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Topic the math of 6 sigma

the math of 6 sigma

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This topic contains 3 replies, has 2 voices, and was last updated by  Darth 12 years, 11 months ago.

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    I’ve seen lots of explanations regarding six sigma and the classical graphical representation of the curve but everyone seems to assume some level of understanding and not relly answer the question…and no the little blue bar at the left “new to six sigma” doesn’t cut it. What’s confusing to me is I see a LCL and UCL with a graph that represents variation of your process for a 6 sigma spread which is much wider than a 1 sigma spread…why do you want a six sigma spread and not the tighter 1 sigma spread…I thought thats what all this was about, keeping the tolerances tight and not varying….help please, Mike


    Regardless of what you do, a normal distribution will contain about 68% within plus/minus 1 s.d. about 95% within plus/minus 2 s.d. and about 99.7% within 3 s.d..  The key is the reduction of the s.d. not the fact that you want everything within 1 s.d.  Reduce the variation and the curve narrows but the same proportion will still exist relative to the 1, 2 and 3 s.d.  Understand the statistics of the normal distribution and you might understand the math.  Plus you refer to UCL and LCL which are control limits on control charts.  When referring to capability you want to be concerned about USL and LSL which do not appear on control charts. 


    Darth, thanks for taking the time for an explanation. do you have any recommendations for further reading on the statistics of normal distribution. Also, although I mistated it, I meant USL and LSL. I have a strong background in Calculus but very little in statistics. I’m having difficulty with the relationship of the graph that we want to be narrow and the fact that we want to allow it to have a lot of room to vary. Is this the key…the fact that we want our process to allow a six sigma variance while our product is allowed to vary within six sigma and still meet the customers expectations?


    The concept of six sigma is simple.  In simple terms, you want your closest specification to be no closer than 6 s.d. from the mean.  That means that your process will be very narrow compared to your spec making the likelihood that something will be out of spec very small.  Since most customers are reluctant to widen specs, the only option is the reduction of the s.d.  Depending on the centering of the process, possibly you can achieve what you want by moving the mean of the distribution.  But, reduction of variation is what we are after.

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