# Dr. Montgomery

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• #34405

Reigle Stewart
Participant

On January 27, 2004, a technical review of the
1.5 sigma shift was conducted by Dr. Douglas
C. Montgomery, Professor of Engineering, Ira A.
Fulton School of Engineering, Arizona State
University, Tempe, Arizona. As commonly
known, Dr. Montgomery is a world-renowned
statistician and engineer. He has published
many books and articles on the subject of
mathematical statistics, quality engineering,
design-of-experiments, and statistical process
control methods. In support of this technical
review, Dr. Montgomery called upon his recent
book Introduction to Statistical Quality Control
(2001) Fourth Edition, John Wiley and Sons, Inc.
This book shall herein be refered to as Ref.
1.0. Where appropriate, citations will be made
from this book (Ref. 1.0). Furthermore, Dr. Mikel
J. Harry provided Dr. Montgomery with the
equations presented in his recent book:
Resolving the Mysteries of Six Sigma:
Statistical Constructs and Engineering
Rationale. Dr. Harry also provided Dr.
Montgomery with the so-called proofs that
Statman posted to the iSixSigma forum (from
January 19, 2004 through January 23, 2004). All
of the arguments related to the on-going on-
line debate were openly and objectively
discussed, evaluated, or otherwise considered
by Dr. Montgomery. These points were
synthesized to several key issues. ISSUE 1:
The +/- 3S limits of a process can be (and often
are) used to define the limits of capability.
Statmans position: No. Dr. Harrys position:
Yes. Dr. Montgomerys position: Yes. In
support of this position, Dr. Montgomery cited
page 350, section 7.1 of Ref. 1.0. The quote is:
It is customary to take the six-sigma spread in
the distribution of the product quality
characteristic as a measure of process
capability  The upper and lower natural
tolerance limits of the process fall at M+3S and
M-3S, respectively. ISSUE 2: The idea that
process capability can be made fully
independent of specification limits. Statmans
position: No. Dr. Harrys position: Yes. Dr.
Montgomerys position: Yes. Dr. Montgomery
cited page 351, section 7.1 of Ref. 1.0. The
quote is:   a process capability analysis may
be performed without regard to specifications
on the quality characteristic  However,
specifications are not necessary to perform a
process capability analysis. ISSUE 3: An
expansion of the standard deviation (owing to
random sampling error) can be made
equivalent to a linear off-set in the mean.
Statmans position: No. Dr. Harrys position:
Yes. Dr. Montgomerys position: Yes. Dr.
Montgomery concurred that the quantity (3S.a 
3S.b)/3S.a fully constitutes a Z shift in the
points of unity and can be made directly
equivalent to a shift in the mean. In other
words, an expansion of the standard deviation
(denominator term) can be calibrated to a linear
shift in the mean (numerator term). Doing so,
will (in fact) provide probabilistic equivalency
with respect to the inner most limits of the
design margins. He indicated that such a shift
has HUGE implications for design engineers
and product reliability. He also recognized that
this is the basis of the proverbial 1.5 sigma shift
and concurred with the process qualification
procedure that Dr. Harry outlined (in the shift
book). ISSUE 4: Per Dr. Harrys book, there are
two types of shift, static and dynamic. Static
shift is given as a linear off-set in the mean
such that Z.shift.1 = Z.st(1-k1) and dynamic shift
(owing to expansion in the short-term standard
deviation) is computed as Z.shift.2 = Z.st(1 
k2). In this context, we understand that k1 = |T-
M| / |T-SL| and k2 = 1  1/c. Thus, we are able
to algebraically establish that Z.shift = Z.st 
Z.st/c = Z.st  Z.lt. Statmans position: BS (i.e.,
no). Dr. Harrys position: Yes. Dr.
Montgomerys position. Yes. ISSUE 5: The
quantity Z.shift=1.5 is a rational correction when
no other information or data is available to
establish the short-term capability of a process
when only the long-term is currently known
(especially in design engineering work).
Statmans position: BS (i.e., no). Dr. Harrys
position: Yes. Dr. Montgomerys position: Yes.
Dr. Montgomery elaborated that the idea of a
1.5S shift is certainly in line with classic
reliability engineering practice, where an
engineer will provide safety margins of 1.5X to
2.0X, 25% to 50% design margins (to
compensate for uncertainites in process
centering). In conclusion, Dr. Montgomery
concluded that setting specifications such that
Z.st=6.0 is rational and perhaps prudent in
many cases. He also concluded that Dr. Harry
has provided several unique perspectives from
which to rationally justify the shift: 1) the .9973
confidence interval of the mean given the case
N=4, 2) the magnitude of expansion in the
instantaneous standard deviation (using the
chi-square distribution with df=29 and alpha=
.005), 3) the use of one-way analysis-of-
variance for the case c=1.8, n=5, and g=25, 4)
published empirical benchmarking data, 5)
previously published research material, and 6)
the magnitude of conventional safety margins.
Dr. Montgomery indicated that these sources of
evidence provide sufficient reason for using the
1.5S shift when no other information or data is
available.
Respectfully,Reigle Stewart

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#94769

Anonymous
Guest

Hi Reigle,
Dr. Montgomery’s book “Design and Analysis of Experiments” is a fine book: I even have my own copy. Unlike most statisticians, he has confirmed the importance of  the ‘transmission of error’ in experimental design, as originally described by Taguchi.
Unfortunately, he has failed has to identify the importance of ‘scaling,’ among other things, so I’m not surprised that he would agree with your position.
Now to use scaling processes have to be characterised and adjusted. Surely this would imply that process capability is no longer valid. Of couse the advantage of parameter design is to ‘desenstiize’ the process to any source of variation, by scaling back the response, which in turn reduces the variance by the same scaling factor. What could be more simple!
Accordingly, it is my view that the 1.5 sigma shift is irrelevant. There has been no Kuhn paradigm shift and there has been no ‘invention.’ All six sigma really means is that Cpk = 2, which is why I encourge statistical engineers to study all kinds of statistics and methods, whether you agree with them or not.
Cheers,
Andy

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#94770

Mikel
Member

Reigle,
What business relations does Doug have with Mikel. We already know you are in business with him even though you wanted to deny it.
Do you really think anyone cares what Doug has to say about Mikel?
Tell Doug to stick to DOE and wine.

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#94781

Reigle Stewart
Participant

Andy:Thank you for providing your perspective and
beliefs, but don’t you mean that Cp=2.0? Or are
you saying that “Six Sigma” translates to Cp=
Cpk=2.0?RegardsReigle Stewart

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#94782

Reigle Stewart
Participant

Stan:As normal, your position is colorful, imaginative,
and full of wisdom.From your humble whipping post and effigy.Reigle Stewart

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#94788

Mikel
Member

Reigle,
My position was sarcastic and demeaning – not colorful, imaginative, and full of wisdom.
I save the later for answering wise posts.
I am surprised you have not noticed the difference.

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#94792

Bob M.
Participant

Ho: Stan’s response was sarcastic and demeaning.
Ha: Stan’s response was colorful, imaginative, and full of wisdom.
Regal must have observed a p-value less than .05, perhaps because his vision was so clouded by the 1.5 stigma shift.

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#94794

Sam Orez
Member

Andy,
Sam

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#94795

Mikel
Member

Vision? It is hard to see with your head burrowed a few feet up Mikel Harry’s …
Well, you know what I mean.

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#94803

Anonymous
Guest

Sam,
The use of scaling is best illustrated by a diagram. I shall put a diagram on my website shortly. My URL can be found by searching Andy Urquhart. (I’d like to avoid putting up my email address to avoid spammers.)
Cheers,
Andy

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#94840

Statman
Member

Book ain’t sellin is it?
Reigle,
I have been very busy this week and haven’t nor have I time to respond to your assertations about my claims in full I will try to get back to you this week end.
Mean time, I think that you need to go back and re-read my poistion.  I stated them very clearly in 5 points and a proof in at least two posts.  Please re-read the points and you will find that this so-called technical review has not addressed any of them the way that I have stated them.  I will state them again.
The mysteries that Dr Harry has (knowingly or otherwise) uncovered:
1.  There is no constant shift of 1.5 (or any other number)
2.  The shift from short to long term depends on the Zst ratio and the sigma inflation coefficient
3.  A six sigma process short term will be 4sigma long term (owing to the worse case sampling error c=1.5) not a 4.5 sigma process long term (since Z.lt = Z.st/c)
4.  Because of point #3, a six sigma process will have a DPMO of 31.69 not 3.4 long term.
5.   A sigma shift of K in the numerator of the Z equation does not equate to a Z with a K*sigma inflation.

I will debate any one that thinks that they can support a statistical rational for the 1.5 shift in the applications recommended by Dr. Harry.  (ie Z.lt = Z.st – 1.5).  Including Douglas.
Statman

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#94875

Reigle Stewart
Participant

Statman:Concerning your 5 points, you have been duly
informed about these points on multiple
occasions (from multiple expert sources).
References have been provided to you.
Technical reviewers have validated the math.
Experts have shown that you have serious
errors (and unsubstantiated assumptions) in
your so-called proofs. For example, you
continually insist that Dr. Harry treats the shift as
a constant, but this is blatantly and knowingly
false, as has been pointed out in several
previous posts. You have declared, There is
no constant shift  and make it appear that Dr.
Harry says there is constant shift. For the last
time, I quote from the forward to Dr. Harrys
book: As will be demonstrated, the shift factor
is merely an algebraic byproduct of the chi-
square distribution that will vary depending on
the accepted level of risk and prevailing
degrees-of-freedom. However, when typical
application circumstances are postulated and
rationally evaluated, the resulting shift will prove
to be approximately equivalent to 1.5 sigma.
How much clearer can this point be made? You
are not willing to even acknowledge the most
directly verifiable flaws in your statements
(such as just pointed out). At this point, it has
been formally requested that you prepare a
technical white paper on the subject (perhaps
addressing these 5 points, among other related
things). Doing so will provide two source
documents (your formal position paper and Dr.
Harrys book). From these two sources, the
panel of experts will define the central issues.
In turn, the debate questions will be formulated
ensure that the debate remains centered on
documented facts, statistics, and practices (as
related to design and process engineering).
Classic debate practices will govern the nature
and course of the debate. It has been
recommended that you provide a final
submission date for your technical position
paper not later than February 15, 2004. Your
selected submission date can be provided to
me through iSixSigma channels. Until this time,
we should refrain from any further discussion
on this topic (per the request of several thread
participants).Respectfully,Reigle Stewart

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#94876

Savage
Participant

Reigle,
Who’s coming up with the questions for the debate?  Just curious.

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#94879

Mikel
Member

Reigle, you stated “For the last time, I quote from the forward to Dr. Harrys book”.
Please oh please tell us it’s true and you are not just toying with my emotions.
By the way, if Statman does not take you up on the challange of a position paper, I will. I will take the point of view that in an environment where SPC thinking is in place, it is pure foolishness to talk about a 1.5 sigma shift – it simply will not exist. We would include with your statistical “experts” persons who only have taken two days worth of SPC. The “experts” will feel foolish about the extra years of their life they spent only to understand what is blatently obvious to all except the most ignorant of people.
I knew your teasing us with a real face-to -face debate was something you and Mikel would run away from.

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#94883

Reigle Stewart
Participant

accordance to the guidelines of the previous
post. The debate “will” occur, rest assured of
that, assuming that Statman (and now you) will
not defer. Now that you have committed to a
position paper, I will ensure your opportunity to
be a part of the debate. Now, lets stop talking

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#94885

Tim
Member

Reigle,
Are you participating in the debate.  I’d love to read YOUR white paper.  I’m sure you can’t write one without drooling over Mr. Harry.
Stop being an instigator for the fool from AZ.  Let Mr. Harry come fight his own battles.

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#94886

Mu Joe
Participant

Please forgive my invasion into this long going debate. I refrain from taking sides in the issue of the 1.5 sigma shift because quite frankly, I not smart enough to contribute an opinion.
However, there was one statement that makes me stop and ponder:
“ISSUE 2: The idea that process capability can be made fully independent of specification limits. Statmans position: No. Dr. Harrys position: Yes. Dr. Montgomerys position: Yes. Dr. Montgomery cited page 351, section 7.1 of Ref. 1.0. The quote is:   a process capability analysis may be performed without regard to specifications on the quality characteristic  However, specifications are not necessary to perform a process capability analysis.
Here’s my question. How can you calculate a process capability without at least some indication of the customer requirement (specification limit)? That is, if you are producing widgets, you MUST know the level of quality that your customer requires in order to determine what constitutes a “defect” and therefore how capable your process is at meeting the needs of your customer. Otherwise, you are just stamping out widgets without any regard to quality. Now, I do agreee that you would never put spec. limits on a control chart, but wouldn’t you at least need to know what constitutes a defect, and wouldn’t that come from VOC, and isn’t that a form of specification limit? (“I won’t buy any of your widgets that are smaller than 10mm.”)So how could process capability be made “fully independent of specification limits?”
Maybe it’s just that I haven’t read all of the background in the forum on this particular subject, but am I missing something obvious on this issue?
If I’m totally out in left field here, please forgive me. My brain hasn’t fully recovered from the New Year’s Party.
Joe

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#94887

Reigle Stewart
Participant

Matt:Thank you for your inquiry. The debate
questions will be formulated in accordance to
the issues. Of course, the issues will be will be
surfaced by reviewing these posts and
examination of the submitted documents (i.e.,
Statman’s and Stan’s white papers and Dr.
Harry’s book). The issues can only be
established after the panel of experts have been
exposed to the content that is to be debated.
The postion papers from Stan and Statman will
ensure this is professionally achieved. Once
the questions have been defined, the opposing
parties will be contacted and provided a listing
(broken down by topic). Of course, the answers
will be presented by each contestant during the
each party will have the opportunity to accept or
reject the fact. If the fact is rejected, rebutal will
he heard. All contestants will be given the
opportunity for closing arguments. Following
this, the debate will be closed and the panel of
experts will convene to review the debate
content. After this, they will issue a position.
That is the current planning.Reigle Stewart

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#94888

Reigle Stewart
Participant

Tim:I will not be a participant at the debate.Reigle Stewart

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#94891

Tim
Member

Of course not – what a big surprise, you sidekick, weasel.  Just stir up the pot then jump out because it’s too hot.  If I were Mr. Harry, I’d be pissed that you’re dragging my name through the mud – making me the butt of all the jokes.  But I guess that doesn’t matter to you, or him for that matter.

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#94894

Reigle Stewart
Participant

Mu Joe:Conventionally, process capability is given as
M+/-3S, where M is the process mean and S is
the standard deviation. This represents the
performance range of the process (also called
process capability). This particular form of
capability reports on the “repeatability” of the
process. Another form is to make the process
capability relative to the specification limits,
thereby providing the “probability of defect,” and
often given as a standard normal deviate (Z
value), such as Z.usl = 6.0. Yet another form is
to report one or more indices of capability, such
as Cp, Cpk, and so on. Yield is also a measure
of process capbility. So is DPMO. As you can
see, there are several meaningful ways to
assess and report on process capability. For
further information, please reference the source
provided (Dr. Montgomery’s book).
Furthermore, there is the issue of process
reliability, also involving the concept of process
capability (but factoring the dimension of time).Reigle Stewart

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#94895

Reigle Stewart
Participant

Tim:Thank you for your input. It is most unfortunate
that you choose not to be civil and respectful.
For your information, the “profit” from Dr. Harry’s
book is dedicated to a local charity. Second, my
participation in the debate was never a part of
the plan, nor do I seek to debate. Third, I
seriously doubt that your unprofessional like
comments are of any interest to him. If
speaking like this makes you feel powerful or
strong, then please, by all means, continue —
we have thick skin and its like water off a duck’s
back.Reigle Stewart

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#94896

Tim
Member

Reigle,
Can you consider separating your single paragraph posts into multiple paragraphs? I find it difficult to read your posts when they’re all in one paragraph (especially online). Plus, it would easily segment your response into multiple points.
Thanks for considering it. I like to read what you have to say, but it would be much more enjoyable if it were easier to read.
Tim

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#94913

John H.
Participant

AndyI wholeheartedly agree with your view that the 1.5 sigma shift is irrelevent and your “Non-Flat Earth Society” opinion that statistical engineers should study all kinds of statistics and methods. Your Variance scaling idea for processes is very interesting. The period doubling Article ” A Simple Model of A Variance Stable Process”(https://www.isixsigma.com/library/content/c020310a.asp) illustrates some of the basic effects of a scaling parameter on Variance.If you convert it to a Fourier power spectrum the coefficients scale. “Tuning out Variances” in complex processes based on parameter adjustments is a facinating concept. Weather forecasting for example is based on parameter adjustment models.-John H.

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#94916

Anonymous
Guest

Thanks … and for the reference John, but I can’t take credit for it; the first example is standard fare in Taguchi Classes.
I found your article most interesting; especially as I share your interest in chaotic systems and chemometrics. In the past I’ve even tried to teach a robot Tai Chi so that it wouldn’t forget what it was doing!
Cheers,
Andy

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