Six Sigma 4

[Iskit4iam]

We're having a discussion about certain aspects of six sigma. Some texts include a chart that list sigma values for each yield percentage and include instructions on how to calculate yield percentage so you can look up your sigma performance level. The instructions don't indicate a test for normal distribution is needed. One faction contends that everything is "normal". Another says the books are wrong except for cases where the distribution is normal. A third faction chimes in with it doesn't matter if the distribution is normal, its just a convient way to compare results between projects.

We were wondering what other people thought?

 

[PSE]

From my experience, most "published" results and calculations for the standard deviations and Cpk's assume a normal distribution as it simplifies the calculations. However, to truly delve into what the data is and to have confidence in the result, you should at least test it for normality. There are a multitude of statistical software packages that are capable of assisting these types of analyses.

Regards

 

[jpankask]

In my black belt class, the instructors, all very seasoned statisticians with PhD's, stated that it didn't matter. As a matter of fact, if we used the term normal distribution we were given wedgies...just kidding but we were told every time "normal distribution" was mentioned by someone in class that we needed to get that out of our vocabulary.

 

[Kenneth]

I am fundamentally ill-equipped to enter into any intelligent discussion of statistics, but my personal inclination would be to give those PhDs a wedgie (see page 12 at

http://www.statoek.wiso.uni-goettingen.de/forschung/pdf/six_sigma.pdf

and

http://www.metalcastingworld.com/educast/papers/papers2000/200001001.html)

and start looking for some new ones...

 

[Kenneth]

Comment on the Assumption of a Normal Distribution in Known-Sigma and Unknown Sigma Plans

The frequency distribution of many industrial quality characteristics is roughly normal. This is particularly so where the product comes from a single source within a short period of time. For this reason, the assumption of a normal distribution is good enough for practical purposes in many instances. This assumption is most likely a reasonable where inspection lots are formed close to the point of production, so that the chance for the mixing of product having different frequency distributions is held to a minimum.

Nevertheless, even though inspection lots have been produced under apparently homogenous conditions, it is always well to view the assumption of normality with a somewhat critical eye, investigating to see whether conditions exist that are likely to cause serious departure from a normal distribution. Sometimes the underlying frequency distribution is skewed, or it may be symmetrical but either peaked or flat-topped. The percentages in the extreme tails of such distributions may differ considerably from those obtaining under a normal distribution, and the protection against stated percentages of defectives given by the variables acceptance criteria may be either greater or less than the protection indicated by QC curves computed on the assumption of normality. The tighter the quality standards (for example the smaller of the AQL), the less reasonable it is to use the acceptance criteria based on the assumption of normality.

One important departure from normality exists when a producer has given 100% screening inspection by attributes to a lot prior to its variables sampling inspection by the customer. In such a case the frequency distribution in the screened lot may be truncated; one or both of the tails of the distribution may have been removed. With such truncated distributions, the variables criteria based on the assumption of normality may indicated that a lot should be rejected even though the actual nonnormal distribution in the lot may contain no defectives.

From “Statistical Quality Control”, Eugene L. Grant and Richard S. Leavenworth, 5th Edition , Page 527

http://www.alibris.com/search/searc...tistical Quality Control&S=R&browse=0&qsort=r

(Yeah, I know it’s old, but so am I. And I don’t think frequency distribution has changed too much in the intervening years…)

 

[flexibility]

Six sigma comes from the field of SPC - Statistical Process. Machine capability (dimension dispersion range)is regarded as 3 sigma. It is always considerd as normal distribution. The process must be stable, otherwise it is not controlleable and not suited for SPC.

The purpose of the 3 , 6, 9 sigma is to determine the sample size and the frequency of taking samples. and the anticipation of production problems.
It means the ratio of tolerance given to machine capability.
You do not need equations, the normal distribution probability table can give you the answers you need.

 

[Kenneth]

From

http://www.research.ge.com/cooltechnologies/pdf/2002grc119.pdf:

"Many well educated and very intelligent engineers, scientists, and financial professionals with only brief introductions to statistics expect the normal distribution to fit everything. Six Sigma training does not always help here. Although other distributions, primarily the t, F, and chi-square distributions, are presented in basic Six Sigma training, many Six Sigma professionals feel that they have to force-fit the normal distribution to every data set."

Also see

http://www.research.ge.com/cooltechnologies/pdf/2001crd119.pdf(starting

about page 9) for an interesting list of some processes reported to be non-normal..

 

[leanIE]

For the faction that contends that 'everything' is normal I would direct them to the link below and then ask them to maintain their assertion w/ a straight face.

One of the main reasons for applying 6-sigma/statistical methods to our everyday world is to help increase our probability of making the correct decision.

It seems that lately there have been several discussions concerning cycle times on this board. Every mfg. process has a cycle time. This however, is a classic non-normal situation. Please see link below.

http://www.isixsigma.com/library/content/c020121a.asp

 

[calpoly]

Data will eventually approach normality as n increases, and is free from special and common causes, but we shouldn't assume that any process follows a normal distribution until normality is proven. You could be faced with a situation where the manner in which you collected the data was not truly randomized or the process itself gives a population distribution that is nonnormal. The Central Limit theorem is a good shortcut because it will allow you to average and come up with a distribution more bell-shaped than the one being sampled. The larger the value of n in Xn the better the approximation. NEVER, EVER assume normality!! People who say otherwise have no practical experience. Heck I don't think they've even graphed actual process data, and seen the difference.

 

[BillPSU]

Any statistical analysis of a process assumes the process is in statistical control. Lets examine a hot forging process. Assuming the main controlling factor is wear on the dies. The "best" parts are achieved early in the life cycle of the dies and dimensions either increase or decrease as the die wears. If you were to take samples at the beginning of the life of the die and the end of the life of the die the parts would seem to be out of control. Assignable causes must also be removed.
Statistical analysis needs a hands on approach. Just looking at inspection reports is unacceptable. Hands-on is required and understanding the process is a requirement.
Proper inspection equipment, calibration and use must be followed. Management must also repair equipment, tooling, and gaging when they are supposed to.

 

[jrhols]

Six sigma is an american misinterpretation of Japanese thinking. Just like the Japanese got calculus right with their version and we got it all wrong and it became useless. Likewise will be the fate of six sigam and their stupid black belt and 'opportunities' and 'yield' nonsense.
There isn't an original thought in all of their body of work. The intent was that CPK can be used to focus more attention in ways I can't begin to get in to here but they involve thinking about which side the mean and nominal fall into in relation to the specification limits and how repeatable the metrics are, especially since you have the same methods in industry applied to almost every specification, from stacked tolerances to you name it - I just said a lot if you think about it - which is what the Japanese intended. They actually sit around at work and talk to each other about their ideas. Imagine that!

 

[Biffi]

I'm working now a days as black belt, and in my opinion to calculate the sigma value of the process, your process must follow a normal distribution and more must be under control. This lead to a good capability calculation. So, depending your data type you can calculate the DPMO and as a result you match the sigam value. There some books showing how to do that.