I'm trying to figure out if a chart or cross-reference exists that compares PPM rates to sigma levels. I.E. How is it calculated that 6 sigma is 3.4 parts per million defects? What is 5 sigma? What is 4 sigma? How many sigma is 230 ppms? If anyone has any ideas, please let me know.

I'm trying to figure out if a chart or cross-reference exists that compares PPM rates to sigma levels. I.E. How is it calculated that 6 sigma is 3.4 parts per million defects? What is 5 sigma? What is 4 sigma? How many sigma is 230 ppms? If anyone has any ideas, please let me know.You can find the answer in the attachment, DPMO to Sigma conversion (http://elsmar.com/Forums/attachment.php?attachmentid=1551), in the cove.

Remember also that the whole "Six Sigma" system is set up with the mysticalhttp://elsmar.com/Forums/images/smilies/magic.gif "1.5 sigma shift" built in. That is why you can't simply look up the numbers in standard Z tables.

For 6 sigma, you would look up the Z table for 6-1.5 = 4.5 and find 1-0.9999966 = 3.4 x 10^(-6) = 3.4 PPM are in the upper tail. Then look up Z = -6-1.5 = -7.5 and find that basicallly none are in the lower tail. (OK, OK, I'm sure some of you are dying to know. The actual number is 3.2 x 10^-(14) = 32 PPQ (thats parts per quadrillion, at least in the US).)

Tim F

I'm thoroughly impressed. I've looked for this conversion on and off over the years. I even asked a professor from a college in Dayton and he could only quote the emperical rule. Thank you for your help. I only hope that I can help someone else someday.

Totumfrog

Here is a quick comparison of what Tim is talking about -

Comparison of Process Fallout

Based on Cpk values with 1.5 sigma allowance for normal shift (modern)
Vs
Cpk values assuming no process shift (traditional)

Both methods assume a stable process with normal distribution.


Sigma Cpk PPM Fallout
Modern Traditional
6 2.0 3.4 2 ppbillion
5 1.67 230 2 ppm
4 1.33 6,210 96
3 1.0 66,800 2,700
2 .66 308,000 71,860
1 .33 690,000 >134,000

Dave

Figures I would mess up the formatting :bonk:

I am attaching a doc file that should be easier to read.

Dave

Here is a link from isixsigma which can be useful to you:
Six sigma Calculator (http://www.isixsigma.com/sixsigma/six_sigma_calculator.asp?m=advanced)
Regards,
Govind.
Note: Donot forget to read the formula rationale and assumptions.
Process Sigma Calculator Assumptions (http://www.isixsigma.com/library/content/c020507a.asp)

http://elsmar.com/Forums/showthread.php?p=114131#post114131

Oh wise 6 Sigma gurus...why a 1.5 sigma shift? What does that shift apply to all processes and products? In some applications, a 1.5 sigma shift is critical. I just do not understand why when we say 6 sigma it means 6 sigma and not 4.5 sigma!

Oh wise 6 Sigma gurus...why a 1.5 sigma shift? What does that shift apply to all processes and products? In some applications, a 1.5 sigma shift is critical. I just do not understand why when we say 6 sigma it means 6 sigma and not 4.5 sigma!
The 1.5 sigma shift is a theoretical abomination which assumes that operators measuring things in production will not react until hit over the head, or that reactions only occur after changes in the process are actually charted, neither of which is true. IMO, the shift is the prime problem with SS, and a sure indication that SS advocates don't understand what production workers do for a living.

The 1.5 sigma shift is a theoretical abomination which assumes that operators measuring things in production will not react until hit over the head, or that reactions only occur after changes in the process are actually charted, neither of which is true. IMO, the shift is the prime problem with SS, and a sure indication that SS advocates don't understand what production workers do for a living.
I agree 100%. The notion of DPMO is meaningless if you build in an assumption of 1.5 sigma shift, when in reality, this might not be the case. I actually read a nice commentary on SS regarding the 1.5S shift. In summary, it stated that with measurement and process improvements, the 1.5S should be reduced to 1.0S with the intention of eliminating it over time.

Maybe they just choose a 1.5 shift because "Six Sigma" sounds much better than "Five Sigma" or "Four point Five Sigma" ;)

Barbara

I usually don't respond to these 6 Sigma discussions but here goes. Having been involved with 6 Sigma in one form or another for about 10 years the following is my understanding of the "1.5 Sigma Shift" concept.

The "1.5 Sigma Shift" does not mean that a stable process will shift 1.5 sigma without being detected but that it could shift 1.5 sigma and since the process is so robust (e.g. 6 Sigma) this shift would be of no consequence to the customer.

Regards

I usually don't respond to these 6 Sigma discussions but here goes. Having been involved with 6 Sigma in one form or another for about 10 years the following is my understanding of the "1.5 Sigma Shift" concept.

The "1.5 Sigma Shift" does not mean that a stable process will shift 1.5 sigma without being detected but that it could shift 1.5 sigma and since the process is so robust (e.g. 6 Sigma) this shift would be of no consequence to the customer.

If there's no concern that the process will shift, then what's the point? My point was that if the process is operating normally, and comfortably within the spec limits but nowhere near six sigma, and things start to change, the change will almost always be detected before it gets to the point where it would be of consequence to the customer. It's called process control. And by the time it is detected (i.e., if a full 1.5 sigma shift happens before anyone notices anything went wrong) there are likely to be consequences anyway. The 1.5 sigma shift concept is theoretical BS because it assumes that operators are robotic dolts who wait for anomalies to actually be charted before responding.

The 1.5 sigma shift concept is theoretical BS because it assumes that operators are robotic dolts who wait for anomalies to actually be charted before responding.


The 1.5 sigma shift or Six Sigma for that matter assumes no such thing about operators. The operators are the process experts and are key players in the implementation of the program and any subsequent process improvement efforts


The following is an excerpt from Six Sigma - Understanding the Concept, Implications and Challenges, by Mario Perez-Wilson, who played a role in the promotion and implementation of Six Sigma at Motorola and is the best explanation of the origins and reason for the use of the 1.5 Sigma Shift I’ve seen:

“Six Sigma is not 3.4 ppm. The whole misunderstanding about 3.4 ppm resulted from Motorola’s document “Our Six Sigma Challenge”. In it Motorola asserted if a process was made to be Six Sigma by having the design specifications be twice the process-width, the process would be extremely robust. Such a process would be robust, even if it was surprised by a significant or detrimental shift in average, as high as +1.5 sigma, the customers would not perceive a degradation in quality. At worst case, a shift of 1.5 sigma, would make a zero-defects product be 3.45 ppm and the customer would only perceive an increase from zero to 3 products defective, assuming a production run of 1,000,000. This was supposed to be the warranty Six Sigma processes brought to the customer, not actual ppm levels for Six Sigma.”

Regards

“Six Sigma is not 3.4 ppm. The whole misunderstanding about 3.4 ppm resulted from Motorola’s document “Our Six Sigma Challenge”. In it Motorola asserted if a process was made to be Six Sigma by having the design specifications be twice the process-width, the process would be extremely robust. Such a process would be robust, even if it was surprised by a significant or detrimental shift in average, as high as +1.5 sigma, the customers would not perceive a degradation in quality. At worst case, a shift of 1.5 sigma, would make a zero-defects product be 3.45 ppm and the customer would only perceive an increase from zero to 3 products defective, assuming a production run of 1,000,000. This was supposed to be the warranty Six Sigma processes brought to the customer, not actual ppm levels for Six Sigma.”

I'm not confused about 3.4 ppm or anything else, so this whole passage is irrelevant. In fact, it only serves to support my contention, because it confirms the purpose of the 1.5 sigma shift mythology in line with my earlier post. It supposes that a significant shift would come as a "surprise." And answer me this: If the process is "robust" after such a surprise, why is it necessary to extend the limits to six sigma? Why not just use the "robust" limits and use process control to insure that it remains "robust"?

the 1.5 sigma shift is an abomination, but since it really has NOTHING to do with six sigma (other than the six sigma = 3.4ppm tag line - as in Nike's "just do it" and Intel's 'Intel Inside') all good - and better - six sigma practitioners simply ignore it. It's not taught and it's not used. We may only use it to designate a process as beign 3 sigma or 5 sigma, but even that is falling away to describe a process by it's real defect performance level.

It's really unfortunate that the bizarre 1.5 sigam shift ever got tacked onto Motorola's Six Sigma approach - it's done nothing but cause diversionary, divisive and ultimately useless discussions that have simply detracted from the real core of Six Sigma...

the real core of Six Sigma...
Which, without the shift, is just good ol' fashioned process control taken to extremes and dressed up in an ill-fitting new suit.

Which, without the shift, is just good ol' fashioned process control taken to extremes and dressed up in an ill-fitting new suit.
I will throw in that is can also be called TQM....

I will go to my grave saying that six sigma is just TQM repackaged.

and your point is? if it works who cares what you call it? I am seeing real statistical engineering quality improvements and control being enacted in numerous organizations under the name of six sigma that I never saw under process control or tqm...i'm just thrilled more people and organizations are actually using and embracing the techniques and systematically ingraining them into their organizations...I just dont get the visceral disdain around the term (seemingly bitter?)


I understand the disdain for the hacks (like Mikel Harry) who used good old american capitilism or snake oil salesmanship and made tons of money off the name gimmick - but these guys are always out there.

and your point is? if it works who cares what you call it? I am seeing real statistical engineering quality improvements and control being enacted in numerous organizations under the name of six sigma that I never saw under process control or tqm...i'm just thrilled more people and organizations are actually using and embracing the techniques and systematically ingraining them into their organizations...I just dont get the visceral disdain around the term (seemingly bitter?)


I understand the disdain for the hacks (like Mikel Harry) who used good old american capitilism or snake oil salesmanship and made tons of money off the name gimmick - but these guys are always out there.
Bev, let me give you my $0.02 as to why six sigma is a sham. Call it bitter, because I am. I spent nearly 20 years as a professional statistician, CQE and quality improvement professional just to be told I am not qualified to be a six sigma black belt. I need to be blessed by some money making organization to learn tools I already have? I guess I just do not get it.

and your point is? if it works who cares what you call it? I am seeing real statistical engineering quality improvements and control being enacted in numerous organizations under the name of six sigma that I never saw under process control or tqm...i'm just thrilled more people and organizations are actually using and embracing the techniques and systematically ingraining them into their organizations...I just dont get the visceral disdain around the term (seemingly bitter?)


I understand the disdain for the hacks (like Mikel Harry) who used good old american capitilism or snake oil salesmanship and made tons of money off the name gimmick - but these guys are always out there.


Mikel Harry is a very divisive character with 6 Sigma practitioners. In my opinion his most significant contribution was the marketing of 6 Sigma. It gave the techniques credibility in the boardrooms due to the emphasis on savings and the bottom line.

I spent nearly 20 years as a professional statistician, CQE and quality improvement professional just to be told I am not qualified to be a six sigma black belt. I need to be blessed by some money making organization to learn tools I already have? I guess I just do not get it.

Now that's a great answer! And I've been there. Back in the mid nineties I was 'doing' six sigma for Honda (although I didn't call it that because Honda likes to do their own thing). I started applying for master balck belt positions since I had a very strong training background and improvement project leadership/success rate. I was told by everyone that since I wasn't 'certified' by GE or Allied or Motorola then I wasn't qualified to be a MBB.. so I bit the bullet, held my nose and went to one of those 3 companies to become certified as a BB...worst 18 months of my life. their program was Mikel Harry joke right down to the powerpoint clip art handouts and the 1.5 sigma shift. As soon as I got thruthe program I was out of there. but I had my golden pass and my career took off in the direction I wanted it to.

But there always these types of artificial barriers - form teh 'need' for a certain 4 year degree to a speicifc experience, etc. the trick is how you manipulate around this and sell your experience and success as meetign and even exceeding the 'piece of paper'...

Hi everybody,

You might say anything you want about Mikel Harry (at the end of the day it's a matter of personal opinion) only that we have to keep in mind that usually a business is run to make profit. From this perspective, what Mikel did was to convince the owners/CEOs/CFOs and so on to start using inteligent tools when running their operations in a structured manner. Is he a salesman? Yes, he is. Is he taking advantage of this system? Yes, he is. But isn't this our society is all about? Yourselfs have said that you tried to sell your knowledge and you couldn't due to various reasons including not being a certified BB (to be honest, why a certification as QE is different than a BB? Both are commercial certification as you have to pay for and other than a certification body saying that you passed their certification criteria there is no guarantee of how the individual is going to perform in real life- wait a minute isn't this what school does too?). So, beyond the phylosophical discussions, as long as a system works it's up to the practitioneer to use those tools that are most suitable to the business they are part of. Do I sound too much like a cold bloded finance-ist? Yes, but take a look around you and see how the world functions lately, look at how many jobs are being lost to low cost countries. Is this a good time to polemize about systems and implementation methods and who makes money out of that? I say let's go back to discussing professional subjects and see how we can help each other progress in what we do every day.

Regards

Now that's a great answer! And I've been there. Back in the mid nineties I was 'doing' six sigma for Honda (although I didn't call it that because Honda likes to do their own thing). I started applying for master balck belt positions since I had a very strong training background and improvement project leadership/success rate. I was told by everyone that since I wasn't 'certified' by GE or Allied or Motorola then I wasn't qualified to be a MBB.. so I bit the bullet, held my nose and went to one of those 3 companies to become certified as a BB...worst 18 months of my life. their program was Mikel Harry joke right down to the powerpoint clip art handouts and the 1.5 sigma shift. As soon as I got thruthe program I was out of there. but I had my golden pass and my career took off in the direction I wanted it to.

But there always these types of artificial barriers - form teh 'need' for a certain 4 year degree to a speicifc experience, etc. the trick is how you manipulate around this and sell your experience and success as meetign and even exceeding the 'piece of paper'...


:applause: Good for you Bev, I agree.

I found a formula that I entered in excel.
You can see the formula in column B.
Hope this could help you.

Narfeldt,

That's a rather good approximation for converting between sigma levels and PPM. It seems to be good to within about 2% over the range of 2 sigma to 6 sigma.

Still, why not just use the "true" conversion?

=(1-NORMSDIST(A2-1.5))*1000000

Granted, calculators often don't have the inverse normal function built in, so then your equation

=EXP(-((A2-0.8406)^2-29.37)/2.221)

would be a handy alternative. But since Excel (and many other similar programs) can do the true function, we might as well use it there. The true version also lets you remove the 1.5 sigma shift if you so desire.


Tim F