Setting the Stage
To this day, some industry professionals are still perplexed by Six Sigma, especially when it comes to using the 1.5 sigma shift, often referred to as the shift factor. In this context, the shift factor has been the subject of many quality articles, books and forum discussions. In spite of all this, the theoretical basis and practical use of the shift factor is still largely misunderstood. This is particularly true among quality professionals, process improvement specialists and a host of so-called subject-matter-experts within the field of Six Sigma.
So why does such confusion exist? Well, it’s mainly a matter of application context. The shift factor was originally created to facilitate and augment the engineering analysis of a product design configuration, not the statistical control and monitoring of its corresponding processes. For a great many practitioners in the field of Six Sigma, this point is frequently overlooked, not known or largely ignored.
To this point, the continued propagation of such misguided understandings of the shift factor is akin to the age old saying: “When all you have is a hammer, everything looks like a nail.” This is to say that quality professionals are largely process-centric when it comes to quality improvement, not design-centric. Owing to this, their body-of-knowledge is founded on the statistical tools of process control and improvement, not the tools commonly associated with product design analysis and optimization. In this regard, their tool box only contains a wide range of hammers, so to speak.
Context is Everything
To the latter point, we should consider the thoughts of Donald J. Wheeler, as he is one of the world’s foremost experts on the subject of statistical process control (SPC) and monitoring (SPM). In Dr. Wheeler’s treatise entitled “The Six Sigma Zone,” he stated: “The objective of having a process operate with a capability index of 1.5 to 2.0 is a reasonable and economic objective.” Certainly, this writer and researcher is delighted to see that Dr. Wheeler was able to confirm what we initially established at Motorola over 30 years ago – a process capability of Six Sigma is reasonable and economic to operate, especially when compared to less capable processes.
Let’s consider another key point that Dr. Wheeler makes in The Six Sigma Zone: “A process operated with the benefit of an efficient mechanism for monitoring the process location will occasionally drift off center.” He latter says: “However, in the absence of an efficient mechanism for monitoring the process location, there is no limit on the size of the shifts that can occur.” Here again, Dr. Wheeler merely reaffirms what has already been discovered by Walter A. Shewhart. Mr. Shewhart discovered and demonstrated many of these foundational understandings while working at Bell Laboratories in the early 1920’s.
In today’s world of quality and process improvement, Dr. Wheeler’s points (see above quotations) are fully self-evident to even the most novice practitioner. It goes without saying that, without some type of effective control system, a process cannot be expected to operate within a statistically predictable range of performance (to any degree of decision certainty).
Considering the Source
Although Dr. Wheeler is greatly admired by this writer and is unquestionably a global expert in his field, he has little experience (if any) in design engineering or business management, especially when it comes to the theory and practice of concurrent engineering methods. Owing to this, it’s only logical that his academic-like publications are built around a framework of statistical process control and monitoring (SPC and SPM). This is most evident from the nature of Dr. Wheeler’s books and articles.
In spite of this; and without any attempt to discuss his reasoning with this author and co-creator of Six Sigma, he prematurely labeled the 1.5 sigma shift as “goofy” because of its seemingly arbitrary and unfounded nature. Here again, when all you have is a hammer, everything looks like a nail. Using Dr. Wheeler’s logic, it would be said that if it doesn’t look like a nail, then someone used the wrong type of fastener. Of course, the hammer is never suspect.
In Dr. Wheeler’s treatise on the subject he also stated:
“The common practice of listing these recomputed values along with the original unshifted capability indexes has generated many questions about the origin of the “goofy” DPM numbers found in the six-sigma literature. Thus the third problem with the six-sigma parts-per-million values is their dependence upon the assumption that a 1.5 standard deviation shift in location is a worst-case scenario. Not only is this incorrect, it is actually the opposite of the truth.”
Breaking It Down
For purposes of the ensuing discussion, we’ll employ a very simple production scenario. In this way, the reader can intake the author’s comments in a more intuitive and palatable way. To do this, we’ll first say that each of the components that comprise a particular product design have been assigned a symmetrical bilateral specification by a certain design engineer. We shall also say that each of the design components were all known to be normally distributed and statistically stable within and between sampling subgroups, where each subgroup consisted of N=4 observations.
Of interest, Dr. Wheeler would be absolutely correct in saying that the shift factor is a best-case scenario – assuming the related process is not governed by a statistical means of control, such as SPC charts. This is to say that the process centering condition of each sampling subgroup would be subject to the influence of both random and assignable causes. Under this assumption, the shift factor could theoretically extend to infinity for any given subgroup. Owing to this, it would not be possible to establish a meaningful worst-case condition.
However, recall that the conversational scenario is related to a process that is operating in a state of statistical control. In this situation, the shift factor would be considered a worst-case condition. This is because only random causes would influence the resulting performance measurements, not assignable causes. Consequently, the worst-case centering condition of a sampling subgroup would have to be encountered before any type of corrective action would be initiated. Shifts less than the worst-case condition would require no action.
While this seemingly molecular discussion might be viewed as an academic exercise in “he said, she said” among the experts, it takes on great meaning during the course of product configuration, analysis and optimization. To perform such tasks, design engineers often select Monte Carlo simulation as their tool of choice. As many know, the mechanics associated with this type of simulation rely on a random model. Thus, for purposes of a design simulation, the shift factor would be rightfully deployed as a statistical worst-case case centering condition.
At this point, the design engineer would contrast the best-case simulation (all component means located on target) to the worst-case simulation (all component means off-set from their respective targets by a factor of 1.5 sigma, but done so in their respective worst-case direction). Through such contrasts, the design engineer can gain better insights into such things as design robustness and component sensitivities.
As previously stated, the origins of the 1.5 sigma shift factor have little to do with SPC, but have much to do with product design and reliability engineering. In other words, the shift factor was born in the arena of design engineering and optimization, not the pasture of process control and monitoring. This point cannot be overstated or overused. It’s the crux of the issue. In order to fully grasp and better understand the true import of the shift factor, one must change his or her context of reasoning, not the context of the tool. Again, this means reasoning from a design configuration and optimization point of view, not a process control perspective.
Along these lines, this writer remembers a time (back on the ranch) when his daughter was inspecting her horse’s leg in the roping arena. At the same time, an angry cow got out of the pen and was bearing down on her. Fortunately, one of the cowboys shouted at her to get out of the way, but before he finished yelling the message, another cowboy diverted the cow’s attention. Quite surprised by all of the sudden yelling, my daughter responded: “What’s going on, there’s nothing wrong with my horse.” In a deep voice with a slow draw, the lead cowboy said to her: “Well, you might find out what’s wrong if you just turn your head a little.” It would seem we have far too many Six Sigma practitioners looking at their horse and not on what’s happening around them. This is often called the “Tunnel Vision.”
From a different perspective, it can be said that the shift factor was originally conceived as a means to inject a higher level of reality into the product design process. By employing the shift factor at certain specific points during the design cycle, product configurations and specifications can be made more functional, producible, reliable and robust while concurrently improving total production cost.
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Copyright 2013 Dr. Mikel J. Harry, Ltd.