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The Essential Six SigmaHow successful Six Sigma implementation

can improve the bottom line

by

James M. Lucas

OU CAN HARDLY pickup a news or businessmagazine these dayswithout coming acrossan article about SixSigma. It originated atMotorola in the early

1980s, and its implementationhelped the company win the 1988Malcolm Baldrige National QualityAward.

Fundamentally, Six Sigma is amethodology for disciplined qualityimprovement. Because this qualityimprovement is a prime ingredientof total quality management (TQM), many compa-nies find adding a Six Sigma program to their cur-rent business system gives them all or almost allthe elements of TQM:

[current business system] + [Six Sigma] =

[total quality management (TQM)].

It is often much easier to add a disciplined qualityimprovement system, such as Six Sigma, to a compa-ny’s current business system than it is to implementa TQM system. Simply put, Six Sigma uses a modi-fied Shewhart cycle (the plan-do-check-act cycleoften attributed to Deming) as its BreakthroughStrategy for its Americanized kaizen system.

Joseph M. Juran’s statement that “all qualityimprovement occurs on a project-by-project basisand in no other way”1 can be considered an essen-

tial element in the foundation ofSix Sigma, though you seldom seethis statement credited in SixSigma literature. Operationally,Six Sigma is the methodology thatgets more good improvement pro-jects carried out.

A major advantage of Six Sigmais it does not have “quality” or“statistics” in its name. It is per-ceived to be a business systemthat improves the bottom line andonly brings in technical details asneeded; TQM is perceived to be atechnical quality system owned

by technical specialists rather than all employees. Six Sigma’s simple and effective management

structure is one of its strengths; I could notdescribe the management structure used by TQMin such a succinct fashion. As an example of theoperational effectiveness of Six Sigma, it is worth-while to point out that GE’s implementation isbeing widely imitated, while there was little copy-ing of the kaizen program it tried to implementbetween 1988 and 1992.

Six Sigma’s heroic goalSix Sigma’s goal is the near elimination of defects

from any process, product or service—far beyondwhere virtually all companies are currently operat-ing. The numerical goal is 3.4 defects per millionopportunities (DPMO) while higher levels of defectsare associated with lower sigma levels (see Table 1).

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S I X S I G M A

This table, except for some changes in the defectsper million column discussed in the sidebar, “SixSigma 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 goaldoes not seem unrealistic.

Juran gave similar numbers when he estimated that,“in the United States, close to a third of the work doneconsisted of redoing what had been done before.Depending on the nature of the industry, the COPQ con-sumed between 20 and 40% of the total effort.”3 Settinggoals involving DPMO uses an easily understood metricthat handles both counts and continuous variables(whatever their distribution) critical to quality (CTQ).The identification of CTQ variables is one of the firststeps carried out after a Six Sigma project is identified.

The use of DPMO also avoids the slightly sticky techni-cal point that the Six Sigma goal of 3.4 DPMO is actuallythe 4.5 sigma one-tailed probability for a normal distribu-tion. Most Six Sigma proponents explain this as a typicalshift in the mean that happens for most responses.

Due to my experience developing and implement-ing a product quality management system that recog-nized and estimated both long-term and short-termvariability,4 I prefer to think of the 4.5 versus 6 sigmadifference as a simplification that recognizes long-term variability.

While the appropriate variance component break-down is process dependent, it is often appropriate toconsider the short-term variance component to be the“within the day” variability and the long-term compo-nent the day-to-day variability. Long-term variabilitywill show up as a shift from goal at any sampling time.

The Breakthrough StrategyThe Breakthrough Strategy is usually presented as a

four-step improvement process: measure, analyze,improve, control. This is very much like the Shewhartplan-do-check-act cycle. A define step is often addedbefore the measure step; and recently Harry describedan eight-step process beginning with recognize andending with standardize and integrate.5 There arenumerous descriptions of the steps in an improve-

ment process, but the description is less importantthan the implementation.

The improvement projects must be integrated withthe overall goals of the organization. The top-level sup-port for and overview of the planning, implementationand evaluation of projects are important aspects of thisintegration. Harry also claims: “In essence, Six Sigma isdriven by a divide and conquer strategy, not a continu-ous improvement philosophy. It rolls out not accordingto a vague notion of improving everything we do forev-er, followed up by a sporadic and disconnected set ofinitiatives. Rather, it begins by first dividing the qualitypie into comprehensive compartments, or dimensions,that form a holistic focus at all levels of the businessenterprise.”6 This last statement explains what isachieved by top-level support for, and overview of, pro-jects in an effective continuous improvement system.

Six Sigma implementationSix 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 pro-ject, providing necessary resources and breaking downorganizational barriers. It is typical for a large part of aChampion’s bonus to be tied to his or her success inachieving Six Sigma goals. (The fraction is 40% at GE.7)Getting upper management Champions involved in theproject selection process helps guarantee the projectswill have a large impact on the business.

The project leader is called a Black Belt (BB). It isimportant to select BBs with different experience lev-els and pay grades because there is a wide range ofprojects. However, all BB candidates should have ahistory of accomplishment. Employees selected for BBtraining should be on the fast track.

A BB assignment typically lasts for two years duringwhich the BB leads from eight to 12 projects, each last-ing approximately one quarter. (Large projects are bro-ken down into segments of approximately one quarter.)The projects will likely come from different businessareas, thereby giving the BB a broader view of the busi-ness. Reporting on the projects and documenting theirimpact are important aspects of the BB experience. They

enhance the fast-track aspects of the BB experi-ence.

The project team members are called GreenBelts (GBs), and they do not spend all theirtime on projects. GBs receive training similarto that of BBs, but possibly for less time. Theytypically get their training to participate in animportant project for their business.

It is important to note Six Sigma project par-ticipants such as BBs and GBs tend to beagents of change who thrive in the new busi-ness climate of constant change. They are

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Six Sigma Process CapabilityTABLE 1

Sigma Defects per million Cost of poor quality

6 sigma 3.4 defects per million <10% of sales World-class

5 sigma 230 defects per million 10 to 15% of sales

4 sigma 6,200 defects per million 15 to 20% of sales Industry average

3 sigma 67,000 defects per million 20 to 30% of sales

2 sigma 310,000 defects per million 30 to 40% of sales Noncompetitive

1 sigma 700,000 defects per million

open to new ideas and are used to rigorously evaluat-ing new ideas. For this reason a company should traina large number of employees. For example, as ofJanuary 1998, employees at GE will not be consideredfor promotion to any management job without BB orGB training.

Master Black Belts (MBBs) are resources for the pro-ject teams. MBBs are often experienced BBs who haveworked on many projects. They generally haveknowledge of advanced tools, business and leader-ship training, and teaching experience. A primaryMBB responsibility is training and mentoring new BBsin the organization.

Project evaluationAll Six Sigma projects are rigorously evaluated for

financial impact. The CFO is an important member ofthe executive management team, and most projectteams have a member fromfinance who documents the finan-cial impact. The expectation is thateach project has a financial impactof about $175,000. Therefore, eachBB has a financial impact of about$1 million per year from the fourto six projects per year he or sheleads.8 Because project-to-projectcost savings are highly variable, Ithink these expectations are medi-an or modal values with a higherarithmetic mean financial impact.

More important than the financial impact of indi-vidual projects is the cumulative financial effect on theorganization. Larry Bossity, CEO of Allied Signal,says, “With $1.5 billion in estimated savings alreadyachieved, Six Sigma is one of the most ambitious pro-jects we have ever undertaken. It’s been a major factorin the company’s improved performance.”9

GE started Six Sigma in 1995 and claimed net bene-fits by 1997. In 1998, the company claimed benefits of$1.2 billion and costs of $450 million for a net benefitof $750 million.10 The company’s 1999 annual reportclaimed a net benefit of more than $2 billion. I believecompanies that emphasize financial metrics will likelyhave a more successful Six Sigma implementationthan those that emphasize other metrics, such as num-ber of people trained.

While the rule of thumb says one BB per 100employees and one MBB per 100 BBs are adequate,recent implementation experience suggests the BB toMBB ratio should be closer to 10 to 1.11 Rigorous projectevaluation allows the number of BBs to be chosenrationally. As long as the projects have large returns,there can’t be too many projects. There have been noreports yet of diminishing returns because too manyprojects were attempted.

Though some companies think GE’s brand of SixSigma is extreme, a quality director says, “It’s dispro-portionate; GE is 2.5 times bigger than us [in terms ofemployees], but is going to have 50 times the numberof BBs.”12 I also know of a 3,000-person organizationtraining 100 BBs with the goal of achieving $100 mil-lion per year in cost savings. This is more than threetimes the 1% rule of thumb number. We will soonlearn if this larger BB ratio is successful. Getting thecorrect number of BBs for your organization is impor-tant because a major cost of Six Sigma is backfillingfor the employees who become BBs.

Training issuesBB training usually includes four weeks of classroom

training, a week per month over four months. Theremaining time is spent working on projects whilebeing mentored by a MBB. The training can be suc-

cinctly described as three weeks ofstatistical tools: a week of basic sta-tistics, including data analysis andthe seven tools, a week of design ofexperiments and a week of qualitycontrol. This statistical training iscombined with a week of softerskills including project selection,project management and projectevaluation, team selection andteam building. Each week of train-ing 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 ratherthan interactive. But the training is still effectivebecause the trainees are motivated and use their train-ing immediately. There are project reviews on manydays, and work on projects is carried on when BBsand MBBs are not in training.

Members of the management team certify a BB afterhe or she has led two successful project teams; usuallyone is under the guidance of a MBB, and the other isdone more independently. The MBB is also certified.Certification as a MBB usually requires 20 successfulprojects, about half while a BB and the remainderwhile mentoring BBs.

Six Sigma’s success will encourage othersSix Sigma is a business system with many statistical

aspects, and it naturally fits the business systems ofmost companies. It is an operational system that speedsup improvement by getting the right projects conduct-ed in the right way. It drives out fear by makingemployees agents of change rather than resisters tochange. It has been successful for the companies thathave adopted it, and this success will encourage othercompanies to adopt it.

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Getting the correct number ofBBs for your organization isimportant because a major costof Six Sigma is backfilling for theemployees who become BBs.

REFERENCES

1. Joseph M. Juran, Managerial Breakthrough (New York:McGraw-Hill, 1964).

2. Mikel J. Harry, “Six Sigma: A Breakthrough Strategy forProfitability,” Quality Progress, May 1998.

3. Joseph M. Juran and A. Blanton Godfrey, Juran’s QualityHandbook, fifth edition (New York: McGraw-Hill, 1999).

4. Donald W. Marquardt, ed., PQM: Product QualityManagement (Wilmington, DE: E.I. DuPont de Nemours & Co.Inc., Quality Management and Technology Center, 1991). A moreaccessible and shorter version is published here in Joseph M.

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 &

30 I J A N U A R Y 2 0 0 2 I W W W . A S Q . O R G

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The relationship between the sigma level (SL) of a processand the defects per million opportunities (DPMO) is calculatedusing the cumulative distribution function (F(z)) of the normaldistribution where F(z) is the probability of observing a valueless than z. The F(z) values below were calculated using theNORMSDIST(z) function in Excel 2000.

Our calculations show the SL ranging from 0 to 7 in steps of0.25 in the first column. The second and third columns calculateF(SL + 1.5) and F(1.5 - SL). The 1.5 accounts for the 1.5σ shiftassumed by Six Sigma. These values from the cumulative distrib-ution function are used in further calculations. The fourth column(probability good) gives the probability of an observation that isnot a defect. The values in this column are simply the differencebetween 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 adefect to DPMO by multiplying by 1,000,000.

Our defect counts for SL < 3.5 are slightly larger than thecounts shown by Mikel J. Harry because, for these cases, it isnecessary to consider both tails of the distribution.1 When onlyone tail of the distribution is considered, the DPMO values arecalculated as one million times the second column (1,000,000 xF(1.5 - SL)).

When DPMO calculations are carried out to the nearestdefect, the one-tail approximation differs from the correct two-tail value for all SL < 3.5. The most extreme example is that theone-tail zero sigma DPMO value is 933,193 instead of one mil-lion. There is no difference between the one-tail approximationand the correct two-tail calculation when the SL is > 1 and thecalculations are carried out to only two significant figures. Werecommend using the single tail approximation and using onlytwo significant figures when the SL is greater than 1. For small-er SL values, it is necessary to consider both tails of the distrib-ution (see Table 1).

The third or fourth column of the table can be used to con-vert the observed probability of a defect to a SL. Robert J.Gnibus gives a one-tail approximation that usually works ade-quately; however, it will give incorrect answers when the prob-ability of a defect is large.2

Gnibus’ second example concerns processing speeds ofmortgage customers, where "all the defects (loans in a monthlysample taking more than five days to process) are counted, and

it is determined that there are 600 loans in the 1,000 applicationsprocessed last month that don’t meet this new customerrequirement."

For this example, the probability of a defect is 600 / 1,000 =0.6; the rule for our example (Table 1) is to pick the largest SLwhose probability of a defect value is larger than the observedprobability of a defect. Table 1 shows the SL is 1.25 because theSL has the probability of a defect = 0.602. Gnibus’ one-tailapproximation uses the NORMSINV function in Excel to calcu-late the z value for the corresponding “probability good.” Theone-tail approximation (with a 1.5σ shift) is:

SL = 1.5 + NORMSINV (probability good)For the example:

SL = 1.5 + NORMSINV (0.4) = 1.5 + (-0.253) = 1.247Gnibus rounded this to a SL of 1.2, while the correct value is

closer to 1.3. Again, the one-tail approximation for SL gives avalue close to the correct answer because the SL > 1.

Gnibus’ third example shows his and Harry’s one-tailapproximations both agree when SL = 1.0; both give 690,000DPMO where the correct DPMO value is 700,000. When thefraction of defects is larger, the one-tail approximation can givemeaningless answers. The one-tail approximation will givenegative SL values when the probability of a defect is greaterthan 0.933.

This can be clearly seen in an additional example. Pretendyou want to test the computation skills of 1,000 students andgive them slide rules to assist them with their calculations.Slide rules are outdated computing aids, so most of the stu-dents will be unsatisfied. If you find the SL number for thenumber of satisfied students, you will be faced with two cases:zero students who are satisfied and 66 students who are satis-fied. The SLs are zero and 0.25, respectively, when you usetwo-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 usedby Harry to sell Six Sigma to management. This means that it isworthwhile to question other aspects of Six Sigma.

REFERENCES

1. Mikel J. Harry, “Six Sigma: A Breakthrough Strategy forProfitability,” Quality Progress, May 1998.

2. Robert J. Gnibus, “Six Sigma’s Missing Link,” Quality Progress,November 2000.

Sigma Limits and Defects per Million Opportunities

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Relationship Between SL and DPMOTABLE 1

SL F(SL + 1.5) F(1.5 - SL) Probability good Probability of a defect DPMO

0 0.933192771 0.933192771 0 1 1,000,000

0.25 0.959940886 0.894350161 0.065590726 0.934409274 934,409.2745

0.5 0.977249938 0.84134474 0.135905198 0.864094802 864,094.8023

0.75 0.987775567 0.77337272 0.214402846 0.785597154 785,597.1537

1 0.99379032 0.691462467 0.302327853 0.697672147 697,672.1472

1.25 0.997020181 0.598706274 0.398313908 0.601686092 601,686.0924

1.5 0.998650033 0.5 0.498650033 0.501349967 501,349.967

1.75 0.999422914 0.401293726 0.598129187 0.401870813 401,870.8127

2 0.999767327 0.308537533 0.691229794 0.308770206 308,770.206

2.25 0.999911555 0.22662728 0.773284276 0.226715724 226,715.7243

2.5 0.999968314 0.15865526 0.841313054 0.158686946 158,686.9458

2.75 0.999989304 0.105649839 0.894339465 0.105660535 105,660.5348

3 0.999996599 0.066807229 0.93318937 0.06681063 66,810.6296

3.25 0.999998982 0.040059114 0.959939868 0.040060132 40,060.1319

3.5 0.999999713 0.022750062 0.977249651 0.022750349 22,750.34914

3.75 0.999999924 0.012224433 0.98777549 0.01222451 12,224.50961

4 0.999999981 0.00620968 0.993790301 0.006209699 6,209.698895

4.25 0.999999996 0.002979819 0.997020177 0.002979823 2,979.823064

4.5 0.999999999 0.001349967 0.998650032 0.001349968 1,349.968213

4.75 1 0.000577086 0.999422913 0.000577087 577.0866996

5 1 0.000232673 0.999767327 0.000232673 232.673414

5.25 1 8.84446E-05 0.999911555 8.84446E-05 88.44459787

5.5 1 3.1686E-05 0.999968314 3.1686E-05 31.6860359

5.75 1 1.06957E-05 0.999989304 1.06957E-05 10.69568586

6 1 3.4008E-06 0.999996599 3.4008E-06 3.400803094

6.25 1 1.01833E-06 0.999998982 1.01833E-06 1.0183285

6.5 1 2.87105E-07 0.999999713 2.87105E-07 0.287105

6.75 1 7.62014E-08 0.999999924 7.62014E-08 0.076201358

7 1 1.90364E-08 0.999999981 1.90364E-08 0.019036399

SL – Sigma level DPMO – Defects per million opportunities

Organizational Excellence, see reference 7.11. Kymm K. Hockman, moderator, Steve Caffrey, Roger

Hoerl, Patrick Meehan, “Staffing and Deployment Strategies toSupport Six Sigma Implementation: A Panel Discussion,” ASQ’sAnnual Quality Congress, May 2000.

12. Ann Walmsley, “Six Sigma Enigma,” The Globe and MailReport on Business Magazine, October 1997.

13. Roger W. Hoerl, “Six Sigma and the Future of the QualityProfession,” Quality Progress, June 1998.

14. Gerald J. Hahn, William J. Hill, Roger W. Hoerl andStephen A. Zinkgraf, “The Impact of Six Sigma Improvement—A

Glimpse Into the Future of Statistics,” The American Statistician,August 1999.

JAMES M. LUCAS is a Grand Master Back Belt at J. M. Lucasand Associates in Wilmington, DE. He earned a doctorate in sta-tistics from Texas A&M and is a Fellow of ASQ. Lucas alsoreceived ASQ’s 1999 Shewhart Medal. If you would like to com-ment on this article, please post your remarks on the QualityProgress Discussion Board on www.asqnet.org, or e-mail them toeditor@asq.org. QP