the essential six sigma - hec...

The essential Six Sigma Quality Progress; Milwaukee; Jan 2002; James M Lucas; Volume: 35 Issue: 1 Start Page: 27-31 ISSN: 0033524X Subject Terms: Total quality Quality standards Statistical process control Classification Codes: 5320: Quality control 9190: United States Geographic Names: United States Abstract: Six Sigma is a methodology for disciplined quality improvement. Because this quality improvement is a prime ingredient of total quality management (TQM), many companies find adding a Six Sigma program to their current business system gives them all or almost all the elements of TQM. Six Sigma is an opera-tional system that speeds up improvement by getting the right projects conducted in the right way. It drives out fear by making employees agents of change rather than resisters to change. It has been suc-cessful for the companies that have adopted it, and this success will encourage others to adopt it. Full Text: Copyright American Society for Quality Jan 2002 SIX SIGMA How successful Six Sigma implementation can improve the bottom line YOU CAN HARDLY pick up a news or business magazine these days without coming across an article about Six Sigma. It originated at Motorola in the early 1980s, and its implementation helped the company win the 1988 Malcolm Baldrige National Quality Award. Fundamentally, Six Sigma is a methodology for disciplined quality improvement. Because this quality improvement is a prime ingredient of total quality management (TQM), many companies find adding a Six Sigma program to their current business system gives them all or almost all the elements of TQM: [current business system] + [Six Sigma] = [total quality management (TOM)]. It is often much easier to add a disciplined quality improvement system, such as Six Sigma, to a company's current business system than it is to implement a TQM system. Simply put, Six Sigma uses a modified Shewhart cycle (the plan-do-check-act cycle often attributed to Deming) as its Breakthrough Strategy for its Americanized kaizen system. Joseph M. Juran's statement that "all quality improvement oc-curs on a project-by-project basis and in no other way"1 can be considered an essential element in the foundation of Six Sigma, though you seldom see this statement credited in Six Sigma literature. Operationally, Six Sigma is the methodology that gets more good improvement projects carried out. A major advantage of Six Sigma is it does not have "quality" or "statistics" in its name. It is perceived to be a business system that improves the bottom line and only brings in technical de-tails as needed; TQM is perceived to be a technical quality system owned by technical specialists rather than all employ-ees. Six Sigma's simple and effective management structure is one of its strengths; I could not describe the management structure

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used by TQM in such a succinct fashion. As an example of the operational effectiveness of Six Sigma, it is worthwhile to point out that GE's implementation is being widely imitated, while there was little copying of the kaizen program it tried to implement between 1988 and 1992. Six Sigma's heroic goal Six Sigma's goal is the near elimination of defects from any process, product or service-far beyond where virtually all companies are currently operating. The numerical goal is 3.4 defects per million opportunities (DPMO) while higher levels of defects are associated with lower sigma levels (see Table 1). This table, except for some changes in the defects per million column discussed in the sidebar, "Six Sigma and Defects per Million Opportunities" (p. 30) reproduces Table 1 from an article by Mikel J. Harry.2 Harry does not reference the cost of poor quality (COPQ) information shown in the table, but the goal does not seem unrealistic. Juran gave similar numbers when he estimated that, "in the United States, close to a third of the work done consisted of redoing what had been done before. Depending on the nature of the industry, the COPQ consumed between 20 and 40% of the total effort."3 Setting goals involving DPMO uses an easily understood metric that handles both counts and continuous variables (whatever their distribution) critical to quality (CTQ). The identification of CTQ variables is one of the first steps carried out after a Six Sigma project is identified. The use of DPMO also avoids the slightly sticky technical point that the Six Sigma goal of 3.4 DPMO is actually the 4.5 sigma one-tailed probability for a normal distribution. Most Six Sigma proponents explain this as a typical shift in the mean that happens for most responses. Due to my experience developing and implementing a product quality management system that recog-nized and estimated both long-term and short-term variability,4 I prefer to think of the 4.5 versus 6 sigma difference as a simplification that recognizes longterm variability. While the appropriate variance component breakdown is process dependent, it is often appropriate to consider the short-term variance component to be the "within the day" variability and the long-term com-ponent the day-to-day variability. Long-term variability will show up as a shift from goal at any sampling time. The Breakthrough Strategy The Breakthrough Strategy is usually presented as a four-step improvement process: measure, analyze, improve, control. This is very much like the Shewhart plan-do-check-act cycle. A define step is often added before the measure step; and recently Harry described an eight-step process beginning with rec-ognize and ending with standardize and integrate.5 There are numerous descriptions of the steps in an improvement process, but the description is less important than the implementation.

The improvement projects must be integrated with the overall goals of the organization. The top-level support for and overview of the planning, implementation and evaluation of projects are important aspects


of this integration. Harry also claims: "In essence, Six Sigma is driven by a divide and conquer strategy, not a continuous improvement philosophy. It rolls out not according to a vague notion of improving every-thing we do forever, followed up by a sporadic and disconnected set of initiatives. Rather, it begins by first dividing the quality pie into comprehensive compartments, or dimensions, that form a holistic focus at all levels of the business enterprise."6 This last statement explains what is achieved by top-level support for, and overview of, projects in an effective continuous improvement system. Six Sigma implementation Six Sigma implementation is top-down: The CEO is usually the driving force, and an executive manage-ment team provides the Champion for each project. The Champion is responsible for the success of the project, providing necessary resources and breaking down organizational barriers. It is typical for a large part of a Champion's bonus to be tied to his or her success in achieving Six Sigma goals. (The fraction is 40% at GE.7) Getting upper management Champions involved in the project selection process helps guarantee the projects will have a large impact on the business. The project leader is called a Black Belt (BB). It is important to select BBs with different experience levels and pay grades because there is a wide range of projects. However, all BB candidates should have a history of accomplishment. Employees selected for BB training should be on the fast track. A BB assignment typically lasts for two years during which the BB leads from eight to 12 projects, each lasting approximately one quarter. (Large projects are broken down into segments of approximately one quarter.) The projects will likely come from different business areas, thereby giving the BB a broader view of the business. Reporting on the projects and documenting their impact are important aspects of the BB experience. They enhance the fast-track aspects of the BB experience. The project team members are called Green Belts (GBs), and they do not spend all their time on projects. GBs receive training similar to that of BBs, but possibly for less time. They typically get their training to participate in an important project for their business. It is important to note Six Sigma project participants such as BBs and GBs tend to be agents of change who thrive in the new business climate of constant change. They are open to new ideas and are used to rigorously evaluating new ideas. For this reason a company should train a large number of employees. For example, as of January 1998, employees at GE will not be considered for promotion to any manage-ment job without BB or GB training. Master Black Belts (MBBs) are resources for the project teams. MBBs are often experienced BBs who have worked on many projects. They generally have knowledge of advanced tools, business and leader-ship training, and teaching experience. A primary MBB responsibility is training and mentoring new BBs in the organization. Project evaluation All Six Sigma projects are rigorously evaluated for financial impact. The CFO is an important member of the executive management team, and most project teams have a member from finance who documents the financial impact. The expectation is that each project has a financial impact of about $175,000. There-fore, each BB has a financial impact of about $1 million per year from the four to six projects per year he or she leads.8 Because project-to-project cost savings are highly variable, I think these expectations are median or modal values with a higher arithmetic mean financial impact. More important than the financial impact of individual projects is the cumulative financial effect on the organization. Larry Bossity, CEO of Allied Signal, says, "With $1.5 billion in estimated savings already achieved, Six Sigma is one of the most ambitious projects we have ever undertaken. It's been a major factor in the company's improved performance."9 GE started Six Sigma in 1995 and claimed net benefits by 1997. In 1998, the company claimed benefits of $1.2 billion and costs of $450 million for a net benefit of $750 million." The company's 1999 annual report claimed a net benefit of more than $2 billion. I believe companies that emphasize financial metrics will likely have a more successful Six Sigma implementation than those that emphasize other metrics, such as number of people trained. While the rule of thumb says one BB per 100 employees and one MBB per 100 BBs are adequate, recent implementation experience suggests the BB to MBB ratio should be closer to 10 to 1.(11) Rigorous pro-ject evaluation allows the number of BBs to be chosen rationally. As long as the projects have large re-turns, there can't be too many projects. There have been no reports yet of diminishing returns because too many projects were attempted.


Though some companies think GE's brand of Six Sigma is extreme, a quality director says, "It's dispro-portionate; GE is 2.5 times bigger than us [in terms of employees], but is going to have 50 times the num-ber of BBs."12 I also know of a 3,000-person organization training 100 BBs with the goal of achieving $100 million per year in cost savings. This is more than three times the 1% rule of thumb number. We will soon learn if this larger BB ratio is successful. Getting the correct number of BBs for your organization is important because a major cost of Six Sigma is backfilling for the employees who become BBs. Training issues BB training usually includes four weeks of classroom training, a week per month over four months. The remaining time is spent working on projects while being mentored by a MBB. The training can be suc-cinctly described as three weeks of statistical tools: a week of basic statistics, including data analysis and the seven tools, a week of design of experiments and a week of quality control. This statistical training is combined with a week of softer skills including project selection, project management and project evalua-tion, team selection and team building. Each week of training may include topics from every area. More training details can be found elsewhere.13,14 The training has a large trainer-to-trainer variability, and much of the training is in lecture format rather than interactive. But the training is still effective because the trainees are motivated and use their training immediately. There are project reviews on many days, and work on projects is carried on when BBs and MBBs are not in training. Members of the management team certify a BB after he or she has led two successful project teams; usually one is under the guidance of a MBB, and the other is done more independently. The MBB is also certified. Certification as a MBB usually requires 20 successful projects, about half while a BB and the remainder while mentoring BBs. Six Sigma's success will encourage others Six Sigma is a business system with many statistical aspects, and it naturally fits the business systems of most companies. It is an operational system that speeds up improvement by getting the right projects conducted in the right way. It drives out fear by making employees agents of change rather than resisters to change. It has been successful for the companies that have adopted it, and this success will encourage other companies to adopt it.


THE ESSENTIAL SIX SIGMA Sigma Limits and Defects per Million Opportunities The relationship between the sigma level (SL) of a process and the defects per million opportunities (DPMO) is calculated using the cumulative distribution function (F(z)) of the normal distribution where F(z) is the probability of observing a value less than z. The F(z) values below were calculated using the NORMSDIST(z) function in Excel 2000. Our calculations show the SL ranging from 0 to 7 in steps of 0.25 in the first column. The second and third columns calculate F(SL + 1.5) and F(1.5 - SL). The 1.5 accounts for the 1.5( shift assumed by Six Sigma. These values from the cumulative distribution function are used in further calculations. The fourth column (probability good) gives the probability of an observation that is not a defect. The values in this column are simply the difference between the second and third columns: probability good = F(SL + 1.5) - F(1.5 - SL)


The fifth column calculates the probability of a defect as 1 (probability good). The last column converts the probability of a defect to DPMO by multiplying by 1,000,000. Our defect counts for SL < 3.5 are slightly larger than the counts shown by Mikel J. Harry because, for these cases, it is necessary to consider both tails of the distribution.' When only one tail of the distribution is considered, the DPMO values are calculated as one million times the second column (1,000,000 x F(1.5 - SL)). When DPMO calculations are carried out to the nearest defect, the one-tail approximation differs from the correct twotail value for all SL < 3.5. The most extreme example is that the one-tail zero sigma DPMO value is 933,193 instead of one million. There is no difference between the one-tail approximation and the correct two-tail calculation when the SL is > 1 and the calculations are carried out to only two significant figures. We recommend using the single tail approximation and using only two significant figures when the SL is greater than 1. For smaller SL values, it is necessary to consider both tails of the distribution (see Table 1). The third or fourth column of the table can be used to convert the observed probability of a defect to a SL. Robert J. Gnibus gives a one-tail approximation that usually works adequately; however, it will give incor-rect answers when the probability of a defect is large.2 Gnibus' second example concerns processing speeds of mortgage customers, where "all the defects (loans in a monthly sample taking more than five days to process) are counted, and it is determined that there are 600 loans in the 1,000 applications processed last month that don't meet this new customer requirement." For this example, the probability of a defect is 600 11,000 0.6; the rule for our example (Table 1) is to pick the largest SL whose probability of a defect value is larger than the observed probability of a defect. Table 1 shows the SL is 1.25 because the SL has the probability of a defect = 0.602. Gnibus' one-tail approxi-mation uses the NORMSINV function in Excel to calculate the z value for the corresponding "probability good." The one-tail approximation (with a 1.5a shift) is: SL = 1.5 + NORMSINV (probability good) For the example: SL = 1.5 + NORMSINV (0.4) = 1.5 + (-0.253) = 1.247 Gnibus rounded this to a SL of 1.2, while the correct value is closer to 1.3. Again, the one-tail approxima-tion for SL gives a value close to the correct answer because the SL > 1. Gnibus' third example shows his and Harry's one-tail approximations both agree when SL = 1.0; both give 690,000 DPMO where the correct DPMO value is 700,000. When the fraction of defects is larger, the one-tail approximation can give meaningless answers. The one-tail approximation will give negative SL values when the probability of a defect is greater than 0.933. This can be clearly seen in an additional example, Pretend you want to test the computation skills of 1,000 students and give them slide rules to assist them with their calculations. Slide rules are outdated computing aids, so most of the students will be unsatisfied. If you find the SL number for the number of satisfied students, you will be faced with two cases: zero students who are satisfied and 66 students who are satisfied. The SLs are zero and 0.25, respectively, when you use two-sided limits. Using the one-sided approximation gives for the first SL and zero for the second. Note I am pointing out technical errors in a basic table used by Harry to sell Six Sigma to management. This means that it is worthwhile to question other aspects of Six Sigma. REFERENCES 1. Mikel J. Harry, "Six Sigma: A Breakthrough Strategy for Profitability," Quality Progress, May 1998. 2. Robert J. Gnibus, "Six Sigma's Missing Link," Quality Progress, November 2000. 1. Joseph M. Juran, Managerial Breakthrough (New York: McGraw-Hill, 1964). 2. Mikel J. Harry, "Six Sigma: A Breakthrough Strategy for Profitability," Quality Progress, May 1998. 3. Joseph M. Juran and A. Blanton Godfrey, Juran's Quality Handbook, fifth edition (New York: McGraw-Hill, 1999). 4. Donald W. Marquardt, ed., PQM: Product Quality Management (Wilmington, DE: E.I. DuPont de Ne-mours & Co. Inc., Quality Management and Technology Center, 1991). A more accessible and shorter version is published here in Joseph M. Reference Juran, Juran's Quality Handbook (see reference 3).


5. Mikel J. Harry, "Framework for Business Leadership," Quality Progress, April 2000. 6. Ibid. 7. GE Capitol Service, The Center for Learning & Organizational Excellence, May 1999. 8. Mikel J. Harry, "Six Sigma: A Breakthrough Strategy for Profitability" see reference 2. 9. William J. Hill, "Six Sigma at Allied Signal Inc.," Presentation at the 1999 Q&P Research Conference, May 1999. 10. GE Capitol Service, The Center for Learning & Organizational Excellence, see reference 7. 11. Kymm K. Hockman, moderator, Steve Caffrey, Roger Hoerl, Patrick Meehan, "Staffing and Deploy-ment Strategies to Support Six Sigma Implementation: A Panel Discussion," ASQ's Annual Quality Con-gress, May 2000. 12. Ann Walmsley, "Six Sigma Enigma," The Globe and Mail Report on Business Magazine, October 1997. 13. Roger W. Hoerl, "Six Sigma and the Future of the Quality Profession," Quality Progress, June 1998. 14. Gerald J. Hahn, William J. Hill, Roger W. Hoerl and Stephen A. Zinkgraf, "The Impact of Six Sigma Improvement-A Reference Glimpse Into the Future of Statistics," The American Statistician, August 1999. [Author note] JAMES M. LUCAS is a Grand Master Back Belt at J. M. Lucas and Associates in Wilmington, DE. He earned a doctorate in statistics from Texas A&M and is a Fellow of ASQ. Lucas also received ASQ's 1999 Shewhart Medal. If you would like to comment on this article, please post your remarks on the Quality Progress Discussion Board on www.asqnet.org, or e-mail them to [email protected]. -------------------------------------------------------------------------------- Reproduced with permission of the copyright owner. Further reproduction or distribution is prohibited without permission.


the essential six sigma - hec...

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