‘Sick’ Sigma and zero defects

Two recent articles in Quality Digest received a lot of comments. The articles are here:

Sick Sigma

Zero Defects

Here are my comments (1).

Re: Sick Sigma

Dr. Burns questions the origin of the 1.5 drift that is part of a six sigma process and pretty much implies that having a 1.5 sigma bias is intended as part of six sigma. Does he really believe that someone will build in a 1.5 sigma bias into their product to conform to six sigma? He then goes on to talk about control limits. This is irrelevant with respect to attribute defects in many cases, such as in medical errors. One can have attribute control limits, say to control the proportion of bad pixels in an LCD screen. But for wrong site surgery, control limits make no sense since the allowable number of defects is zero. Yet, one can still count defects and relate them to six sigma terms, and improve the process until the observed defect rate is zero.


Dr Tony Burns responds

Unfortunately there are hundreds of thousands of people who do build in the 1.5 sigma bias. There are millions of people using 3.4 ppm based on the 1.5 drift. A quick google search revealed a quarter of a million sites promoting averages unavoidably drifting by 1.5 sigma. It all started with a theoretical error by Mikel Harry, that no one bothered to check. The erroneous theoretical drift over 24 hours then became an empirical “long term” drift. The 1.5 drift is nonsense. It has set the quality world backwards by many years. World class quality can only be “on target with minimum variation”.

You are mistaken. Control limits do apply to attribute data. Attribute control charts are of 4 main types, “pn”, “p”, “c”, “u”. I suggest that you read any basic text on Statistical Process Control (SPC), such as “Analysis of Control and Variation” by John McConnell. Before speaking to your clients, I would strongly suggest reading more advanced texts such as Don Wheeler’s “Understanding SPC” and “Advanced Topics in SPC”. In the example that you quote, either a pn, p or an XmR chart might be used, depending on the details of the situation. The texts mentioned above will describe how to calculate and draw the appropriate control limits.

Jan replies

Thanks for your reply.

 As for people actually building in the bias, this is not my experience. I’m not sure how you can come to your conclusion from a Google search.

 Yes, you are right about control charts for attribute data. Perhaps I got carried away. But my point was based on reading your article. Let me state it differently. If one is producing LCD screens, one can set up attribute charts to control the number (or proportion) of bad pixels in a screen. But in my area of interest – medical errors – one does not do this. For example, the proportion of wrong site surgeries has been estimated at 0.00085%. This not an acceptable rate (which of course is zero) so there is no control chart that one can set up as one does not wish to control to an acceptable level of defects (e.g., >0). One continues to measure the rate and improve the process until one is observing a rate of zero. (After which, one still measures but does not change the process.) Six Sigma is sometimes used as a benchmark in medical error opinion articles. That is, one would rather have a six sigma than a three sigma process since less medical errors are implied. But for serious medical errors, a six sigma process is unacceptable.

 As it turns out, I am not a fan of Six Sigma and I am suspicious of all of these people who have no experience analyzing data all of a sudden becoming experts (black belts).

Dr Tony Burns responds

Regarding six sigma’s 1.5 sigma bias, perhaps I should explain further.  Anyone who is using six sigma tables to calculate a “sigma level” for a process, is making the assumption of a 1.5 sigma bias.  Anyone quoting 3.4 DPMO has assumed the erroneous 1.5 sigma drift in averages.  Not only is the bias fallacious, but the assumption of process normality used in six sigma tables is grossly in error, as is using counts at the extreme tail of any distribution as an estimator of the distribution’s dispersion (sigma).  I have drafted a second paper “Tail Wagging It’s Dog” that has been submitted to Quality Digest, which describes the latter in more detail.  You may wish to read more in the various papers referenced at our site http://www.q-skills.com/sixsigtools.htm


Attribute control charts can fortunately still come to the rescue, even with rare events such as you suggest. Chapter 11.9 “Advanced topics in SPC” gives a lovely example of how to use an XmR chart for this purpose.  Zero wrong site surgeries may be a desirable target but chaos, human error and variation will inevitably occur, even in the most ideal system.


Comparisons such as “… rather have a six sigma than a three sigma process since …” are meaningless. Six sigma relates to the specification, that is, the voice of the customer.  Three sigma relates to the voice of the process. The specification may be set at any level you wish, four, five, six, seven sigma, whatever. The voice of the process is always three sigma. 


I won’t get started on black belts.  I feel quite sorry for these unfortunate people who are grabbed from the shop floor and expected to become overnight statisticians and process magicians.  It baffles me how they can be expected to understand Students-T and Box Wilson experimental design, when they clearly don’t understand the even the meaning of sigma.

Jan replies

Well, I don’t belong to the “anyone” group, lol cause I don’t assume a 1.5 sigma bias when I calculate DPMO, but I get it and agree with you about the origin of the 1.5 sigma bias. This has always been mysterious to me – the 1.5 bias and Normal assumptions, because one can always calculate DPMO, without knowing anything about Six Sigma (or assumptions about the data) yet one can relate DMPO to the defects expressed by a table (e.g., 6 sigma = 3.4, 5 sigma=I forgot the number, etc.). So in this sense, six sigma is just a level of desirability with six sigma = very good, five sigma = pretty good, etc.

My other point was mainly to express the fact that one does not use quality control rules for a process whose desired defect level is zero. I realize that defects still may occur. So one uses risk analysis tools such as fault trees and calculates probability of failure events. If the probability of a failure event is low enough (the goal is never zero), then one can have both acceptable risk and zero defects (zero not theoretically, but zero for practical purposes – e.g., one failure event in the next million years).

I will look at your web site and thanks for stimulating me to think about things more.

Dr Tony Burns responds  

Being able to compare processes by quoting a “sigma level” is appealing to management, however it simply doesn’t work.  For example, consider comparing two processes, one of which has a histogram skewed to the left and the other to the right. They may both appear “very good” with an assumption of normality, however one might be far more poorly controlled than the other.  The situation is even worse because defects counts and “sigma levels” give no indication of process capability.  A process can only be “capable” (of producing product or service within specification) that is, “very good”, if it is “in-control”.  If the process average is drifting, as assumed in six sigma, the process is out of control and therefore unpredictable.  An unpredictable process is certainly not a “very good” thing.  Only control charts and histograms can give this information.


Thank you for your final comment.  My aim is to encourage people to question the accepted norms (no pun intended) rather than to accept them blindly.

Re: Zero Defects

Mr. Crosby would have us believe that a zero defects program is inexpensive, especially compared to six sigma. Well, I remember spending 5 days in Corning, NY as part of Total Quality training (which included zero defects, a la Crosby). Everyone in our company (Corning Medical, Medfield, MA) received training in quality. The cost of this program across Corning must have been substantial.

Mr. Crosby also talks about the zero defects concept as “Work right the first time and every time” and the performance standard is that “No defects are acceptable.” This gives one the impression that without this program, inept engineers and production staff are creating poor quality products and if only they had this quality training … . Well, things aren’t that simple. The number of defects in a design relate to the state of knowledge of the technology. No defects are possible when the state of knowledge is high. However, for many systems, the state of knowledge is not high enough to design a product with no defects and a common and efficient development process is to go through a test and improvement loop until the number of problems reaches an acceptable level and this number is not zero.


Well I realize that in my comments about Sick Sigma I talk about processes whose defect rate should be zero (e.g., wrong site surgery) and in the comments about “Zero Defects” I talk about processes with allowable defects rates greater than zero (e.g., proportion of bad pixels in an LCD screen) but that’s the real world.


  1. Sick sigma comments amended after an email from Dr. Burns, the article’s author, since I had provided comments to the journal in which his article appeared.



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