Question
I need to understand the statement, “Adding a 1.5 sigma shift in the mean results …….”
I’m used to the bell curve and + /- three sigma.
How does the extra +/- three sigma fit in, and what is this about moving the mean?
Does ASQ have a good book that includes this detail in with basic statistics?
Answer
The idea of 6-sigma leading to a process with 3.4 parts per million defective is not a totally statistical statement. Using the normal distribution, we know that a process that is centered on its mean will have 0.135% of the distribution outside 3 standard deviations on each tail. That same process would have 0.00000010% outside of 6 sigma, which does not lead to the aforementioned 3.4 million parts per million outside. Dr. Mikal Harry in 1992 published a book (see chapter 6) entitled Six Sigma Producibility Analysis and Process Characterization, written by Mikel J. Harry and J. Ronald Lawson. In it is one of the only tables showing the standard normal distribution table out to a z value of 6. Here is where he stated that processes can shift by 1.5 sigma leading to only having 4.5 sigma limits and the 3.4 parts per million outside the “6-sigma” limits. I would suggest you look at ASQ’s Six Sigma Forum Division that will help to better explain the rationale for the shift.
Steven Walfish
Secretary, U.S. TAG to ISO/TC 69
ASQ CQE
Principal Statistician
http://statisticaloutsourcingservices.com
For more on this topic, please visit ASQ’s website.