New to Six Sigma – need help on statistics
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 This topic has 10 replies, 6 voices, and was last updated 17 years, 6 months ago by SemiMike.

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November 18, 2004 at 12:23 am #37579
I have made numerous aborted attempts to learn SixSigma 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 SixSigma. 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 SIXSIGMA using easy to grasp real world examples?
All help would be truly appreciated.
Thank you for your time.0November 18, 2004 at 2:59 am #110898You 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.
0November 18, 2004 at 5:24 pm #110931Hello 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 SixSigma and statistical terms, explanations such as the one you shared with me?
Thank you & have a nice day!0November 19, 2004 at 2:56 am #110958GR, perhaps I can be of assistance. I am willing to help for free. Contact me at [email protected].
0November 19, 2004 at 6:59 am #110963
Ron ManubayMember@RonManubay Include @RonManubay in your post and this person will
be notified via email.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.
0November 19, 2004 at 7:34 am #110966
Johnny GuilhermeParticipant@JohnnyGuilherme Include @JohnnyGuilherme in your post and this person will
be notified via email.Ron
Can you go through that last sentence “On the other hand…….nearest spec limit”. Now I am a little confused.
Johnny0November 19, 2004 at 8:50 am #110967
Ron ManubayMember@RonManubay Include @RonManubay in your post and this person will
be notified via email.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 3sigma 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 3sigma process which is centered between your spec limits. The problem with this 3sigma 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 3sigma 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 6sigma 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 6sigma 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 6sigma away from your nearest spec limit.Regards,
Ronnie0November 19, 2004 at 9:11 am #110968
Johnny GuilhermeParticipant@JohnnyGuilherme Include @JohnnyGuilherme in your post and this person will
be notified via email.Ron
Thanksit was long but its makes sense. Thanks for clearing this up for me.
Johnny0November 22, 2004 at 1:06 am #111085
Ron ManubayMember@RonManubay Include @RonManubay in your post and this person will
be notified via email.Hi Johnny, No problem. I’m glad to be of help.Ronnie
0November 22, 2004 at 2:03 am #111089
Goulais RiverParticipant@GoulaisRiver Include @GoulaisRiver in your post and this person will
be notified via email.I have made numerous aborted attempts to learn SixSigma 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 SixSigma. 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 SIXSIGMA 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
0November 22, 2004 at 5:41 am #111100If 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 level0 
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