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New to Six Sigma – need help on statistics

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  • #37579

    G R
    Participant

    I have made numerous aborted attempts to learn Six-Sigma concepts and apply them, however, there are so many statistical terms that tend to unsettle me. I have taken a basic course in statistics but that doesn’t seem to help much – I still can’t seem to grasp the concepts behind Six-Sigma. E.g. 1) what does a sigma REALLY mean ? 2) what is a z score? can someone explain in easy to grasp examples?
    Is there some website (university study site etc.) that offers a introduction to statistics in understandable language
    Is there some website (university study site etc.) that offers a introduction to SIX-SIGMA using easy to grasp real world examples?
    All help would be truly appreciated.
    Thank you for your time.

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    #110898

    Whitehurst
    Participant

    You know what the “average” of some data is.  To get the average you add all the data together and divide by how many numbers you had.  How much variation is in your data?  For teaching purposes, I like to call “sigma” the average amount of variation in your numbers. Take the average of the data and subtract it from each one of your data entries.  Square each of the differences you get.   Sum up all your squared differences to get a total.  Divide this total by the number of data entries you started with to get an average.  This is the average amount of variation…squared.  Take the square root to get “sigma”.  Sigma is another name for STANDARD DEVIATION.  It is the average amount of variation in your data.  The larger sigma is, the greater is the amount of variation in your numbers.  This explanation is for 30 or more individual pieces of data.  If you have less data, divide the sum total of squared deviations by the amount of data you had minus one.  (20 samples? Divide by 19)  There is an altogether different calculation for subgroups of data which I will not go into.  The definition, the logic, the probabilities, and the effect of the variation has on the width of the histogram, the upper and lower limits (99.73%) are all the same regardless if your data is individual data entries, more than 30, less than 30, or sampled by subgroups.  The logic remains the same, the calculations change for subgroup sampling.  This is a good beginners deffinition.  Standard deviation, or sigma, is a measure of the average amount of variation in the data.  Now you can compare not only averages of different groups of data, but you can also compare the amount of variation in each group.

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    #110931

    G R
    Participant

    Hello Joe,
    Thank you SO MUCH for taking time to write the explanation. I now understand it better. Do you have any site links you can share with me that offer easy explanations of Six-Sigma and statistical terms, explanations such as the one you shared with me?
    Thank you & have a nice day!

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    #110958

    Whitehurst
    Participant

    GR, perhaps I can be of assistance.  I am willing to help for free.  Contact me at [email protected].

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    #110963

    Ron Manubay
    Member

    Hi GR,I think that part of the confusion in learning statistics and the Six Sigma concept introduced by Motorola, is the fact that the meaning of SIGMA differs between the two.Joe has given you an excellent description of what SIGMA is as a statistical term. It is – standard deviation or simply, the average deviation of each data in your sample from the mean. Six Sigma concept is different. In the context of a manufacturing process where you have a process distribution and spec. limits, SIGMA in this case, is the number of Std.Deviations your process mean is away from your nearest spec limit (either LSL or USL). So, the more “sigma” you have, means the farther your process mean is from the nearest spec limit. This translates to much fewer rejects even if your process distribution shifts. Here’s where the confusion starts. If you are talking about sigma in statistical context, the lower it is, the better, since it means better precision or repeatability. On the other hand, if you talk about sigma in the context of the Six Sigma concept, the higher the sigma, the better, since it talks about the number of sigma your mean is away from your nearest spec limit. Did I confuse you more?Regards.

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    #110966

    Johnny Guilherme
    Participant

    Ron
    Can you go through that last sentence “On the other hand…….nearest spec limit”. Now I am a little confused.
    Johnny

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    #110967

    Ron Manubay
    Member

    Hi Johnny,Let’s take this example to illustrate what I meant. This would be long so bear with me.In a manufacturing process, you normally take some quality measurements and compare it to your spec. limits. Right? Let’s say that these measurements form a normal distribution, characterized by a mean and a standard deviation.Let’s assume further that we have an ideal situation wherein the said distribution is centered between your spec limits (LSL and USL). In a 3-sigma process, your mean is about 3 standard deviations (sigma) away from your nearest spec limit. If this is the case in our example, it means that 99.73% of the time, your measured value will fall within your spec limits and that, about 0.27% will fall outside. That’s about a 2700 ppm defect level.That is assuming you have a 3-sigma process which is centered between your spec limits. The problem with this 3-sigma capability is this. Studies showed that a typical process distribution shifts by as much as +/- 1.5 std. dev.(sigma).If this shift do happen, a 3-sigma process would then have a rejection rate of about 66000 ppm, up from the 2700 ppm rate when the process was centered. Since this 1.5 sigma shift is something that is almost inherent to your process and hard to control, there are two things that you can do to make sure that this shift won’t cause chaos on your rejection rate. One, widen your spec limits (which I don’t recommend of course), or two, minimize the amount of inherent variations in your process such that your process variability (sigma) is decreased.How much reduction is appropriate? If you can have a distribution that has a mean that is 6-sigma away from your nearest spec limit, then, you have achieved what the Six Sigma proponents are aiming for. The spec.limits is the same. In this 6-sigma capability, your rejection rate would be 2 ppb (centered) and 3.4 ppm when the mean shifts by 1.5 sigma. In summary, the six sigma concept is: reducing your process sigma (std. dev.) such that your distribution mean is 6-sigma away from your nearest spec limit.Regards,
    Ronnie

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    #110968

    Johnny Guilherme
    Participant

    Ron
    Thanks-it was long but its makes sense. Thanks for clearing this up for me.
    Johnny

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    #111085

    Ron Manubay
    Member

    Hi Johnny, No problem. I’m glad to be of help.Ronnie

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    #111089

    Goulais River
    Participant

    I have made numerous aborted attempts to learn Six-Sigma concepts and apply them, however, there are so many statistical terms that tend to unsettle me. I have taken a basic course in statistics but that doesn’t seem to help much – I still can’t seem to grasp the concepts behind Six-Sigma. E.g. 1) what does a sigma REALLY mean ? 2) what is a z score? can someone explain in easy to grasp examples?
    Is there some website (university study site etc.) that offers a introduction to statistics in understandable language
    Is there some website (university study site etc.) that offers a introduction to SIX-SIGMA using easy to grasp real world examples?
     
    GR,
    I am curious as to what your bussiness is and why you think you need 6sigma. Are you currently doing any other continuous improvement initiative?
    If you have been reading up and taken courses, and still cant see what it’s all about, I bet you don’t need 6sigma, and all the statistacal BS that comes with it.
    Just a thought.
    GR
     

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    #111100

    SemiMike
    Member

    If you are TOLD that you need this, then begin the long slow journey of undertstanding by IGNORING mathematical statistics and just jump in and GRAPH THE DATA.   After many attempts at graphing data over time, by machine, by part, by site within part, etc etc you may begin to see why people use DESCRIPTIVE statistics to talk to each other. 
    Then try IMPROVING a process by making small adjustments and plotting the results.  After a while you will see why people invented Design of Experiments, Anova, Mulitple Linear Regression, and other tools for INFERENTIAL statistics. 
    But if you must learn fast, start with a class in an Industrial Engineering department, not a Math department…in my opinion.  And Six Sigma is more about PROJECT MANAGEMENT and TEAM LEADERSHIP and INDUSTRIAL KNOWLEDGE than it is about statistics, IMO.
    Web sites that help:
    http://www.ruf.rice.edu/%7Elane/rvls.html  basic with animations
    http://www.itl.nist.gov/div898/handbook/  higher level

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