Simple Explaination of Shift

Now it makes sense.           No, wait….. sorry, no, it still seems like an illogical fudge factor.  I thought I had it for a minute, but it slipped away.       Thanks though.  I was almost there.  It’s just too illusive for me.  A few more examples, and I think I’ll be on board.    It’s a darn shame that there is nobody either posting on the forum that was actually there when it was derived – or that can at least access one of the original Six Sigma thought leaders.    I’d really like to know the true genesis of the shift.

I’m also curious why General Custer went into Little Big Horn like he did.  That made no sense either.    Then there’s the German army’s march into Russia in the dead of winter – what was up with that?     And Clinton, throwing away his presidential legacy over Monica!!  What a dufus. Geeze…. Where’d that come from???    But as odd as those and other historical incidents are, they pale in comparison to best and the brightest in industry and academia accepting the concept of a 1.5 sigma process shift.    3.44 DPMO is Six Sigma?? – no, stat people, it’s not – regardless of the convoluted rationales presented.  

Here is the explanation I hear from a resource that WAS at Motorola at the time.
They wanted to move the improvement bar up. At the time, the recommended Cpk as 1.33, so they considered moving it to 1.5 – a reasonable increase, but not a dramatic one.  This equates to 4.5 sigma, but unfortunately that is not a “cool logo”.  They liked the 6 sigma looks…. 6 turn on it side…wa la… sigma.  Hence the development of the dreaded long term versus short term variation and the 1.5 shift.  Convinent so that 4.5 becomes 6.0!
Hence, it wasn’t statistical in its nature at all, rather marketing driven…desire to use 6sigma, instead of 4.5! 
Oh, same resource says she does not no of any study by Motorola where “world class quality” companies were equated to operating at Six Sigma in their process.  Another folklore story!

Reigle, you now did screwed it up. Your concepts are more confused than what I thought. You are just confusing “sampling variation” with “shift”.
COUNTER-EXAMPLE 1:
Repeat your example but with the following differences:
– Instead of taking subgroups of 5, take subgroups of 20.
– We will consider this test as a multiple parallel simulation made with subgroups ranging from 2 to 20.
– For that, we will compute the subgroups range for the size 2 as = max(A1:B1) – min(A1:B1) to = max(A50:B50) – min(A50:E50) and the grand range for size 2 as = max(A1:B50) – min(A1:B50). The same will be done for all the subgroups sizes until you get to the size 20: range = max(A1:T1) – min(A1:T1),…, = max(A50:T50) – min(A50:T50), and grand range = max(A1:T50) – min(A1:T50).
Now draw 19 charts, each of them will show for one subgroup size the grand range as a stright line and all 50 individual subgroup ranges.
My God! The “shift” between the average subgroup range and the grand range is, for subgropup size 2, much larger than for subgroup size 5, which itself is much larger than for subgroup size 20! By the way, for subgroup size 20 the difference is nearly negligible! Wait a minute, these subgroups are all sequential samples of the same process. It is the same process, and there is no way to say that the process shifted more or less deppending on the subgroup size used. It is history, either the process shifted or not.
Know the following, Reigle: If a process shifted by this much, it shifted by this much whether you are taking subgroups of size 1, of size 20, or not measuring anything at all.
COUNTER-EXAMPLE 2:
Say that you have on batch of say 1,000,000 of parts which have a characteristic that is randomly and uniformily distributed beween 0 and 1. These parts were produced in a proces in sequencial order, but now they are all mixed so the original order is lost forever.
Step 1: Take 5 samples, measure them and write down the 5 values in the cells A1:D1.
Step 2:  Repeat with another five and another five until you fill 50 subgroups (i.e. to the cells A50:E50).
Steps 3 to 6: As you explained.
You will arrive exactly to the same conclusions that you arrived with your example. Now tell me, which process shifted in this case? When did it shift, since the parts within each subgroup can represent any time in the process?
COUNTER-EXAMPLE 3:
Repeat exactly the six steps of your example, just replacing the sindividuals subgroup ranges by the unbiased subgroup standard deviation (in Excel, make =stdev(A1:E1)/0.94 and so on, 0.94 is c4 for n=5) and replacing the grand range by the grand standard deviation (=stdev(A1:E50)). Add to the chart a third stright line with the average of the unbiased subgroup standard deviation. Press F9 several times to see what you get in different trials of the same simulation.
Holly S##T! Not only that the average standard deviation is, in every trial, very very close to the grand standard deviation. But in some cases it is even greater!!!!! This means that….. THE SHORT TERM STANDARD DEVIATION CAN BE SMALLER THAN THE LONG TERM STANDARD DEVIATION! A NEGATIVE SHIFT! EUREKA! (of course, all this according to Reigle reasoning, which is wrong)
One thing is an outlier, another thing is sampling variation, and a third and different thing is a shift in the process.

Craig,
I have to agree with Reigle on this one. Your resource does not know of what they speak. What nonsense.

Stan,
Ok, so can you explain why Six Sigma? Why not 5 Sigma, why not 7 Sigma or 4.5 Sigma? Also, is this a  short term or a long term capability?
P.S. you insulted Craig quickly but did not provide your version of the story.
 

Stan,
You didn’t answer the question. Can you then explain where the name Six Sigma come from? Why not 5 Sigma, why not 7 Sigma or 4.5 Sigma? Also, is this a  short term or a long term capability? We all know SSA’s version of this naming. What’s your version?

Yes I can.
With the exception of giving all credit for everything Six Sigma to Mikel, Reigle’s answer is correct.

Gabriel,
I asked the following two questions:
Why would anyone want to estimate a process performance – average and sigma – based on a subgroup?
Why would anyone then want to take the worse case of several subgroups?
If I have understood the debate so far, I believe the answer might be provided by the way Motorola engineers controlled their processes prior to 1984. At that time, few Motorola statisticians, quality engineers, or device engineers recognised the importance of rational subgrouping, so that in photo processing for example, a subgroup actually corresponded to an individual wafer – with measurements taken from the top, centre, bottom, left, and right,  providing a subgroup of 5.
This approach was widely used across most of the semiconductor industry at the time – for example, at Inmos, TI (Houston)  GI(Scotland), and Siemens in Ballanstrasse, but not at one excellent bipolar Fab in Phoenix, where they had an excellent SPC engineer. He used wafer averages as individuals, while in Austin we – process and yield enhancement engineers – preferred to use Multi-vari chart to order to study sources of variation, as recommended by Shewhart.
Presumably, this is why certain individuals tried to ‘improve’ the statistical methods that had previously make Motorola’s waferfabs so successful. Like many others, they were more interested in ‘statistical political correctness’ than actual improvements.
In summary, subgroups are not entities and should not be treated as such. If a process engineer uses a subgroup size of 3 and takes 10 subgroups giving a n = 30, then the population x-bar-bar can be estimated to within about 0.6 sigma.
I believe this is an important issue because as Stan previously pointed out, many USA companies are already uncompetitive due lack lustre ‘system performance,’ mainly because they have not understood the ‘step by step confirmation’ method (100% inspection) of the Toyota Production System. Allowing for a 1.5 sigma shift will only make a bad situation worse, which is why the Japanese company I worked for did not use any shift to design its world-class image setter.
Respectfully,
Andy Urquhart