# Control Limits : Uniform Distribution

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- This topic has 6 replies, 4 voices, and was last updated 15 years, 2 months ago by Tom Dyer.

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- November 26, 2004 at 10:27 am #37675
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.0November 27, 2004 at 4:43 am #111360Tom,

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.0November 27, 2004 at 6:59 am #111362Tom,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 F0November 27, 2004 at 8:56 am #111363Tim,

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,

Andy0November 29, 2004 at 7:55 am #111400Tim,

Please eloborate your point.

Tom.0November 29, 2004 at 6:00 pm #111435

beverly danielsParticipant@beverly-daniels**Include @beverly-daniels in your post and this person will**

be notified via email.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…0November 30, 2004 at 2:35 pm #111487Sloping 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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