stop the process. Even with larger subgroups, the odds of a “false positive” remain less than the 0.3% for a normal distribution.Does that help?
    Tim F

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    #111363

    Tim,
    A uniform distribution I’ve often encountered is what I call a truncated distribution, which is typically unform between tolerance limits  and with very few points outside. I generally put it down to the use of a single first-off, but I might be mistaken …
    I’ve never investigated trying to control this distribution with a Shewhart chart, for obvious reasons, but if anyone had the time or inclination, I’d be interested to know if this type of distribution can be put under SPC, and discriminte between assignable and common causes of variation.
    Cheers,
    Andy

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    #111400

    Tom Dyer
    Member

    Tim,
    Please eloborate your point.
    Tom.

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    #111435

    beverly daniels
    Participant

    Tool wear has a uniform distribution…if you use a traditional Xbar R chart approach you will have very narrow limits and most of the subgroup averages will be outside teh limits.
    Search for “Can I Have Sloping Limits” by Donald Wheeler….there are also approaches, search for tool wear and control charts…

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    #111487

    Tom Dyer
    Member

    Sloping control limits is quite familiar concept. But what about an automatic selective assembly process? A machine measures 3 parts & selective assembles so as to obtain an assemble length within a desired tolerance intervals. Hope I am correct in identifying this process as “uniform distribution”.

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