Pei-Chi Chiu　|　February 23, 2023

What exactly is the standard deviation?

The standard deviation (SD) is a statistical term (its symbol is “σ,” pronounced “Sigma”).

The standard deviation is the statistical term used to describe the “variation” or “inconsistency” of a population.
In the past, most companies were accustomed to using the “average” to represent their performance — for example, average cost, average capacity, average delivery time, average wages, and so on. But this concealed many problems, one of the most important being that it ignored the degree of variation.

The reason the “standard deviation” is so valued today is precisely that it can be used to measure the variation in a product’s quality distribution.

And what is Six Sigma?

By its statistical definition, Six Sigma means that, under perfect conditions, out of every 1 billion measured values there are only 2 chances of a defect — that is, 2 PPB (Part Per Billion), which equates to a yield of 99.9999998%.

Companies often take great pride in stating that their yield reaches 99%, but 99% is only 3.8 sigma, meaning that out of every one million times there will be more than 6,000 errors — a figure that is truly alarming.

According to Harry’s (1978) research, in the United States an average quality level of 99% is equivalent to: (1) 20,000 pieces of mail lost per hour, equivalent to a 1% misdelivery rate; (2) 15 minutes per day during which the tap water supplied is unfit to drink; (3) 5,000 incorrect surgical diagnoses per week; (4) 7 hours of power outage per month.

Clearly, even though 99% may look quite perfect on paper, such a level is in fact not only far from excellent performance but cannot even meet the needs of our daily lives. So what about an average quality level of 99.9%?
Even though the “risk” has already dropped to one-tenth of the level described above, if a certain hospital declared that the average success rate for delivering newborns in its obstetrics department was 99.9%, most people would probably still not feel comfortable having that hospital deliver their baby!
We believe that in many such “no joking around” situations, people’s demands for yield are absolutely viewed with an almost “exacting” mindset.

Because technology management today has entered a stage where everything is discussed in terms of “nanometers” — meaning everything must be made as small and as fine as possible — it is hardly surprising that quality defects are scrutinized in terms of “number of nonconforming items per million” (ppm; part per million).

Thus, if a product’s quality follows a normal distribution and falls within 3 standard deviations on either side of the specification center value, then on each of the positive and negative sides of the mean μ there are 1,350 defects per million, for a total of 2,700 ppm. If some airline suddenly took it into its head to publicly claim that its flight safety rate could be “as high as” 99.73% — that is, about 2,700 accidents per one million takeoffs and landings — would you dare to fly with it?

Since pushing all the way to 3 standard deviations still cannot satisfy the demands of modern people, the only choice is to be even stricter, and so “Six Sigma” came into being.

In business practice, because a process is dynamic rather than static — that is, factors such as the process’s materials, personnel, environment, and tools are constantly undergoing small changes — the mean value shifts up and down accordingly.
Pushing to the “Six Sigma” quality level is equivalent to 99.99966% of products being acceptable — that is, only 3.4 defects per one million, or a defect count of 3.4 ppm (also called DPMO; defects per million opportunities).

What is “Six Sigma”? What does this term — which over the past decade has attracted the attention of business owners and Wall Street financial analysts to the tune of billions of dollars — represent? Six Sigma is a business strategy supported by a quality improvement program.

It uses tools such as statistics, problem elimination, and problem prevention to raise customer satisfaction to a perfect level of 99.999% by eliminating and preventing most of the errors in processes, products, services, documents, and decisions.

In addition, total quality management seeks to achieve customer satisfaction and the highest quality at the lowest cost, whereas Six Sigma provides a strategic approach to business improvement, aimed at increasing customer satisfaction and strengthening the company’s finances.

Six Sigma provides a set of operating methods, emphasizing a fundamental reduction in expenditure as well as measurable and documentable results.
Motorola’s Six Sigma
In 1985, Motorola discovered that its process center value and the specification center value could not coincide, with a shift of 1.5σ. Therefore Motorola assumed that the process mean was at a point shifted 1.5σ from the specification center value, with the upper and lower specification limits fixed at 6 times the standard deviation; the estimated number of nonconforming points beyond the upper and lower specification limits was 3.4 per million, i.e., 3.4 ppm, which was called the 6 sigma quality level.
Although Motorola called it 6σ management, the 6σ quality level Motorola actually achieved at that time was only a 4.5σ quality level, with a process capability index of Cpk = 1.5.
Therefore, the probability of a product falling outside specification was 3.4 ppm.

6 sigma management originated in 1986, when Motorola’s communications division was the first to adopt it, and the following year it was rolled out across the entire company; in 1987 Motorola formally launched the “Six Sigma Program.”
The then-CEO Bob Galvin declared that the 6s quality level would be achieved within five years.

Motorola University then launched a 6s training course focused on improving process and product quality, and in 1988 Motorola won the U.S. National Quality Award.

6 sigma is a management approach developed by Motorola in the 1980s. Six Sigma is not just a set of tools, but also a method of corporate transformation — a method driven jointly by communication, training, leadership, teamwork, collaboration, and a customer-centric focus.