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Home › Forums › General Forums › Tools & Templates › Stability and Normality
This topic contains 10 replies, has 8 voices, and was last updated by Rip Stauffer 2 years, 3 months ago.
Hi All,
I am new to Isix Sigma…hope this would be a fruitful engagement….
Could you let me know the key difference between stability and normality of data?
thanks,
IRock
The key difference is that the two are not related in any way.
IRock, there under “New to Six Sigma” there is a dictionary of terms that will give you an idea of what each term means – better than us re-typing it here.
Robert is right – the two are completely different. Normal processes can be unstable and stable processes can be non-normal.
Robert Butler wrote:
The key difference is that the two are not related in any way.
Robert: How uncharacteristically blunt of you. You feeling yourself (or are you feeling like Stan)?
I’m ok MBBinWI thanks for asking – in this instance I just didn’t have anything more to add. What I wish I could have done was link back to the discussion on this subject we had a couple of years ago but the “archives” are a frozen block of postings with a search capability that exists in name only thus making finding the relevant posts impossible.
How True……a great resource, yet inaccessible. Hopefully changes are planned.
Normality : Random Data when plotted follows the Normal probabilty density function (pdf). This histogram/plotted curve has bell shape.
Stability: Data points beyond 3-sigma limits are un-stable points
The statement “Normality : Random Data when plotted follows the Normal probabilty density function (pdf). This histogram/plotted curve has bell shape.” is in error. Random data will follow the underlying distribution from which it is drawn regardless of the sample size.
For example, if the distribution is binary the only values you will get from a binary distribution are 0′s and 1′s and no matter how many 0′s or 1′s you might have the shape of the distribution of those 0′s and 1′s will not follow a normal PDF. The idea that data will follow a normal distribution applies to distributions of averages of numbers from random distributions…and depending on the underlying distribution those averages can consist of as few as 2 numbers per average or more than 100 numbers per average.
As for the definition of stability – not really. There is the issue of simple chance – and there is the fact that a process can be wildly unstable and yet not have a single point outside of 3-sigma.
To demonstrate the last – take your computer and have it generate 100 random numbers from a normal distribution. Test this random draw to make sure that none of the points is outside of 3-sigma. Next rank order the numbers from lowest to highest and assign the dummy ID of 1 to the first 25, 2 to the second 25 3 to the third 25 and 4 to the last 25 (if you want, you can tinker with these sub-distributions to make sure that they too are normal). Assume 1-4 correspond to 4 production lines within the plant. Run a one way ANOVA on the production lines – they will be significantly different from one another, thus one or more of them are out of control and the process is unstable and yet, when considered from the standpoint of the overall output of the plant none of the data points are outside of 3-sigma.
Stability is a word which is used in Control Charts. Normality is a word which is used while checking the Goodness Of Fit of the data.
Certain control charts require data should be normally distributed. During such case, normality is checked.
Stability says whether the Process is Stable or Not Stable.
rabaos wrote:
Normality : Random Data when plotted follows the Normal probabilty density function (pdf). This histogram/plotted curve has bell shape.
Stability: Data points beyond 3-sigma limits are un-stable points
Where did you learn statistics? Both of these definitions are totally wrong.
See good description of normality by Robert Butler (excellent, as always).
To expand on stability, it is the relative constancy of the descriptors for the data being evaluated (for a normal distribution, the mean and std dev – are they constant or are they changing over time. For other underlying distributions, you’ll need to evaluate the appropriate descriptors).
In his original book, Walter Shewhart concluded that normality was neither sufficient nor required for a state of statistical control. In point of fact, most control charts actually do not “require” normality. Normality is nice, but what’s important is that the data be reasonably unimodal and symmetrical. For some of the WE Zone tests, a bell shape is also useful. This is why the Binomial and Poisson distributions are so useful in quality applications…once the counts are high enough, they model unimodal, symmetrical, bell shaped distributions that work well in control charts.
You cannot assess stability with a histogram; for reasons given by others and for a more fundamental reason; a histogram is a snapshot in time. Stability by definition must be assessed over time. That’s why you need a control chart. It plots the data over time, using local dispsersion measures to estimate the within-process variation so that you can tell when excursions from natural process variation happen.
Actually, if you must test for normality with process data, you’d better check to see if the process is stable first. If the process is not stable, you can’t say anything about the shape or the distribution.
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