Dr. Montgomery

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    Reigle Stewart

    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 = and dynamic shift
    (owing to expansion in the short-term standard
    deviation) is computed as Z.shift.2 = –
    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 = – = – 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 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
    Respectfully,Reigle Stewart



    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.



    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.


    Reigle Stewart

    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


    Reigle Stewart

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



    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.


    Bob M.

    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.


    Sam Orez

    Where can I learn more about scaling?



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



    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.)



    Book ain’t sellin is it?
    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 =
    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 = – 1.5).  Including Douglas.


    Reigle Stewart

    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
    and made available in advance. Doing so will
    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



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



    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.


    Reigle Stewart

    Stan:Please submitt your technical white paper in
    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
    about it and set about the tasks at hand.Thank YouReigle Stewart



    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.


    Mu Joe

    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.


    Reigle Stewart

    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
    debate. As these answers are made known,
    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


    Reigle Stewart

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



    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.


    Reigle Stewart

    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


    Reigle Stewart

    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



    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.


    John H.

    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”( 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.



    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!

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