Mystery of 1.5 sigma shift

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    N.Sridhar, Bangalore

    The long term sigma  level (SLT) is said to be lesser than the short term sigma level (SST) by 1.5; if so, then how come we add 1.5 to SST ? If in a project, after going thru DMAI phases, we reach a level of 3.4 dpmo, then we actually rach ea level of 4.5 sigma. This is short term sigma level.  Now, the long term sigma level should be only 3.0, since it is less than SST. But why do we add 1.5 to make 4.5 as 6.0?
    -N.Sridhar, Six Sigma BB



    This topic has been discussed over and over again on this forum. I think there are multiple articles on the topic. Have you tried searching for “1.5 sigma shift”? Search both the “Entire Site” and “Discussion Forum” and then come back and tell us if you still have your question.
    In the technical world, people often say RTFM. It’s an acronym that people use when an answer lies in the manual, and can be easily read there.
    Good luck in your quest. I look forward to your question once you’ve done some reading.



    It is a very valid question, one the I have had discussions with other MBBs about.  You happen to have the same point of view that I do when it comes to the sigma shift.  You can read all the manuals you want, the point is often glossed over and dismissed without a very good reason for the shift.  I’ve yet to find a good explanation of why 1.5 is added to your short term sigma, it seems like it should be subtracted.  Truthfully, I stopped repoting the change in sigma levels for my projects.  It doesn’t make sense for me to use a measure that I can’t get behind to explain how well my project did.  But that’s a different story…


    T. Minor

    Someone please correct me if I am incorrect, but I am under the impression that the 1.5 sigma shift refers back to the measured/observed  standard deviation (ranges) that were measured in the initial Motorola processes.  Subsequently, Motorola’s research became the de facto (industry) accepted sigma shift for processes.
    In any case, the tables we now use for sigma measurement are calculated to include the 1.5 sigma shift.  Although in reality, we could encounter processes in each of our companies with “Real” sigma shifts that could be (1) greater than 1.5, (2) less than 1.5 or (3) equal to 1.5 .



    Dear  Sridhar, Ralph, Zilgo and  T. Minor
    Following are my views on 1. The significance of ‘shift’ , and 2. ‘why 1.5 times the std. dev.
    1. The significance of ‘shift’ 
    Every process, howsoever sophisticated/automated due to advancement of science/technology, undergoes change in the short, as well as the long, term, irrespective of the life of the process. short/long term is always related to span of timetime. It is simple logic that the no. of opportunities for the occurence of errors/mistakes/deviations/…, etc. in the process is proportional to the span of time.
    Please note the following equation;
    Process performance = f{Hardware (variables related to M/c, Eqpt., gages, etc., and Software (variables related to people, method, material, etc)}
    Note: ‘f’ stands for ‘the function of”
    Because all the process variables related to hardware and software of the process are more likely to vary in the longer term than in the shorter term, the long term performance of the process is expected to be inferior in natural course, as compared with the short term performance. The concept of shift is actually related to this differential in the long term and short term performances.  Once we know the connection (equation) linking the two, one can find out the the other longterm/shortterm sigma level given the shortterm/longterm sigma level.
    2. Why 1.5 times the std. dev.?
    An explanation of this has been given in one of the volumes of a set of books, authored by Dr Mikel Harry.
    K.M.Date, Indian Statistical Institute, Pune, India



    firstly I would like to correct the statement made on Z-short term value when dpmo is 3.4. When we reach a dpmo of 3.4, the Z-short time is 6.0, and hence the Z-long term is 4.5 after subtracting 1.5 of Z-shift, which is correct. It is incorrect that when dpmo is 3.4 Z-short term is 4.5.
    Now, Z-shift = 1.5 because this is an empirical value arrived after research done by statisticians. May be someone can collect more data which can challenge this.


    Robert Butler

      If you are looking for articles that provide the assumptions underlying the 1.5 figure as well as a discussion of the concept, the paper you want to read is the one by Bothe.  You can find a listing of his paper and the other three papers that have been written on this subject in the discussion thread “Is There Any Empirical Evidence to the 1.5 Shift” which ran on this site in October 2002.



    If you were doing a project and you reached a dpmo of 3.4 and you plugged that into a normal inverse distribution, you would get back 4.5, not 6.0.  So in the short-term you are really at 4.5 because that is what you reached with the project.  Your long-term should be three because long-term should be less than short-term due to variation added in over time.  So then the long-term sigma for 3.4 dpmo should be 3.0 (if we want to keep the 1.5 assumption.)  But it isn’t, instead it is added and we then say that we have a six sigma process.  Like before, I don’t really agree with the 1.5 sigma shift as it is currently used.  It just doesn’t make a lot of sense.



    The 3.4ppm equals 6.0 sigma with the 1.5 shift already taken into account.  Without the 1.5 shift, 6 sigma is somewhere around 2 parts per billion.


    Edgar Aznar

    Does it have any sense to shift a 1.5 sigma on a process that follows a binomial distribution?.
    The point of asking this question is because some of the processes that I evaluate follow normal distributions  and others follow binomial distributions. If SIGMA is a “universal measure” that allows us to evaluate different processes, the effect that would cause to top management the comparison of different processes (normal, binomial distribution, etc), some with the 1.5 shift and some without the shift is very hard to explain and defend.
    I know that a lot of thought has gone into this topic but I have never found a straight forward answer.
    Thanks in advance



    Thanks, friends,  for responding to my topic. Zilgo is of the same opinion as I. And Ravishankar has also explained the 1.5 sigma shift well.
    Ralph, I took your advise and found some good responses posted in Oct’02 on a similar topic (with sub: Is There Any Empirical Evidence To The 1.5 Shift?). This topic looks rather controversial.
    I liked the reply of Ron which I copy-paste here for your convenience.
    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.
    – N.Sridhar

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