iSixSigma created a process sigma calculator that allows the operator to input process opportunities and defects and easily calculate the process sigma to determine how close (or far) a process is from 6 sigma. One of the caveats written in fine print refers to the calculator using a default process shift of 1.5 sigma. From an earlier poll, greater than 50% of polled quality professionals indicated that they are not aware of why a process may shift 1.5 sigma. This article revisits the discussion to help clarify what the 1.5 sigma process shift is, and why it is necessary -- if at all.
In a previous article, Zack Swinney [bio] discussed the fact that a 6 sigma process produces about 2 defects per billion opportunities, and 3.4 defects per million opportunities, which we normally define as 6 sigma, really corresponds to a sigma value of 4.5. Where does this 1.5 sigma difference come from? We learned that Motorola has determined, through years of process and data collection, that processes vary and drift over time - what they call the Long-Term Dynamic Mean Variation. This variation typically falls between 1.4 and 1.6.
iSixSigma user Ken Myers presented another reason for Motorola specifying the 1.5 sigma shift: 'There might be another possible reason for Motorola specifying the 1.5 'Sigma Shift' from the target in mean of a stable process. Consider, if one were to control a particular process using a typical statistical process control chart of averages, the maximum expected shift using a sample size of four measures per subgroup would be ~1.5 standard deviations.
"This maximum shift is calculated as the standard error of the mean, (short term SD)/(n)^1/2). For a sample size of 5 measures per subgroup the maximum shift for a stable process would be ~1.34 standard deviations. For most processes where samples could be drawn and measured rather inexpensively, 4 or 5 samples per subgroup provides the best economic trade-off between cost and the speed of detecting a shift in the mean from the target. This detection is characterized in the Average Run Length curve prepared for a given measure, i.e., average or individuals, using a fixed sample per subgroup. There actually might be some science behind Motorola's mysterious requirement of a 1.5 'Sigma' shift."
Finally, iSixSigma user Joe Perito eloquently recaps the reason for the 1.5 sigma shift and it's application to your processes: 'Why would you want to use the fluctuation (variation) in coffee bean prices in Brazil to infer any kind of performance measurement in your processes or your suppliers' [processes]? The derivation...of the 3.4 PPM is the proportion defective outside of a normal curve assuming the normal curve has drifted off target by 1.5 sigma.
"This figure (3.4) goes from the data that Motorola has collected off of their processes after finding that their processes have a history of drifting about the mean by 1.5 sigma. This figure is useful only to those processes measured at Motorola and must be verified every time they want to check the performance of those processes, because historical performance may not be relevant to the current process if it has improved or deteriorated.
"A really distorted and egotistic application of this data is to assume that [Motorola's] data is applicable anywhere else in the world. What has Motorola's process variation got to do with U.S. Steel, Pampers, Frisbies, or your and my processes until data from our processes is evaluated? If you or others would like a table of zero to 6 sigma listings verses PPM rates and Verses PPM rates after a 1.5 sigma shift, just write me. You will see that 6 sigmas are equal to 0.002 PPM, or, 3.4PPM after a 1.5 sigma shift off target."
Thank you to Ken and Joe for their open and immensely helpful discussion. You can read more from these two Quality experts, as well as hundreds of other posts, at the iSixSigma Discussion Forum. Be sure to sign up for the weekly iSixSigma Insights newsletter... you'll be notified of new tools, articles and discussions that will help you be more productive in your daily work activities.
