# Is there any empirical evidence to the 1.5 shift?

Six Sigma – iSixSigma Forums Old Forums General Is there any empirical evidence to the 1.5 shift?

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• #30531

Ron Tozydlo
Member

I understand that using a subgroup size of 4 will detect a 1.5 sigma shift 50% of the time.  However, I have yet to see any empirical evidence that a process shifts 1.5 sigma “over time.”  By the way, how much time is “over time”?

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#79592

Ashman
Member

First, a long time is years.  Long-term variation should only be talked about for a process that has been observed over years, not months or weeks as some would like to think.  The empirical evidence comes from Motorola.  They studied processes that they had applied Six Sigma to years after the project ended and that is when they noticed a 1.5 Sigma Shift, on average.  I don’t whether that is published anywhere.  Anybody with a link?

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#79593

Robert Butler
Participant

You’ve asked a very good question.  The empirical evidence rests on three old studies –
Bender-Statistical Tolerancing as It Relates to Quality Control and the Designer-Automotive Division Newsletter of ASQC 1975,
Evans-Statistical Tolerancing:The State of the Art, Part III, Shifts and Drifts. JQT 1975, 7 (2), 72-76,
Gilson-New Approach to Engineering Tolerances: Machinery Publishing Co., London, 1951
In the past issue of Quality Engineering 14(3), pp.479-487 Davis Bothe pulled these together with some additional research that he had done in the article ‘Statistical Reason for the 1.5 Shift’.
At the very end of his article Bothe points out that the 1.5 shift is reasonable but that it is based on the assumption of a stable process variance.  If the variance is not stable then the 1.5 shift may or may not occur and may or may not be larger or smaller.  He also points out that the above assume normality and that the situation may be different (or maybe not) for non-normal responses. I think the Bothe article is the best article on the subject that I have read.  His point concerning variance stability is one that has bothered me in the past.  In particular, given that you have a process that is in control and that you are making adjustments to keep it in control,  the random walk nature of such a process coupled with both a drift in the mean and changes in variance could just as likely result in a drift in the process that resulted in improvement over time.
Thus, this rather lengthly reply to your question can be summarized by recommending that you read the Bothe article not only to understand the justification for the 1.5 shift but to also know the assumptions that have been made concerning its validity.

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#79599

Ron Tozydlo
Member

Does anyone know how I can obtain the three references that Robert Butler lists?  I know I can copy the JQT article from the library at North Park University in Chicago, but can I get any of them quickly on-line?  I will call ASQ after posting this message.

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#79605

Ron
Member

There is a great deal of discussion here regarding the assumed 1.5 sigma shift.  Okay deal with it statistically someone somewhere made a lot of observations and so here we are.
What does it mean to you as a six sigma practitioner? It means that in most cases you will overstate your actual results by 1.5 sigma in the long term.
Long term is not relevant in a continuous improvement culture. Strive to maintain and develop a six sigma continuous improvement culture and the question becomes mute.
The answers to the 1.5 sigma shift have been weel documented on countless number of responses.

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#79609

chencan
Participant

Is there any e-version of David Bothe’s article-“Statistical Reason for the 1.5 drifts”?
Thanks and Best Regards,

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#79610

Ron Tozydlo
Member

To buy or review the article, go to http://www.dekker.com

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