# Lean Six Sigma

## (6σ)

Six Sigma () is a set of techniques and tools for process improvement. It was introduced by engineer Bill Smith while working at Motorola in 1986.  Jack Welch made it central to his business strategy at General Electric in 1995.  It seeks to improve the quality of the output of a process by identifying and removing the causes of defects and minimizing variability in manufacturing and business processes.  It uses a set of quality management methods, mainly empirical, statistical methods, and creates a special infrastructure of people within the organization who are experts in these methods. Each Six Sigma project carried out within an organization follows a defined sequence of steps and has specific value targets, for example: reduce process cycle time, reduce pollution, reduce costs, increase customer satisfaction, and increase profits.

The term Six Sigma (capitalized because it was written that way when registered as a Motorola trademark on December 28, 1993) originated from terminology associated with statistical modeling of manufacturing processes.  The maturity of a manufacturing process can be described by a sigma rating indicating its yield or the percentage of defect-free products it creates. A six sigma process is one in which 99.99966% of all opportunities to produce some feature of a part are statistically expected to be free of defects (3.4 defective features per million opportunities). Motorola set a goal of “six sigma” for all of its manufacturing operations, and this goal became a by-word for the management and engineering practices used to achieve it.

Six Sigma doctrine asserts:

• Continuous efforts to achieve stable and predictable process results (e.g. by reducing process variation) of vital importance to business success.
• Manufacturing and business processes have characteristics that can be defined, 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.
• An increased emphasis on strong and passionate management leadership and support.
• A clear commitment to making decisions on the basis of verifiable data and statistical methods, rather than assumptions and guesswork.

The term “six sigma” comes from statistics and is used in statistical quality management, which evaluates process capability.  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). The 3.4 DPMO is based on a shift of +/- 1.5 sigma … based on the tolerance in the height of a stack of discs. Six Sigma’s implicit goal is to improve all processes, but not to the 3.4 DPMO level necessarily. Organizations need to determine an appropriate sigma level for each of their most important processes and strive to achieve these. As a result of this goal, it is incumbent on management of the organization to prioritize areas of improvement.

In recent years, some practitioners have combined Six Sigma ideas with lean manufacturing to create a methodology named Lean Six Sigma.  The Lean Six Sigma methodology views lean manufacturing, which addresses process flow and waste issues, and Six Sigma, with its focus on variation and design, as complementary disciplines aimed at promoting “business and operational excellence”.  It serves as a foundation for innovation throughout the organization, from manufacturing and software development to sales and service delivery functions.

## Methodologies

Lean management and Six Sigma are two concepts which share similar methodologies and tools. Both programs are Japanese influenced, but they are two different programs. Lean management is focused on eliminating waste and ensuring efficiency while Six Sigma’s focus is on eliminating defects and reducing variability.  Six Sigma projects follow two project methodologies inspired by Deming’s Wheel Cycle (Plan, Do, Check, Act). These methodologies, composed of five phases each, bear the acronyms DMAIC and DMADV.

• DMAIC  is used for projects aimed at improving an existing business process (improve/control).
• DMADV  is used for projects aimed at creating new product or process designs. (design/verify).

### DMAIC

The DMAIC project methodology has five phases:

• Define the system, the voice of the customer and their requirements, and the project goals, specifically.
• Measure key aspects of the current process and collect relevant data; calculate the ‘as-is’ Process Capability.
• Analyze the data to investigate and verify cause-and-effect relationships. Determine what the relationships are, and attempt to ensure that all factors have been considered. Seek out root cause of the defect under investigation.
• Improve or optimize the current process based upon data analysis using techniques such as design of experiments, poka yoke or mistake proofing, and standard work to create a new, future state process. Set up pilot runs to establish process capability.
• Control the future state process to ensure that any deviations from the target are corrected before they result in defects. Implement control systems such as statistical process control, production boards, visual workplaces, and continuously monitor the process. This process is repeated until the desired quality level is obtained.

### DMADV

The DMADV project methodology, known as DFSS (“Design For Six Sigma”), features five phases:

• Define design goals that are consistent with customer demands and the enterprise strategy.
• Measure and identify CTQs (characteristics that are Critical TQuality), measure product capabilities, production process capability, and measure risks.
• Analyze to develop and design alternatives
• Design an improved alternative, best suited per analysis in the previous step
• Verify the design, set up pilot runs, implement the production process and hand it over to the process owner(s).

## Implementation roles

One key innovation of Six Sigma involves the absolute “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. Formal Six Sigma programs adopt a kind of elite ranking terminology (similar to some martial arts systems, like judo) to define a hierarchy (and special career path) that includes all business functions and levels.

Six Sigma identifies several key roles for its successful implementation.

• 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 by transcending departmental barriers and overcoming inherent resistance to change.
• Champions take responsibility 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, they spend their time 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 valued time to Six Sigma. They primarily focus on Six Sigma project execution and special leadership with special tasks, 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, operating under the guidance of Black Belts.

According to proponents of the system, special training is needed for all of these practitioners to ensure that they follow the methodology and use the data-driven approach correctly.

Some organizations use additional belt colours, such as Yellow Belts, for employees that have basic training in Six Sigma tools and generally participate in projects and “White belts” for those locally trained in the concepts but do not participate in the project team. “Orange belts” are also mentioned to be used for special cases.

### Certification

General Electric and Motorola developed certification programs as part of their Six Sigma implementation, verifying individuals’ command of the Six Sigma methods at the relevant skill level (Green Belt, Black Belt etc.). Following this approach, many organizations in the 1990;s started offering Six Sigma certifications to their employees. Criteria for Green Belt and Black Belt certification vary; some companies simply require participation in a course and a Six Sigma project.  There is no standard certification body, and different certification services are offered by various quality associations and other providers against a fee.

## Etymology of “six sigma process”

The term “six sigma process” comes from the notion that if one has six standard deviations between the process mean the nearest specification limit.  Capability studies measure the number of standard deviations between the process mean and the nearest specification limit in sigma units, represented by the Greek letter σ (sigma). 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 and increasing the likelihood of items outside specification. One should also note that calculation of Sigma levels for a process data is independent of the data being normally distributed. In one of the criticisms to Six Sigma, practitioners using this approach spend a lot of time transforming data from non-normal to normal using transformation techniques. It must be said that Sigma levels can be determined for process data that has evidence of non-normality.

Graph of the normal distribution, which underlies the statistical assumptions of the Six Sigma model. In the center at 0, the Greek letter µ (mu) marks the mean, with the horizontal axis showing distance from the mean, marked in standard deviations and given the letter σ (sigma). The greater the standard deviation, the greater is the spread of values encountered. For the green curve shown above, µ = 0 and σ = 1. The upper and lower specification limits (marked USL and LSL) are at a distance of 6σ from the mean. Because of the properties of the normal distribution, values lying that far away from the mean are extremely unlikely: approximately 1 in a billion too low, and the same too high. Even if the mean were to move right or left by 1.5σ at some point in the future (1.5 sigma shift, colored red and blue), there is still a good safety cushion. This is why Six Sigma aims to have processes where the mean is at least 6σ away from the nearest specification limit.

## Role of the 1.5 sigma shift

Experience has shown that processes usually do not perform as well in the long term as they do in the short term.  As a result, the number of sigmas that will fit between the process mean and the nearest specification limit may well drop over time, compared to an initial short-term study.  To account for this real-life increase in process variation over time, an empirically based 1.5 sigma shift is introduced into the calculation.  According to this idea, a process that fits 6 sigma between the process mean and the nearest specification limit in a short-term study will in the long term fit only 4.5 sigma – 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.

Hence the widely accepted definition of a six sigma process is a process that produces 3.4 Defective Parts Per Million Opportunities (DPMO). This is based on the fact that a process that is normally distributed will have 3.4 parts per million outside the limits, when the limits are six sigma from the “original” mean of zero and the process mean is then shifted by 1.5 sigma (and therefore, the six sigma limits are no longer symmetrical about the mean).  The former six sigma distribution, when under the effect of the 1.5 sigma shift, is commonly referred to as a 4.5 sigma process. The failure rate of a six sigma distribution with the mean shifted 1.5 sigma is not equivalent to the failure rate of a 4.5 sigma process with the mean centered on zero. This allows for the fact that special causes may result in a deterioration in process performance over time and is designed to prevent underestimation of the defect levels likely to be encountered in real-life operation.

The role of the sigma shift is mainly academic. The purpose of six sigma is to generate organizational performance improvement. It is up to the organization to determine, based on customer expectations, what the appropriate sigma level of a process is. The purpose of the sigma value is as a comparative figure to determine whether a process is improving, deteriorating, stagnant or non-competitive with others in the same business. Six sigma (3.4 DPMO) is not the goal of all processes.

Sigma levels:  A control chart depicts a process that experienced a 1.5 sigma drift in the process mean toward the upper specification limit starting at midnight. Control charts are used to maintain 6 sigma quality by signaling when quality professionals should investigate a process to find and eliminate special-cause variation.  The table below gives long-term DPMO values corresponding to various short-term sigma levels.

These figures assume that the process mean will shift by 1.5 sigma toward the side with the critical specification limit. In other words, they assume that after the initial study determining the short-term sigma level, the long-term value will turn out to be 0.5 less than the short-term value.  Note that the defect percentages indicate only defects exceeding the specification limit to which the process mean is nearest. Defects beyond the far specification limit are not included in the percentages.  The formula used here to calculate the DPMO is thus:

{\displaystyle DPMO=1,000,000\centerdot (1-\phi (level-1.5))}
Sigma level Sigma (with 1.5σ shift) DPMO Percent defective Percentage yield Short-term Cpk Long-term Cpk
1 −0.5 691,462 69% 31% 0.33 −0.17
2 0.5 308,538 31% 69% 0.67 0.17
3 1.5 66,807 6.7% 93.3% 1.00 0.5
4 2.5 6,210 0.62% 99.38% 1.33 0.83
5 3.5 233 0.023% 99.977% 1.67 1.17
6 4.5 3.4 0.00034% 99.99966% 2.00 1.5
7 5.5 0.019 0.0000019% 99.9999981% 2.33 1.83

## Application

Six Sigma mostly finds application in large organizations. An important factor in the spread of Six Sigma was GE’s 1998 announcement of $350 million in savings thanks to Six Sigma, a figure that later grew to more than$1 billion.  Six Sigma however contains a large number of tools and techniques that work well in small to mid-size organizations. The fact that an organization is not big enough to be able to afford Black Belts does not diminish its abilities to make improvements using this set of tools and techniques. The infrastructure described as necessary to support Six Sigma is a result of the size of the organization rather than a requirement of Six Sigma itself.  Although the scope of Six Sigma differs depending on where it is implemented, it can successfully deliver its benefits to different applications.

Manufacturing:  After its first application at Motorola in the late 1980;s, other internationally recognized firms currently recorded high number of savings after applying Six Sigma. Examples of these are Johnson and Johnson, with $600 million of reported savings, Texas Instruments, which saved over$500 million as well as Telefonica de Espana, which reported \$30 million euros of revenue in the first 10 months.

Engineering and Construction:  Although companies have considered common quality control and process improvement strategies, there’s still a need for more reasonable and effective methods as all the desired standards and client satisfaction have not always been reached.

Finance:  Six Sigma has played an important role by improving accuracy of allocation of cash to reduce bank charges, automatic payments, improving accuracy of reporting, reducing documentary credits defects, reducing check collection defects, and reducing variation in collector performance.

Supply Chain:  In this field, it important to ensure that products are delivered to clients at the right time while preserving high-quality standards from the beginning to the end of the supply chain. By changing the schematic diagram for the supply chain, Six Sigma can ensure quality control on products (defect free) and guarantee delivery deadlines, which are the two major issues involved in the supply chain.

Healthcare:  This is a sector that has been highly matched with this doctrine for many years because of the nature of zero tolerance for mistakes and potential for reducing medical errors involved in healthcare. The goal of Six Sigma in healthcare is broad and includes reducing the inventory of equipment that brings extra costs, altering the process of healthcare delivery in order to make more efficient and refining reimbursements.

The 1.5 sigma shift has also become contentious because it results in stated “sigma levels” that reflect short-term rather than long-term performance: a process that has long-term defect levels corresponding to 4.5 sigma performance is, by Six Sigma convention, described as a “six sigma process.” The accepted Six Sigma scoring system thus cannot be equated to actual normal distribution probabilities for the stated number of standard deviations, and this has been a key bone of contention over how Six Sigma measures are defined. The fact that it is rarely explained that a “6 sigma” process will have long-term defect rates corresponding to 4.5 sigma performance rather than actual 6 sigma performance has led several commentators to express the opinion that Six Sigma may lack merit.