Negative Sigma?

[Removed at the request of the author.]

There is no such thing as a negative standard deviation.

John J. Flaig, Ph.D.

Jerome - my guess is you are probably not accounting for the "1.5 shift" assumption.  Your next question might be "what's the shift"...there are plenty of posts on that fun topic...doing a search on "1.5 shift" in Google also helps.

The other possibility for a negative sigma is that your process is radically off center.

John F - thanks for sharing that wonderful insight into statistics.  I'm sure your response helped Jerome with his problem. 

Joe

I am not sure what the sigma formula is , but if you are looking at the Ppk ratio, (usually referred to as the Cpk), a negative value means the mean falls outside the specification window. To find to number of standard deviation of the process mean from the closest specification, multiply the Ppk times three. If the Ppk =1 of the process mean is three standard deviation from the closest spec limit. If the Ppk is -0.5, then the mean of the process is 1.5 standard deviation outside the closest tolerance.

The problem in this discussion is that sigma has multiple meanings.  As was noted, you can't have a negative sigma when sigma refers to the standard deviation of a process.  For the six sigma calculator the sigma value that is produced is (assuming a normal process) just the Z score.  Thus a Z score (Sigma Value) of 4.5 corresponds to .9999966 or 99.99966%.  Consequently, your "negative sigma" value is a Z score indicating that your process has something less than one half of its output in spec. 

  In this context, a Sigma Value (Z score) of 0 would correspond to .5 which would translate into 50% of your product in spec and a Sigma Value of say -.2 would indicate that only 42.07% of your product met spec.

While many things are interesting to play with the answer to your question is that a process that is that broken does not warrant a sigma calculation.

Keep in mind that when you talk about a process, there are two different terms; Sigma and Sigma Level. Sigma is the standard deviation. Sigma Level is the number of standard deviations from the mean to your specification. With the information that is entered into the Sigma Calculator, the only thing that can be calculated is the Sigma Level. A negative Sigma occurs when your mean moves outside of your specification.

Another thing to remember is that you are comparing the voice of the customer to the voice of the process. What you now need to do is compare the process to itself by using control charts to see if you are in or out of control.

Good Luck 

I pose this question....What is the relationship between zero and infinity?  Do these points ever meet?

Show me how to get a negative St Dev, I don't think you can.

Zero defects per million = a Sigma Value of 6.7 Short Term and 5.2 Long Term (1.5 Sigma Shift/Drift)

You're thinking about this wrong.  Six Sigma is just measured as six standard deviations away from the mean (above or below).  When your process is operating at Six Sigma, your upper and lower spec limits should both be within six standard deviations from the mean. 

For example, if your mean is 18 and your upper spec limit is 20 and your lower spec limit is 16 and your standard deviation is .333333, then 6 standard deviations lower than the mean is 16 and 6 standard deviations higher than the mean is 20.

Where negative sigma might come into play is if the mean of 18 in the previous paragraph is the industry standard and you measure your data against this.  If the mean of your data is say -- 15 -- then it's more than 6 standard deviations away from the mean.

You really can't have such a thing as negative sigma but it's just that we identify what is "Six Sigma" as being the span from 16 to 18 and 18 to 20.  If the mean of data is 6 standard deviations away from the target of 18, then we say it's Zero Sigma.  If more than six standard deviations away, then it could be negative sigma (but it's only called that because we're only measuring against a maximum of six standard deviations).

More on point, if you're 7 standard deviations away from the mean, then we would say that you're at -1 sigma (only because we're listing 6 standard deviations away from the mean as 0 sigma)...  You could theoretically be 20 standard deviations away from the mean and be at a level of -14 sigma.  This still wouldn't mean that your defects are greater than your total number of opportunities for defects and you couldn't be truly at negative sigma, it just means that you're 14 more than six sigma away from the mean.

Hope this helps.

KMB,

That was an excellent response. Thank you for sharing. I had a co-worker asking about the same topic so I'll be sure to share your forum posting with him.

Tammi

KMB,

That is truely an original interpretation. I do not know of anyone that would agree with you. It is the distance between the mean and the closest spec limit. If it goes over 6 it counts up just like a Z table does. When the mean is going the other direction and hits the spec limit hits the value goes to zero and stops. There is no negative Sigma - it doesn't mean anything logical.

As far as your comment  "Six Sigma is just measured as six standard deviations away from the mean (above or below)." - it doesn't work. Not every process operates centered. Start plating precious metals and see how long you stay employed if you plate at nominal.

The bottom line is when you hit 100,000 ppm and above you are so screwed up you are wasting time calculating Sigma. Go fix something, Anything.

One can have literally an infinite number of standard deviations away from the mean.  In the original example, if the mean is 18 and the standard deviation is .333333333, then you could be as much as 54 standard deviations away from the mean with a result of zero.  Of course, it would mean failure in all but one trillion-trillion opportunities (or more) but you could end up 54 sigma away from the mean.  Since we're only concerned with 6 sigma, anything that falls within those 6 standard deviations is a pass and anything that falls outside is a fail and as the number of failures grows larger, the sigma level gets lower and the mean of your data (not the 18 that you're measuring against) becomes lower and lower.  You could reach a point where the mean of your data is more than six sigma away from the 18 that's the target.  Specifically, you're mean could be 6.1 standard deviations away from the measurement point.  When that occurs, we call it negative sigma.

I understand that there is no such thing as "negative sigma" where the number of failures would be greater than the number of opportunities for failure and I also understand that sigma is an absolute value and it doesn't matter whether you're measuring to the right or the left.  But, if your only interested with 6 standard deviations around a mean, then you would call anything that comes up short of that "negative sigma".

KMB,

I am not sure who filled you full of this.

One of the big selling points to a six sigma program is it standarizes and clarifies communication. You are about as inconsistent as a person can get with the balance of the SS world. I really wish there was a nice way to put this because in most cases answers are conditional but you are wrong.

Wow, what's going on with you, Mike. I was shocked to read what you wrote to Kmb. I usually appreciate what you have to say, but not in this case. I believe your comments were very rude.

Tracey,

There is a point at which it isn't being rude whan someone is so far out of whack with the rest of the world that they are misleading people and continue to masquerade it as a fact. There have been a couple phone calls and a couple emails where pwople are trying figure out what this person is trying to perpetrate and these are people who understand SS. This interpretation in pure nonsense.

I'm not sure what you mean. I think you need to take whatever this is offline and stop using this forum for personal attacks, if that's the case. That's what it seems like.

I think I'll get back to work now and look for a new thread in the morning.

If we go back to Mr. Deveix's original question the issue is not about the standard deviation of a process it is about the sigma value that he is getting when he puts a given defect rate in his sigma calculator.  If you have the table generated by Motorola et al with the headings %Yield, Sigma Value, and DPMO and if you also have a statistics book that has the table for the cumulative normal you can set these side by side and see that the Sigma Value (my Motorola table is the one that does NOT have the 1.5 correction added to the Sigma Value) is the Z statistic and the %Yield divided by 100 is the corresponding area under the normal curve.  If you go back to your sigma calculator in whatever program you are using (mine is on Statistica and it does add 1.5 to the Sigma Value) and plug in values such as 999,999.999 for your DPMO you will get a Sigma Value of -4.49 or -5.99 depending on how your particular calculator uses 1.5 when computing Sigma Values. These Sigma Values just mean that the vast majority of your product is completely outside the customer spec limits. It says nothing about the standard deviation of your process.  Thus, as Mr. Deveix has discovered, the calculator for Sigma Values will indeed return a negative Sigma Value which is what it should do when the defect rate get high enough.

  The real problem here is one of labeling.  Someone made a very poor choice when it came to renaming the Z score.  Whoever they were they at least chose to call the Z score the Sigma Value and not Sigma. Unfortunately, the same cannot be said of any number of articles and computer programs.  I know that Statistica calls their program the Sigma Calculator and the final result Sigma.  The problems that can result from confusing Sigma Value (which can have negative values) with process standard deviation (which cannot have negative values) are too numerous to mention.

Good One !

Hope some one includes this as a foot note in the calculator itself for the benifit of all who discover 'Negative Sigma' using the calculator.

I really appreciate the feedback from everyone.  I was a bit surprised with the intensity of discussion in some cases, but feel it gave me some superb information to take back and digest.

This is truly a frustrating thread. The intent of SS I hope is to provide a tool kit (and they are not new tools) and logical method to solve strategic problems that effect the bottom line of a company. What I see is too many of people trying to become certified to enhance their career without having a clue of the basic fundamentals of statistics. Pp and Ppk, (usually referred to as Cp and Cpk) have been the accepted way to quickly describe a process. The example stated only tells what the process is producing, while if the results where stated in more tradition terms, one would understand the potential of the process and the current state. Far to often people are walking around mumbling the latest acronyms and buzz words like it is some type of Water Buffalo Lodge secret handshake. There are too many people jumping on the bandwagon for financial benefits that are going to kill the culture that was re-established by SS. This is a fad that will be replaced just the same as any other process improvement plan. The greater number of incompetent people that obtain the GB and BB status, the faster this culture will demise and be replaced. It won’t be long before people are getting their BB at JC Penny, and placing it on their resume. People should be required to pass an exam to become certified and the exam should only pass the upper quartile of the population taking it. The BB status has already been watered down to a CQT status. Soon it may not achieve that level of respect.

I enjoy responding to questions where the person has made a genuine effort to understand the material at hand, but some of the questions that are posted are in the frame of mind of tell the answer, I don't want to try understand why.