I've been asked to resume "quality circle meetings." (To increase efficiency, service, etc. I need ideas not just on how to motivate, and keep motivated, but also on discussion topics; should some topics be mandatory at each meeting? What would be some examples? How many times can we ask employees to describe their jobs and ways they feel they can improve the processes?
forrestbreyfogle 4/2/2005
INITIAL POSTING: Can someone explain what a 6 sigma process is said to produce a 3.4 ppm, when the same process could produce 2 ppm if it was centered. I understand the 1.5 sigma shift theory, but I do not understand why we would need to state PPM as 3.4, and assume the shift. I a not "Black Belt" educated, so keep the answer "Green" please.
RESPONSE: I look at sigma quality level, which has the 1.5 standard deviation shift buried into the metric, as simply a different "ruler". If we look at it this way, we don't get hung up about the 1.5 standard deviation shift.
However, it is important that we understand the true implications of this "ruler;" e.g., the relationship relative to PPM is not linear (among other things).
Because of this non-linear relationship and the confusion that the sigma quality level metric causes, I discourage our customers from using the sigma quality level metric within their Six Sigma deployment.
The basic strategy that I suggest for reporting how a process is performing relative to specification limits (in lieu of sigma quality level) is described in two article that I wrote for ASQ "Quality Progress". These articles are part of ASQ's "3.4 PPM series". The articles are in issues November 2003 and November 2004.
Hope this helps. If you would like to discuss further, contact me directly.
Forrest Breyfogle
Quality Digest's Six Sigma Forum Moderator
forrest@smartersolutions.com
www.smartersolutions.com
512-918-0280 X401
10/12/2005
You might be interested in the origins of the "+/-1.5 Sigma Drift"
Everyone with a Six Sigma program knows about the +/-1.5 sigma drift of a process mean, experienced by all processes. What this is saying is that if we are manufacturing a product that is 100 +/- 3 cm (97 - 103cm), over time, it may drift down to 98.5 – 104.5 or up to 104.5-101.5. Something that might be of concern to our customers. So where does the “+/-1.5†come from?
The +/-1.5 shift was introduced by Mikel Harry as most people are aware. Where did he get it? Harry refers to a paper written in 1975 by Evans, “Statistical Tolerancing: The State of the Art. Part 3. Shifts and Driftsâ€. The paper is about tolerancing. That is how the overall error in an assembly is effected by the errors in components. Evans refers to a paper by Bender in 1962, “Benderizing Tolerances – A Simple Practical Probablity Method for Handling Tolerances for Limit Stack Upsâ€. He looked at the classical situation with a stack of disks and how the overall error in the size of the stack, relates to errors in the individual disks. Based on “probability, approximations and experienceâ€, he suggests:
V = 1.5 * SQRT ( var X )
What has this got to do with monitoring the myriad of processes that people are concerned about? Very little. Harry then takes things a step further. Imagine a process where 5 samples are taken every half hour and plotted on a control chart. Harry considered the “instantaneous†initial 5 samples as being “short term†(Harry’s n=5) and the samples throughout the day as being “long term†(Harry’s g=50 points). Because of random variation in the first 5 points, the mean of the initial sample is different to the overall mean. Harry derived a relationship between the short term and long term capability, using the equation above, to produce a capability shift or “Z shift†of 1.5 ! Over time, the original meaning of “short term†and “long term†has been changed to result in “long term†drifting means.
Harry has clung tenaciously to the “1.5†but over the years, it’s derivation has been modified. In a recent note from Harry “We employed the value of 1.5 since no other empirical information was available at the time of reporting.†In other words, 1.5 has now become an empirical rather than theoretical value. A further softening from Harry: “… the 1.5 constant would not be needed as an approximationâ€.
Despite this, industry has fixed on the idea that it is impossible to keep processes on target. No matter what is done, process means will drift by +/-1.5 sigma. In other words, suppose a process has a target value of 10.0, and control limits work out to be, say, 13.0 and 7.0. "Long term" the mean will drift to 11.5 (or 8.5), with control limits changing to 14.5 and 8.5. This is nonsense.
The simple truth is that any process where the mean changes by 1.5 sigma or any other amount, is not in statistical control. Such a change can often be detected by a trend on a control chart. A process that is not in control is not predictable. It may begin to produce defects, no matter where specification limits have been set.
World Class Quality means “On target with minimum variation†.
9/21/2006
I agree with the previous response, that a process that drifts is not in statistical control. I have always had an issue with this aspect of Six Sigma, why is it that they do not wish to identify and eliminate the special causes that result in unwanted shifts in the mean? I guess in real world processes there are always changes that can occur that result in targeting variation, such as tool variation, tool regrind variation, material variation, temperature variation, etc. In practice, to identify and eliminate these things would be an expensive and time consuming effort. The appropriate way to react to these when using SPC would be to allow modified control limits on the x bar chart (assuming the range chart was in control)and perhaps suspending the use of some of the out of control rules as long as the capability of the process was sufficient to allow this. As for the 1.5 number used by Bender in statistical tolerancing, it is a "safety factor" that is applied to the square root of the sum of the squares of the component tolerances to account for the fact that most real world processes are not always nominally targeted, normally distributed, or statistically in control. Bender understood this, and recommended a safety factor between 1.0 and 1.5 to account for the risk. When I worked at GM in the late 80's, our plant used 1.25 as a standard safety factor when using the Bender method or statistical tolerancing.