How does d²σ compare to Six Sigma? To understand the difference one must first recognize that the term “Six Sigma” refers to a program and not to a literal process performance parameter. While it is true that the original goal of Six Sigma (when Motorola introduced the program) was ±6σ process performance, they did not achieve that goal with any degree of consistency. In fact, the published and accepted level of performance resulting from the implementation of a Six Sigma program is process performance at a one-sided 4.5σ level.

The distribution in Figure 1 illustrates ±6σ process performance. In this case, the distribution mean is both 6σ above the lower specification limit and 6σ below the upper specification limit. Assuming the process is stable (i.e., the mean does not drift over time, or from one run to the next), the maximum number of defects expected is 2 parts-per-billion.

In Figure 2, the red and yellow distributions illustrate the range of results expected from Six Sigma implementation. In this case, the process mean is unstable and varies + or - 1½σ from the engineering target (10 in this example). Many individuals will profess that a ±1½σ shift is a “normal” in manufacturing processes. We certainly disagree! While it may be “typical” in many manufacturing processes, it is in no way, shape, or form “normal.” A shift in a process mean is a consequence of incomplete process knowledge. That is, a shift results when manufacturers do not understand all of the process input/output relationships.

A typical Six Sigma program as illustrated in Figure 2 yields a defect rate of 3.4 parts-per-million. Do not be fooled by the similarity in the numbers representing the defect rates for Six Sigma and 6σ. The difference between the two rates is huge! In fact, 3.4 ppm is 1,700 times 2 ppb! The difference between a true 6σ process and a typical Six Sigma process is a multiplication factor of seventeen hundred!

Now that we have covered the difference between Six Sigma and 6σ, what level of performance can one expect from a d²σ process? Figure 3 illustrates a ±10σ process, the lowest level of performance that qualifies for the “d²” designation. If this process distribution is centered between the specification limits and stable, the resulting defect rate is essentially nil (for reference, 1 part-per-trillion occurs when process performance is slightly more than ±7σ). A d²σ condition is, for all practical purposes, a state of zero defects.

It would be a waste of effort and money to pursue a d²σ process for the sake of defect elimination alone, since a 7 or 8 sigma process would easily suffice in most applications. We do not advocate the pursuit of double-digit σ levels solely for defect reduction, nor as an end in itself. A d²σ process, however, often occurs as a natural consequence of process optimization and cost reduction efforts. A process with such extreme capability is frequently “set and forget” and is often the very least expensive way to run a process.