Six Sigma was originally developed as a set of practices designed to improve manufacturing processes and eliminate defects, but its application was subsequently extended to other types of business processes as well.^[2] In Six Sigma, a defect is defined as anything that could lead to customer dissatisfaction.

The particulars of the methodology were first formulated by Bill Smith at Motorola in 1986.^[3] Six Sigma was heavily inspired by six preceding decades of quality improvement methodologies such as quality control, TQM, and Zero Defects, based on the work of pioneers such as Shewhart, Deming, Juran, Ishikawa, Taguchi and others.

Like its predecessors, Six Sigma asserts that –

• Continuous efforts to achieve stable and predictable process results (i.e. reduce process variation) are of vital importance to business success.
• Manufacturing and business processes have characteristics that can be measured, analyzed, improved and controlled.
• Achieving sustained quality improvement requires commitment from the entire organization, particularly from top-level management.

Features that set Six Sigma apart from previous quality improvement initiatives include –

• A clear focus on achieving measurable and quantifiable financial returns from any Six Sigma project.^[1]
• An increased emphasis on strong and passionate management leadership and support.^[1]
• A special infrastructure of "Champions," "Master Black Belts," "Black Belts," etc. to lead and implement the Six Sigma approach.^[1]
• A clear commitment to making decisions on the basis of verifiable data, rather than assumptions and guesswork.^[1]

The term "Six Sigma" is derived from a field of statistics known as process capability studies. Originally, it referred to the ability of manufacturing processes to produce a very high proportion of output within specification. Processes that operate with "six sigma quality" over the short term are assumed to produce long-term defect levels below 3.4 defects per million opportunities (DPMO).^[4][5] Six Sigma's implicit goal is to improve all processes to that level of quality or better.

Six Sigma is a registered service mark and trademark of Motorola, Inc.^[6] Motorola has reported over US$17 billion in savings^[7] from Six Sigma as of 2006.

Other early adopters of Six Sigma who achieved well-publicized success include Honeywell International (previously known as Allied Signal) and General Electric, where the method was introduced by Jack Welch.^[8] By the late 1990s, about two-thirds of the Fortune 500 organizations had begun Six Sigma initiatives with the aim of reducing costs and improving quality.^[9]

In recent years, Six Sigma has sometimes been combined with lean manufacturing to yield a methodology named Lean Six Sigma.

Origin and meaning of the term "six sigma process"

The following outlines the statistical background of the term Six Sigma.

Sigma (the lower-case Greek letter σ) is used to represent the standard deviation (a measure of variation) of a statistical population. The term "six sigma process" comes from the notion that if one has six standard deviations between the mean of a process and the nearest specification limit, there will be practically no items that fail to meet the specifications.^[5] This is based on the calculation method employed in a process capability study.

In a capability study, the number of standard deviations between the process mean and the nearest specification limit is given in sigma units. As process standard deviation goes up, or the mean of the process moves away from the center of the tolerance, fewer standard deviations will fit between the mean and the nearest specification limit, decreasing the sigma number.^[5]

Experience has shown that in the long term, processes usually do not perform as well as they do in the short.^[5] As a result, the number of sigmas that will fit between the process mean and the nearest specification limit is likely to drop over time, compared to an initial short-term study.^[5] To account for this real-life increase in process variation over time, an empirically-based 1.5 sigma shift is introduced into the calculation.^[10][5] According to this idea, a process that fits six sigmas between the process mean and the nearest specification limit in a short-term study will in the long term only fit 4.5 sigmas – either because the process mean will move over time, or because the long-term standard deviation of the process will be greater than that observed in the short term, or both.^[5]

Hence the widely accepted definition of a six sigma process is one that produces 3.4 defective parts per million opportunities (DPMO).^[11] This is based on the fact that a process that is normally distributed will have 3.4 parts per million beyond a point that is 4.5 standard deviations above or below the mean (one-sided capability study).^[5] So the 3.4 DPMO of a "Six Sigma" process in fact corresponds to 4.5 sigmas, namely 6 sigmas minus the 1.5 sigma shift introduced to account for long-term variation.^[5] This is designed to prevent underestimation of the defect levels likely to be encountered in real-life operation.^[5]

Methodology

Six Sigma has two key methodologies: ^[9] DMAIC and DMADV, both inspired by Deming's Plan-Do-Check-Act Cycle. DMAIC is used to improve an existing business process; DMADV is used to create new product or process designs.^[9]

DMAIC

The basic methodology consists of the following five steps:

• Define process improvement goals that are consistent with customer demands and the enterprise strategy.
• Measure key aspects of the current process and collect relevant data.
• Analyze the data to verify cause-and-effect relationships. Determine what the relationships are, and attempt to ensure that all factors have been considered.
• Improve or optimize the process based upon data analysis using techniques like Design of Experiments.
• Control to ensure that any deviations from target are corrected before they result in defects. Set up pilot runs to establish process capability, move on to production, set up control mechanisms and continuously monitor the proc

DMADV

The basic methodology consists of the following five steps:

• Define design goals that are consistent with customer demands and the enterprise strategy.
• Measure and identify CTQs (characteristics that are Critical To Quality), product capabilities, production process capability, and risks.
• Analyze to develop and design alternatives, create a high-level design and evaluate design capability to select the best design.
• Design details, optimize the design, and plan for design verification. This phase may require simulations.
• Verify the design, set up pilot runs, implement the production process and hand it over to the process owners.

DMADV is also known as DFSS, an abbreviation of "Design For Six Sigma".^[9

Implementation roles

One of the key innovations of Six Sigma is the professionalizing of quality management functions. Prior to Six Sigma, quality management in practice was largely relegated to the production floor and to statisticians in a separate quality department. Six Sigma borrows martial arts ranking terminology to define a hierarchy (and career path) that cuts across all business functions and a promotion path straight into the executive suite.

Six Sigma identifies several key roles for its successful implementation.^[12]

• Executive Leadership includes the CEO and other members of top management. They are responsible for setting up a vision for Six Sigma implementation. They also empower the other role holders with the freedom and resources to explore new ideas for breakthrough improvements.
• Champions are responsible for Six Sigma implementation across the organization in an integrated manner. The Executive Leadership draws them from upper management. Champions also act as mentors to Black Belts.
• Master Black Belts, identified by champions, act as in-house coaches on Six Sigma. They devote 100% of their time to Six Sigma. They assist champions and guide Black Belts and Green Belts. Apart from statistical tasks, their time is spent on ensuring consistent application of Six Sigma across various functions and departments.
• Black Belts operate under Master Black Belts to apply Six Sigma methodology to specific projects. They devote 100% of their time to Six Sigma. They primarily focus on Six Sigma project execution, whereas Champions and Master Black Belts focus on identifying projects/functions for Six Sigma.
• Green Belts are the employees who take up Six Sigma implementation along with their other job responsibilities. They operate under the guidance of Black Belts.

Quality management methods used in Six Sigma

Six Sigma makes use of a great number of established quality management methods that are also used outside of Six Sigma. The following table shows an overview of the main methods used.

Example

The following example demonstrates the basic process:

• My car will not start. (the problem)

1. Why? - The battery is dead. (first why)
2. Why? - The alternator is not functioning. (second why)
3. Why? - The alternator belt has broken. (third why)
4. Why? - The alternator belt was well beyond its useful service life and has never been replaced. (fourth why)
5. Why? - I have not been maintaining my car according to the recommended service schedule. (fifth why, root cause)

The questioning for this example could be taken further to a sixth, seventh, or even greater level. This would be legitimate, as the "five" in 5 Whys is not gospel; rather, it is postulated that five iterations of asking why is generally sufficient to get to a root cause. The real key is to encourage the troubleshooter to avoid assumptions and logic traps and instead to trace the chain of causality in direct increments from the effect through any layers of abstraction to a root cause that still has some connection to the original problem.

Analysis of variance

In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance is partitioned into components due to different explanatory variables. The initial techniques of the analysis of variance were developed by the statistician and geneticist R. A. Fisher in the 1920s and 1930s, and is sometimes known as Fisher's ANOVA or Fisher's analysis of variance, due to the use of Fisher's F-distribution as part of the test of statistical significance.

ANOVA Gauge R&R (or ANOVA Gauge Repeatability & Reproducibility) is a Measurement Systems Analysis technique which uses Analysis of Variance (ANOVA) random effects model to assess a measurement system.