# Control charts for non-normal distributions - Do I need to do anything special?

D

#### davis007

Do I need to do anything special if my process variability is not normaly distributed. What I mean is should the control limits and or test for out of control points be calculated differntly?

We have gone through many iterations to identify and remove special causes from our process. But still I get a high number of out of control points when I control chart the process. When I look at a histogram of the data it seems that the distribution is not normal but much higher in the center with long thin tails at both ends. (I cant remember what this is called at this time.) I think the data in the tails pops up as out of control points (+/- >3 sigma) when I control chart the data. However we can find no "cause" for the out of control points. Am I wasting my time trying to set up a control chart for the process at all? We do on occasion find causes for some of the more severe out of control points, but these are also out of spec points and we would have looked at the process in depth even without the control chart.

#### Steve Prevette

##### Deming Disciple
Super Moderator
davis007 said:
Do I need to do anything special if my process variability is not normaly distributed. What I mean is should the control limits and or test for out of control points be calculated differntly?

We have gone through many iterations to identify and remove special causes from our process. But still I get a high number of out of control points when I control chart the process. When I look at a histogram of the data it seems that the distribution is not normal but much higher in the center with long thin tails at both ends. (I cant remember what this is called at this time.) I think the data in the tails pops up as out of control points (+/- >3 sigma) when I control chart the data. However we can find no "cause" for the out of control points. Am I wasting my time trying to set up a control chart for the process at all? We do on occasion find causes for some of the more severe out of control points, but these are also out of spec points and we would have looked at the process in depth even without the control chart.
Control Charts were set up by Dr. Shewhart to be distribution free. They work off the Tchebychev Inequality and the Camp-Meidel extension rather than the normal distribution.

Yes, bigger tails will make it slightly more likely to be outside the control limits (say 3 to 5% instead of the assumed 0.3% based upon the normal). So there can be false alarms. I would say since you are having a noticeable frequency of out of specification points it would be worth reviewing your Out of Control points. Are you only seeing outside the CL's, or are you also seeing patterns like 7 in a row the same side of the average?

One thing that you could do is accumulate all of the OOC data in one file and run analysis against other variables and see if there are differences between that data set and simlar distributions from the in control data.

#### Miner

##### Forum Moderator
davis007 said:
Do I need to do anything special if my process variability is not normaly distributed. What I mean is should the control limits and or test for out of control points be calculated differntly?

We have gone through many iterations to identify and remove special causes from our process. But still I get a high number of out of control points when I control chart the process. When I look at a histogram of the data it seems that the distribution is not normal but much higher in the center with long thin tails at both ends. (I cant remember what this is called at this time.) I think the data in the tails pops up as out of control points (+/- >3 sigma) when I control chart the data. However we can find no "cause" for the out of control points. Am I wasting my time trying to set up a control chart for the process at all? We do on occasion find causes for some of the more severe out of control points, but these are also out of spec points and we would have looked at the process in depth even without the control chart.
The shape parameter that you are describing is Kurtosis. The Normal distibution has a kurtosis-excess of 0. Your process sounds leptokurtic (high middle with long tails), which will have a positive kurtosis-excess. A platykurtic distibution (flatttened) will have a negative kurtosis-excess. (Caution: Kurtosis of a normal distribution is 3. Minitab use Kurtosis-excess which is Kurtosis - 3, yet labels it as Kurtosis.)

What type of control chart are you using?

Xbar control charts should normalize non-normal data. However, IMR charts will not normalize the data. If you are using IMR charts, you may try an Xbar chart as a potential solution.

D

#### davis007

Stratification

Steve:

Thanks for your reply. I have run each suggested test avaliable in Minitab. Tests that look for one or a series of points beyond a given sigma from the center find a lot of out of control points. Test for hugging the center, alternating data or a string of increasing or decreasing values find few if any out of control points.

I have noticed that the data does seem to be runs of data above and then below the center line, BUT even these runs in general have points that are on the other side of the center line. At first I thought that these "shifts" might be related to raw material changes, operator changes or points where the equipment was stopped for a repair or some other reason. However, none of these hypothises have paned out. Often the shift semmingly appears in the middle of a run with no change in material, operator or anything else as far as I can tell.

This is really buging me as I have been trying to figure this out for months now without success. The process is out of control, but 99% of the product we produce is in spec. I am starting to feel that I am wasting time with this line of analysis.

D

#### davis007

X-bar vs. Individuals

Miner:

Thanks for the reply. I am using an X-bar chart. I have two possible sub groups both are in time order. I can group by drum or lot. Each drum is tested in two locations thus I have exactly data points per drum. A lot is typically, but not always, 6 drums of product thus I typically have 12 data points per lot. Changing the groups from drum to lot does smooth out the data a bit but the issue I am having is the same in both cases. On thing that is also interesting is that I did an idividuals plot in minitab grouped by lot. When ploted this way the diferences from lot to lot become much harder to see. My guess is that if I was doing an ANOVA type of analysis I would be hard pressed to find real differences between most lots. As I have ~270 lots I have not tried this.

#### Steve Prevette

##### Deming Disciple
Super Moderator
davis007 said:
This is really buging me as I have been trying to figure this out for months now without success. The process is out of control, but 99% of the product we produce is in spec. I am starting to feel that I am wasting time with this line of analysis.
If you are running only 1% out of specification, I suspect you are running about 3% to 5% outside the control limits? If that is so, you may indeed be just getting false alarms. If the percent not meeting specification is in control (suggest trying a p-chart on that), and you can live with that rate, then perhaps it is unnecessary to chase every point that crosses the control limits.

I would myself probably keep monitoring the control chart, and put a p-chart in place on the specification limits. I'd still look to see in a low-key manner if anything could be found when a CL was crossed, but wouldn't get too spun up unless I got two in a row perhaps.

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