Silly Question About Six Sigma

It's the number of standard deviations between the mean and the limits:

http://www.isixsigma.com/library/content/c010101a.asp

Thanks Tom,

But, I am still not clear after reading that article.It talks about process capability.It talks about the process shift of 1.5 in long term.My confusion is just there.If sigma is std.deviation , how can 6 sigma be better than 4.5 sigma or 3 or 2 sigma?

I have always tried to explain six sigma concept to laymen with my silly explaination too. :-)

Let say you have a 12-meter width fixed goal post.

Two scenarios here,

1) 6 sigma process: You can put 6 pieces of 1-meter size rubbish bin from the middle of goalpost to both sides to fully occupy the goal post.

2) 3 sigma process:  You can put 3 pieces of 2-meter size rubbish bin from the middle of goalpost to both sides to fully occupy the goal post. 

So, 6 sigma process means its process variation (= a single 1-meter rubbish bin) is lesser (only a half!) than 3 sigma process variation. (= a single 2-meter rubbish bin).

So this means that higher is number of sigma, less is the process variation ? 

Peppe

6 Sigma = aproximately 3.2 Defects per Million Opportunities (DPMO) = Cp: 2.0  Cpk: 1.5

4 Sigma = aproximately 6,210 DPMO = Cp: 1.33  Cpk: 0.83

3 Sigma =  aproximately 60,000 DPMO = Cp: 1.00  Cpk: 0.50

There is a big debate about the validity of the 1.5 Sigma shift.   Try searching for this.

Maybe not.  Possibly the specs are set really wide.  Capability only has meaning in the context of the customer specs and less so with the actual process variation.

Just to clarify....

In 6 sigma capability, Cp is equal to or GREATER THAN 2.0, and (if you buy into the crutch of the 1.5 sigma shift garbage) Cpk is equal to BETWEEN 1.5 and Cp.

Just a minor little detail that I wanted to make clear.....

I must say that I have been an instructor in statistics for years and the "mystery" of sigma is always the one that seems to stump beginning students.  Just keep studying and reading and getting examples and one day the light will come on for you.......

RubberDude,

Since you replied to my post, i'll answer.   I wasn't sticking up for the 1.5 shift.   I was pointing out the debate.

Also, be careful about generalizing Cp/Cpk values (i.e. > 2).   The fine points can show staggering differences).   We can get into DPBO/PPB when 6S levels are acheived.

Here are the values for > 6 Sigma (aproximations in effect) per my handy-dandy old school slide rule with the "dreaded shift":  (to excise the shift, , just account for 1.5 Sigma)

6.1 Sig = 2.03 Cp = 1.53 Cpk = 2.1 DPMO

6.5 Sig = 2.17 Cp = 1.67 Cpk = 0.3 DPMO

7.0 Sig = 2.33 Cp = 1.83 Cpk = 0.0 DPMO

-El Guapo, the Certified Master Chimichanga

Rubberdude,

 

What is the extent of your Six Sigma training and project experience?   You present as a subject matter expert and it would be good to know your experience level and background.  After all, we Six Sigma novices tend to take the words of the experts at face value.

 

Todd  

You do have a point there, oh, Wise Master......

The "minimum" Cpk value must be "linearily" (is that even a word?) in proportion to the Cp value.

By the way, my posting was not directed "at" you.  I hope you didn't take it that way.

No harm, no foul...

I did because you replied to my post and not the originator.

-El Guapo, the Certified Master Chimichanga ©

Todd,

A bit of advice from a "wise old owl" or better yet.... A "wise ol' hillbilly from Arkansas...."

NEVER take anything you see, hear, smell, or taste on the internet "at face value."  Especially in a forum or chat.  I might be a SSMBB certified trainer or a 15 year old who has nothing to do but sit here smoking weed and spouting off terminology I've learned by studying the subject.  You never know.

Take this for what it's worth.  I have over 25 years dealing with and teaching statistical methods and quality concepts, but I do not claim to be an expert in Six Sigma or any other of the techniques.  Do I know what I'm talking about when I post?  I do try and "do my homework" before I speak.  But I won't "brag" here about any of my certifications or experiences.

As for taking things at face value, never read only one posting.  Read the thread.... most if not all of it.  You will learn more by taking all the information and verifying it with reference materials or GBs, BBs, and MBBs you may know.

This certainly is a good resource for "novices" to learn, but many of them seem to think this forum is the only place to do so.  Look in the left column of links.  This site has a vast amount of resources much more reliable than this forum.  But, don't let that discourage you from using the forum.  Just back up what you read on here with other resources.

Best of luck in your SS endeavors.....

I don't think it is a "silly" questtion,it could be a wise question because it has triggered a useful debate.

Rubberdude,

 

Thanks for the forthright response regarding your qualifications and your thoughts on putting too much credence in anonymous forum postings.   I take it from your response that you have experience in quality assurance and the statistical and technical tools associated with the field.   And while you have no specific training, certification or project experience in Six Sigma, you try to give fact based and data driven advice when posting in the isixsigma.com forum.  

 

Todd

Peppe,

The higher sigma level of the process, the better the process.  The sigma level "roughly" equates to the number of standard deviations between the mean and the closest spec limit.  If your process becomes less variable, then the standard deviation gets smaller and the sigma level of the process increases. 

Heebeegeebee BB,

Your name is difficult to type :).  I believe 4.5 sigma actually is 3.4 DPMO if one looked up the distribution.  That's why the believers in the shift say you need to have a 6 sigma level (short term capability) such that in the long term you only have 3.4 DPMO--I subscribe to this line of thinking.  Sigma level is defined as the capability in the short term so I think it's important to keep in mind which DPMO, short or long term, is quoted with the sigma level. 

Even if you are referring to the 1.5 shifted sigma level, at 3 Sigma, the DPMO would be 66807 not just 60,000--a difference of nearly 10%.

Again, that's why i used the caveat, "aproximately".  Eyeballing a slide rule, you must allow for some Operator induced variation. ;-)

Geesh...

:)

LOL....yes

I can see how this terminology could be confusing.  The "sigma level" is not measuring the size of sigma (the varitions in the proces) but rather it is measuring a RATIO of the specs to the actual sigma value for your process.

A "six sigma" process means that the goal is 6 times larger than the observed vatiation, NOT that the variation is six times larger than the goal.

Let me build on the goal post example someone else suggested.  If I have a goal 12 m wide and can usually put my shots in a 6 m wide range, then the goal is twice as wide as my variation, and I have a "2 sigma"  process.  If a soccer pro could usually put the ball in a 2 m range, the goals would be 6 times wider than the variation, so we have a "6 sigma" process.

Tim F

P.S.  In terms of sigma specfically, the "spec limits" for the goal are +/- 6m, and sigma is 3m for the first example.  So the allowed variation from the center is 6m = 2 x 3m = 2 x sigma = "2 sigma process". 

P.P.S  The "1.5 sigma shift" would be akin to coming back each day to kick some ball, but having varying winds blow.   On a bad day, the wind could blow the balls up to 1.5sigma = 1.5 x 3m = 4.5m off center.  Even though the shots still are clustered within a 6m range, that range is well off-center and a lot more shots will miss the goal. If you believe that such a 1.5 sigma shift is typical, then calculations of the defects should include this shift of the center.

Good explanation Dog Sxxt (I don't know if I am typing your name correctly. You guys have invented names as confusing as Six Sigma program). Thanks.

Keeping in mind Dog Sxxt's example, try to understand that the standard deviation reduces in a process where SSQL (Six Sigma Quality Level) increases. This would mean that the standard deviation of a Six Sigma process is reduced to half versus that when it was at Three Sigma level. The variation shrinks when quality level increases and now more data will fit under the bell shaped curve rather than going out of spec.

The difference between Six Sigma as quality metric and six sigma as standard deviation is widely discussed. I hope you could find some references.

Sillybutsound:

The sigma level is a term to name the distance from "what your process delivers" to "what your process is requiered to deliver", measured in standard deviations.

I think that the car-garage analogy fits perfectly well here:

Say taht you have a 2m wide car and you want to put it in a garage which is 4m wide. In theory you have 1m of clearance at each side, but say that when you park it you are 0.5m off center so the distance between the center of the car and the closest side of the garage is 1.5m. Put this distance in terms of the "car width" and you have a "0.75 width" garage (2m/1.5m). As the garage width (requirement) is wider and the car (process variation) is narrower and you park closer to middle of the garage (improved process centering), this "with level"  (sigma level) increases and the chances to hit the wall (make a defect) gets reduced.

I don't know if 'Sillybutsound' is more confused or not after the threads, but I'll try to simplify this.

There are 2 ways "Sigma" is interpreted. The first is what you mentioned... standard deviation, which tells you the spread (or variation) of your population data around your mean. The second is the Sigma Level, or the capability of your process in meeting the customer requirements. By this I mean is your current process within the customer spec limits? There can be no Sigma levels if you don't have spec limits. SS practioners use Sigma interchangebly between the two, but the novice SS person will but always get these two confused... not to mention bringing in the 1.5 sigma shift.

Good luck.

Clearer (hopefully)

So, for example, if I have a process without variation, sigma increase to infinite ?

Thanks, Peppe

Thanks all for your inputs.

But, Let me see if I really got the message.I understand that the sigma that we refer to "stad. deviation" is different from the "sigma" used to denote 6sigma.But, is there a formula for the sigma used in six sigma?..How different is it in formula than std. deviation?.

another silly one...

You need to go to the left of this section and look up "Statistics & Analysis" and then look up "Process Capability", The best way to learn is to do your own research... not by others telling you.

"Catch a fish for someone and you feed him for a day. Teach him how to fish and you feed him for life"

You said  "The best way to learn is to do your own research... not by others telling you"

So, you have always learned without any teacher !   Please, be patient with someone that haven't your level of  intelligence.

Thanks, Peppe  

There is a difference between teaching and spoon-feeding. I myself went to left of this section and found the answers to the question posed rather easily. Take the initiative to do your research and you will get more satisfaction out of understanding it than having someone tell you the answers.

... telling us the explanations, not answers.  This is the difference.

Regards, Peppe

.... which is clearly located in the left of your screen.

Could you, kindly, copy here, from left, side the clear explanations to answers raised in this thread ?

This is why I suggest that those using this forum make sure they understand not to take any posting for more than face value and back up the information with research and other resources.

The "sigma" used in Six Sigma methodology and the "sigma" used in statistics are one in the same.  There is NO DIFFERENCE in how you calculate the value of sigma.  The only difference is the differences in population, sample, estimated, etc. sigma.

If you have not already done so, I would suggest taking a good, strong course in statistics, then statistical analysis, then some six sigma training.  You obviously have some background, but seem to need more fact based formal training/education than you can find on the internet.

Good luck in your endeavors.

If you have a process without variation, sigma is 0. Sigma level would be infinite, assuming you have set customer specs.

Sigma is the standard deviation. Sigma level is the number of standard deviations you can fit between your process mean and the nearest spec limit if you allow for a shift of 1.5 standard deviations toward that spec.

Peppe,

Yes, if you process had no variation, the sigma level would be infinite.

Peppe,

Now that was a silly/stupid/lazy question!

Take some initiative and research for yourself!  Step up and sound off like you have a pair.

This is now an official "No Spoon-Feeding Zone".

-Heebee

Hmmmm... mermaids, dragons, unicorns, enough money in the bank, the answer to who killed JFK, processes with no variation.......

HeeBee,

Can you print that article and bring it to my office and read it to me?

(I needed a good laugh.... thanks....)

I really enjoy your "sarcastic" sense of humor.I wonder also  how some "silly"terms like  "SILLY question' and "silly names like "sillysillybuts..." could attract so many contributions and such "not-silly" debate??  Strange Human Nature.    Regards.

I really like your  "reply".

WOW, even old Darth wouldn't be that cold and callous.  Are you sure you aren't another Stan in HeBeGeBe clothing?

Yeah, it was really me.   I tried to steer Peppe to the answers, but it wasn't enough.   If one of my BB's did what he did, they'd have been in a meeting with the Program manager explaining their lack of initiative.

rant off.

Nobody E,

I think a screen name like "sillybuttsound" would have sparked an even more "not-silly" debate...

Sorry couldn't help myself...

-Solo The Clown

Yes, with the assumption that their spec limits are same.

To answer why 6-sigma is better than 3-sigma, plot the data and look at the response surface (curve).  Draw out lines to represent +/- 1 standard deviation, 2, 3, 4, 5, and 6 deviations.  The points within the boundries represent "good" and those outside the boundries (beyond the tails) is bad (defects).  As you move out, 1 std dev at a time, there are less and less defects outside the boundries.  If you plotted 1 million data points, and the process is at 6 sigma, then you would find only 3.4 data points (defects) outside the boundries, and 999,997 data points are within the 6 std dev spread. 

That is true. Many newbies and laymen (even management ppl) are struggling to understand sigma and sigma level concept.

The confusion is when you tell them small variation is better (there are some exceptions in real-life!) and they then wonder why 6 sigma (which is bigger than 3 multiple sigma in their mind) is better than 3 sigma process.  

Hello Sillybutsound,

Let me see if I can put some light on the subject.  First, there is no difference between sigma and how it is used in the expression 6 sigma and the sigma referred to when calcualting standard deviation. 

As you know, the term sigma is used as a measure of spread or variability in the process yeild of production or service delivery.  As you also know, in addition to spread, the performance measurement of average is also considered when calculating process performance.  A third parameter, location - that is what is the actual measurement of the mean outcome in relation to customer requirements/engineering specifications, also must be accounted for. 

Motorola understood that the location or actual measurement of the mean can naturally drift approximately 1.5 standard deviations in either direction.  Because of that drift, the production outcomes observed at each tail of the bell curve can inadvertantly fall outside of the spec limits  - provided that the spec limits are targeted at +/- 3sigma (spec limits and control limits being the same). 

Well, Motorola changed the paradigm by saying that you keep the spec limits in the same place, but you refine the quality of your process work products such that the natural bell curve becomes much thinner.   So much thinner that whereas the "unchanged" spec limits in the new paradigm are now 6 standard deviations from the process mean.  You see, the customer or engineering requirements have not changed but control over the location and spread of the process outputs is much more strict and tight, the process capability can easily account for the 1.5 sigma drift and not produce any defects.  Hence, whereas 99.73% of your process outcomes would naturally fall within your spec limits in the old 3 sigma paradigm, in the 6 sigma paradigm, 99.9997% percent will of your process outcomes will fall naturally fall within your spec limits. 

Clear as mud.   If not, give me a ring at 602 728 0185 and I will try to explain in the plain spoken word.

Helper

Two things -

I really did like the old Darth better.

Hebe is not a Stan, but we would definitely take his application and let him skip the 5 year apprentice program.

See you in Charlotte.

Stan, will u be attending the ISSSSSSSP conference next month?  If so, please send me a note offline and we can plan on meeting.  I can make a reservation for 6 at a good restaurant so I can meet all the Stans and maybe Mrs. and Baby Stan.

Heebee is heebee and Stan is Stan.   I've been on the board forever and a day and can assure you that I am not Stan.

Stan,

Thanks for letting me skip the apprenticeship.

Peppe,

Step up, yo!

-El Guapo, the Certified Master Chimichanga ©

Yes I will be at the ISSSSSSSP. I will be in a short red dress with garters (whoops, no that is RS).

Mrs. and Baby Stan will be at home due to other sibling issues.

But I can tell you that at least one other charter member and one apprentice will be there (hint on the charter member - they are a VP of a financial institution).

Hi

There are following factors are responsible....

1. standard deviation remains as it is

2.

Hi the "quetionier"

There are following factors  to understand :

1.  the value of standard deviation remains constant initially when we are calculating first time

2. only change in the denominator values ( either 3sigma or 6 sigma)

3. since the confidence intervals earlier was 99% (in 3 sigma limits) it is being increased to 99.9% (in 6sigma limits)

Hence capability improvement will be different.

It is how many sigma (standard deviations) you can accomodate in half the tolerance. If the standard deviation is so small that you can accomodate 6 standard deviations in half the tolerance then Sigma Rating is Six. On the other hand if Standard deviation is large and if half the tolerance accomodates only 3 SD then sigma rating is 3

Six Sigma, especially when looking at in terms of deviation, is the calculated based on the number of defects in a process per million.  The higher the sigma the lower the defects/million.  When we look at the variation, the curve should resemble a sharp turning point ( a bell-shaped curve).  The measurement is the can also be identified by the maximum variation from the target.  Hence the calcualtion of Sigma includes the average value and how far each value is from the calculated target.  email me if you further questions,.

Dear Mr. Mahesh

Can you explore on what is half the tolerance?

Hey Rakesh, what you talkin about dude?

Take a look at Helper's response (Thursday Sept. 23, 2004) and read it carefully... He/she did a magnificent job in responding in a clear and concise way to answer the question posed completely. 

You're only confusing people with that babble.  Enough said on this topic, this horse is dead, no use flogging it any more.........

simplify the ratio 2m:1.5m =?