# Six Sigma Calculator

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Viewing 18 posts - 1 through 18 (of 18 total)
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• #35115

Pedro Arroyo
Participant

I have been studying these six sigma concepts and need clarification in one specific point.
Understand that when a process is normal it has a bell shape. 2 thirds of the middle center covers 95.44 % of the area. This represents 2 sigma and would give us 45 600 defects per million. (this is calculated using Z table).
but trying to confirm this using the Six Sigma Calculator that this page is showing give us info that does not match to my understanding:
for 1000000 opportunities and 45600 defects tha calculator give us:
DPMO 45600 which is correct , 4.56 defects in % which is also correct, a yield in % of 95.44, correct as well… but. it give us a sigma of 3.19…. instead of 2 (which to my understanding 2 is the correct one)

If somebody coulf clarify that to me I really would appreciate it.

Pedro Arroyo

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#97764

Malcolm T. Upton
Participant

The really short answer is because there is a 1.5 sigma shift built into the table that the calculator is using. Motorola put it there when they started their six sigma effort (the first six sigma effort) and it has been there ever since.
Some additional clarification. Motorola put it there because they know that processes shift over time and a shift of up to 1.5 sigma is not easily detectable by process control charts. In order to take into account the long-term variability of processes, they put the 1.5 sigma shift in.
For details, I suggest “Understanding the Six-Sigma Philosophy,” chapter 14 in Davis R. Bothe’s Measuring Process Capability, McGraw-Hill, 1997. I’m sure there are other sources, but a copy of that chapter is what I give Black Belts in training who ask the same question and want more detail than I’ve provided here.

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#97841

Pedro A
Participant

1.5 sigma is a lot.

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#97856

Mikel
Member

Malcolm,
With all due respect, if you believe that a 1.5 sigma shift is hard to detect by control charts. I would suggest simulating a 1.5 sigma shift and see what the charts tell you.
You will see the shift immediately.

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#97968

Malcolm T. Upton
Participant

Whether I believe it is easy to detect or hard to detect is immaterial. As I understand it, based on sources I believe are credible, and not having been in the room when the decision was made, that was the reasoning that some folks at Motorola used when they built the 1.5 sigma shift into their Sigma Quality Level tables.
Whether they should have or not is a different discussion.

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#97973

Mikel
Member

The story you are passing along is a fable. the 1.5 shift was strictly an observation, it had nothing to do with SPC.

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#98098

Malcolm T. Upton
Participant

most small shifts in process average will go undetected by the control chart. For an n of 4, there is only a 50 percent chance a 1.5[sigma] shift in [mean] is detected Based on studies analyzing the effects of these changes on process variation (Bender, 1962, 1968; Evans, 1970, 1974, 1975a, 1975b; Gilson), the six-sigma principle acknowledges the likelihood of undetected shifts in the process average of up to [+/-] 1.5[sigma].

Bothe, 1997, p. 832

I suggest you take it up with Bothe, Bender, Evans, and Gilson. I’d suggest you bring more than opinion and strident statements.

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#98104

Ken Feldman
Participant

most small shifts in process average will go undetected by the control chart. For an n of 4, there is only a 50 percent chance a 1.5[sigma] shift in [mean] is detectedI think you ….too early. Is there only a 50% chance of ever detecting?  on the next data point?  after 10 data points?  what is the rest of the quote?

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#98105

Malcolm T. Upton
Participant

“Recall from the graph in Figure 2.13 (p. 16) that most small shifts in the process average will go undetected by the control chart. For an n of 4, there is only a 50 percent chance a 1.5[sigma] shift in [mu] is detected by the next subgroup after this change. By the time this next subgroup is collected, [mu] may have returned to its original position. Thus, this process change will never be noticed on the chart, which means no corrective action is implemented.”
I’d really rather not type in more of the quote, but will if someone thinks its absolutely necessary. Note, however, that I’ll argue that if you want that much more detail, you should go to the source itself.

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#98115

Gabriel
Participant

Malcom,
Not that I want to start a discussion on the 1.5 sigma shif again. But it seems to me that saying that the process can have a 1.5 sigma shift during a short time is not the same that saying that the process is 1.5 sigma worse than wht it seems to be. The rest of the time it will be performing as it seems to be. A 150 sigma shift that happens after the last point but returns to its original value before the next point will also pass undetected in the control chart, and we don’t say that we should take into account undetected 150 sigma shifts.

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#98117

Mikel
Member

Malcolm,
You are showing everyone how little experience you have with actual process behavior. Most shifts occur due to a change that does not just pop in and out as is suggested by your quote.
I don’t need to take up anything with someone trying to make a name in the Six Sigma shift nonsense. I work with processes everyday, I see how they behave when understood and rational controls are put in place and the 1.5 shift does not exist.
Empirical evidence trumps theory every day of the week. Go get some real data.

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#98119

Ken Feldman
Participant

Thanks for posting more of the quote after the original ……  As I suspected the quote says that there is a 50% chance of spotting a shift of 1.5 on the next subgroup.  Stan’s post indicated that a 1.5 shift will be picked up quickly by a control chart, not necessarily the next point.  As suggested, try the empirical approach.  Generate some random data and do a control chart.  Now generate additional data with a shift in the mean of 1.5 sigma and plot it on the original control chart.  See how quickly an out of control situation is generated.  It is pretty quick.

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#98190

Malcolm T. Upton
Participant

Folks, I’m not trying to defend the 1.5 sigma shift built into the Sigma Quality Level tables and calculations. Personally, I tend to agree with those of you beating on me. I think it causes more trouble than it is worth.
Pedro asked the sigma quality level calculator didn’t give him the same results as those he got when he did the calculation by hand. I tried to provide an explanation from a credible source. Whether we agree with it or not, as I understand it, this is the rationale behind the 1.5 sigma shift.
I agree that it isnt practically defensible. I agree it is an academic construct with little tie to real life. Thats one reason I dont use it in my projects or suggest its use with those I coach unless its required by their management. Uncle! As much as we may dislike it, the 1.5 sigma shift is established. No matter how much yall target me, youre just wasting ammo. I cant change it.

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#98198

Statman
Member

Malcolm,

You can try to run from this but you can not hide.

You say that you have provided an explanation from a credible source.  However, any one that has read Bothes book would know that he has no intention to explain the shift.  If you notice, this quote that you posted is in the last chapter (14th) of a book on process capability measurement. It is on the 832 page of a 900 page book.  He has spent 13 chapters and 800+ pages explaining how one should go about measuring and using process capability metrics in just about every imaginable situation.  This chapter is almost like an after thought.  I would think that if this so called short coming of SPC that would leave one to suspect a error of such magnitude, he would have addressed it much sooner than page 832.

Also, this chapter does not provide an explanation nor does it provide a justification but only explains why the shift is used by some six sigma practitioners.  You will also notice that he never makes a judgment as to it being correct or incorrect.  Considering the timing of the publication of Bothes book, (1997) one can only speculate on why he included this add on chapter.

You said that a copy of that chapter is what I give Black Belts in training who ask the same question and want more detail than I’ve provided here.  Maybe you should think about giving them the other 13 chapters and ignore this one because all you are doing is perpetuating this misinformation and propaganda.  It is disingenuous of you to then carp about it not being practically defensible or just a academic construct.

Rather than continuing this perpetuation, maybe you should sit down and try to prove it yourself.  What I think that you will find is even if the source of the shift is transient and not constant (will come and go).  An inflation of the long term variation relative to the short term variation would have to see a rate of transient disturbances in an order of magnitude that would contribute over 55% to the total variation to justify a 1.5 shift and a Shewhart control chart will detect this with an ARL of 2.  Another way to look at is a capability analysis of 25 subgroups of 4 will have a probability of not detecting a special cause using rule 1 of the western electric rules will be 1.59×10^-53 for a process that has a 1.5 shift.

As much as you are trying to show your outstanding wisdom of six sigma on this site lately, I think I will stick to the tried and true advice of Stan, Darth, and Gabriel.

Statman

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#98292

Malcolm T. Upton
Participant

Statman,
I agree with you entirely about the 1.5 sigma shift.
How would you explain to someone new to the field the disconnect between the z table and “6 sigma quality level = 3.5 defects per million opportunities”?

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#98293

Statman
Member

Hi Malcolm,

I do not tell someone something that I dont believe or that I cant justify.

I tell them that a six sigma process does not have 3.4 PPM defective it has .001 PPM.  But I also tell them that a six sigma process will be held in statistical control for the long term.  We all know, however, that a process held in statistical control for the long term is very rare and therefore, we will most likely see more defects than 0.001 PPM.

Knowing that a process will drift and shift over time and the amount of drift and shift will depend on the level, method and economics of control, some have attempted to create a fudge factor (a swag), to estimate the lack of statistical control using a 1.5 shift to the Z-table.  There is no generally accepted mathematical, statistical, or empirical justification for this swag.

The confusion comes from a rather bazaar convention in six sigma to report the process as if it were held in statistical control for the long term, or in other words, the short term performance is equal to the long term performance. After all, if the process is going to produce 3.4 PPM it is a 4.5 sigma process not a 6 sigma process.  When we add to this convention the 1.5 sigma swag, we get this disconnect between the z table and “6 sigma quality level = 3.4 defects per million opportunities.

My hope is that this disconnect will eventually die out and the George Group and other growing contributors to six sigma can help by refusing to continue teaching this mendacity.  After all, Six Sigma draws its strengths from being based in data and sound theory; we should practice what we preach.

Cheers,

Statman

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#100731

Reinaldo Ramirez
Participant

Hi, Statman:
My conclusion is:
Why not to stop teaching this mendacity?
Why most company teaching 6S assume this 3.4 PPM as a dogma? A cost to become a 6S BB cost more than 10.000 dollars. Are we paying to improve our way to communicate mendacities?
After 3.88 sigma there aren´t more data. In the CRC Standard Mathematical Table, 14th Edition; edited by Samuel M Selby, Ph. D; The Chemical Rubber Co.1965, i read: 3.88 sigma,the value of F(x) is 0.9999 (1.000 – 0.9999 = 0.0001). In 3.89, F(x) is 1.000
Thanks
Reinaldo Ramirez

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#100755

Mikel
Member

Try Excel for values greater than 3.88.

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