# Control chart for right-skewed data

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- This topic has 10 replies, 8 voices, and was last updated 13 years, 4 months ago by abdu.

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- July 18, 2006 at 12:51 pm #44052
Hi,

our team has the task of monitoring a process that is inherently right – skewed and non-normal (p=0.0000 in Minitab’s normality tests). We are well below the USL but still, it would be nice to have a way of monitoring the process so that we can detect things starting to go wrong before the USL is reached.

Do you have any ideas of what kind of chart to use? The Box-Cox transformation does not seem to be an option – there is no appropriate lambda between -5 and 5 according to Minitab.

I am thinking of something from the non-parametrics side – like monitoring the inter-quartile range and/or the number of outliers but probably without any control limits. Does this make sense? Do you have other ideas?

P.S. We have about 200 data points generated / day .

Thanks and regards

Sandor0July 18, 2006 at 2:00 pm #140540Assuming that you are talking about continuous data and there is some rational subgrouping that can be done, a simple xbar/r chart will take care of that nasty old skewness.

As a last resort, you can try a Johnson Transformation in Mini if you haven’t tried that already. I have found it more useful than Box-Cox.0July 18, 2006 at 2:45 pm #140547

Wayne LeaoMember@Wayne-Leao**Include @Wayne-Leao in your post and this person will**

be notified via email.waiting for the expert. i do have the same issue like this. but one comment, johnson is different to box. don’t mix them. This question activing in most company as i know, especially at machinary process and molding process.

0July 18, 2006 at 3:10 pm #140550Who said anything about mixing Johnson and Box Cox…they are two separate functions in Mini and use different algorithms for performing a transformation. Both give you a set of transformed data. Subgrouping, if appropriate, is the first step. If that doesn’t make sense then you can transform but remember to transform any specs as well in case you need to calculate capability. The Expert has left the building.

0July 18, 2006 at 3:32 pm #140551

Statistical AnomolyMember@Statistical-Anomoly**Include @Statistical-Anomoly in your post and this person will**

be notified via email.Sandor,

Control charts for continuous data are robust to non-normality. Since 98% or more of data is contained within plus or minus 3 sigma regardless of of the shape of the distribution, control charts do a good job at detecting special cause. Shewhart addressed this in his first book.

A good reference book on the subject of SPC, is by Donald Wheeler and David Chambers, “Understanding Statistical Process Control.” They address several “myths” about control charts, including the need to have normally distributed data (you don’t) and the idea that control charts “work” because of the central limit theorem (CLT isn’t “why” control charts work, Control charts work because of the conservative nature of 3 sigma limits).

Choose the appropriate chart for the type of data you have (continuous or discrete) and subgroup the data if there is a rational way to do so, but don’t feel compelled to subgroup if there is no rational for it.

SA

0July 18, 2006 at 6:30 pm #140585

Orang_UtanParticipant@Orang_Utan**Include @Orang_Utan in your post and this person will**

be notified via email.There is a technical paper published in 2000’s AQC, titled SPC for real-world processes: What to do when the normal assumption does not work.

If you are not a ASQ member, you can still purchase the article from ASQ at non-member price. ASQ member is free to access this article.

Please don’t ask me to circulate any copyrighted materials.0July 19, 2006 at 12:23 pm #140627Hi Darth,

we are measuring the duration of some operation in software over and over again for a whole night, every night. This means there is no immediately apparent subgrouping except maybe taking the whole data set from a night as a group, about 200 data points, but that seems to be excessive.

I tried xbar-R and Xbar-S charts with different group sizes. At 5 and 25 I get a large number of “out of control” points but I am fairly sure that they belong to the voice of the process – it is simply a strongly right-skewed distribution. Certainly, I would not initiate any action around those points.

With larger groups I can get rid of most of the out of control points in the chart – so maybe that could be an answer for me – just take a group size of 35 – 45 ? It seems a bit artificial to do that, what is your opinion?

P.S. I never used the Johnson transform and i could not find it in my Minitab 12.2. Is it in later versions?

Thanks and regards

Sandor0July 19, 2006 at 2:27 pm #140639Sandor, here are a few thoughts:

1. Is the skew of your data due to a few extreme values or pretty consistent? If due to a few points and upon investigation it turns out that they are “different” then maybe you can segregate them out and see what happens. Possibly there are two processes going on that should be viewed separately.

2. Going to high sample sizes to normalize the data seems a bit artificial so I agree with you there.

3. Johnson is one of additions to the newer versions.

4. If you want to send me the data offline, I can look at it and see if I can make some sense of it.

My offline address is @aol.com">drdarth66@aol.com

0July 24, 2006 at 7:25 am #140885I had similar issues to yours ito a positively skewed distribution. My data set consisted of a continuous data set (turnaround times). In the end I sorted out the problem with subgrouping.

Initially though I found it useful to use simple box plot and to use the median as the best measure of location. You can use a very simple non-parametric technique to find the confidence interval for the median. I also used the Mann-Whitney-Wlicoxon test to determine whether 2 distributions of the same shape differed in location.

Hope this is useful.

Popeye0July 26, 2006 at 7:27 pm #141016if your data is right skewed, you need to check first the randomness and how you have subgrouped the data, there maybe initial problems on these.

you can’t go directly to SPC because using other test for outliers might conclude that your graph is out of control

if the data cannot be transformed, you can use non-parametric tests0September 30, 2006 at 8:08 pm #144084Dears Darth and Sandor,

I want to use Xbar/ S chart But my broblem is how Ican get the formula for C4 for skewed data such as weibull and burr Distributions, please tell me if you know the formula of C4 for nonnormal0 - AuthorPosts

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