Showing posts with label Stastical Formulae. Show all posts
Showing posts with label Stastical Formulae. Show all posts

Sunday, February 9, 2014

Six sigma

Six Sigma is a set of techniques and tools for process improvement. It was developed by Motorola in 1986,[1][2] coinciding with the Japanese asset price bubble which is reflected in its terminology. Six Sigma became famous when Jack Welch made it central to his successful business strategy at General Electric in 1995.[3] Today, it is used in many industrial sectors.[4]
Six Sigma seeks to improve the quality of process outputs by identifying and removing the causes of defects (errors) and minimizing variability in manufacturing and business processes. It uses a set of quality management methods, including statistical methods, and creates a special infrastructure of people within the organization ("Champions", "Black Belts", "Green Belts", "Yellow Belts", etc.) who are experts in the methods. Each Six Sigma project carried out within an organization follows a defined sequence of steps and has quantified value targets, for example: reduce process cycle time, reduce pollution, reduce costs, increase customer satisfaction, and increase profits. These are also core to principles of Total Quality Management (TQM) as described by Peter Drucker and Tom Peters (particularly in his book "The Pursuit of Excellence" in which he refers the Motorola six sigma principles).
The term Six Sigma originated from terminology associated with manufacturing, specifically terms 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 the products manufactured are statistically expected to be free of defects (3.4 defective parts/million), although, as discussed below, this defect level corresponds to only a 4.5 sigma level. 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.

Doctrine

Six Sigma doctrine 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, controlled and improved.
  • 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 control, 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).[5][6] 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 organisation to prioritize areas of improvement.
"Six Sigma" was registered June 11, 1991 as U.S. Service Mark 74,026,418. In 2005 Motorola attributed over US$17 billion in savings to Six Sigma. [7] Other early adopters of Six Sigma who achieved well-publicized success include Honeywell (previously known as AlliedSignal) and General Electric, where Jack Welch introduced the method.[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, some practitioners have combined Six Sigma ideas with lean manufacturing to create a methodology named Lean Six Sigma.[10] 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".[10] Companies such as GE,[11] Verizon, GENPACT, and IBM use Lean Six Sigma to focus transformation efforts not just on efficiency but also on growth. It serves as a foundation for innovation throughout the organization, from manufacturing and software development to sales and service delivery functions.
The International Organisation for Standardisation (ISO) has published ISO 13053:2011 defining the six sigma process.[12]

Methodologies

Six Sigma projects follow two project methodologies inspired by Deming's Plan-Do-Check-Act Cycle. These methodologies, composed of five phases each, bear the acronyms DMAIC and DMADV.[9]
  • DMAIC is used for projects aimed at improving an existing business process.[9] DMAIC is pronounced as "duh-may-ick" (<ˌdʌ ˈmeɪ ɪk>).
  • DMADV is used for projects aimed at creating new product or process designs.[9] DMADV is pronounced as "duh-mad-vee" (<ˌdʌ ˈmæd vi>).

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.
  • 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 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.
Some organizations add a Recognize step at the beginning, which is to recognize the right problem to work on, thus yielding an RDMAIC methodology.[13]

DMADV or DFSS

The DMADV project methodology, known as DFSS ("Design For Six Sigma"),[9] features five phases:
  • 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
  • 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).

Quality management tools and methods used in Six Sigma

Within the individual phases of a DMAIC or DMADV project, Six Sigma utilizes many established quality-management tools that are also used outside Six Sigma. The following table shows an overview of the main methods used. (Note: In the American universities in the curriculum of Industrial Engineering, the techniques taught in couple of courses are repackaged and sold under the banner of Six Sigma because of the appealing name. Six Sigma does not guarantee Six Sigma yield).

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 Kung-Fu and Judo) to define a hierarchy (and special career path) that kicks across all business functions and levels.
Six Sigma identifies several key roles for its successful implementation.[14]
  • 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 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.
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.[15]

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 1990s started offering Six Sigma certifications to their employees.[9][16] Criteria for Green Belt and Black Belt certification vary; some companies simply require participation in a course and a Six Sigma project.[16] There is no standard certification body, and different certification services are offered by various quality associations and other providers against a fee.[17][18] The American Society for Quality for example requires Black Belt applicants to pass a written exam and to provide a signed affidavit stating that they have completed two projects, or one project combined with three years' practical experience in the body of knowledge.[16][19] The International Quality Federation offers an online certification exam that organizations can use for their internal certification programs; it is statistically more demanding than the ASQ certification.

University certification programs

In addition to certification service provider institutes, there are Six Sigma certification programs offered through a few four-year colleges and universities. These programs provide the same courses verifying individuals' command of the Six Sigma methods at the relevant skill level from Green Belt to Black Belt etc.

Origin and meaning of the term "six sigma process"

The term "six sigma process" comes from the notion that if one has six standard deviations between the process mean and the nearest specification limit, as shown in the graph, practically no items will fail to meet specifications.[5] This is based on the calculation method employed in process capability studies.
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.[5]
Graph of the normal distribution, which underlies the statistical assumptions of the Six Sigma model. The Greek letter σ (sigma) marks the distance on the horizontal axis between the mean, µ, and the curve's inflection point. The greater this distance, 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 (USL and LSL, respectively) 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. Even if the mean were to move right or left by 1.5σ at some point in the future (1.5 sigma shift, coloured red and blue), there is still a good safety cushion. This is why Six Sigma aims to have processes where the mean is at most 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.[5] 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.[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.[5][52] 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.[5]
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 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 sigma, namely 6 sigma minus the 1.5-sigma shift introduced to account for long-term variation.[5] 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.[5]
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 depicting 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.
See also: Three sigma rule
The table[53][54] below gives long-term DPMO values corresponding to various short-term sigma levels.
It must be understood that 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 Cpk value will turn out to be 0.5 less than the short-term Cpk value. So, for example, the DPMO figure given for 1 sigma assumes that the long-term process mean will be 0.5 sigma beyond the specification limit (Cpk = –0.17), rather than 1 sigma within it, as it was in the short-term study (Cpk = 0.33). 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.
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

Software used for Six Sigma

Statistics analysis tools with comparable functions

Application

Main article: List of Six Sigma companies
Six Sigma mostly finds application in large organizations.[60] 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.[60] According to industry consultants like Thomas Pyzdek and John Kullmann, companies with fewer than 500 employees are less suited to Six Sigma implementation, or need to adapt the standard approach to make it work for them.[60] 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.[60]

Criticism

Lack of originality

Noted quality expert Joseph M. Juran has described Six Sigma as "a basic version of quality improvement", stating that "there is nothing new there. It includes what we used to call facilitators. They've adopted more flamboyant terms, like belts with different colors. I think that concept has merit to set apart, to create specialists who can be very helpful. Again, that's not a new idea. The American Society for Quality long ago established certificates, such as for reliability engineers."[61]

Role of consultants

The use of "Black Belts" as itinerant change agents has (controversially) fostered an industry of training and certification. Critics argue there is overselling of Six Sigma by too great a number of consulting firms, many of which claim expertise in Six Sigma when they have only a rudimentary understanding of the tools and techniques involved, or the markets or industries in which they are acting.

Potential negative effects

A Fortune article stated that "of 58 large companies that have announced Six Sigma programs, 91 percent have trailed the S&P 500 since". The statement was attributed to "an analysis by Charles Holland[disambiguation needed] of consulting firm Qualpro (which espouses a competing quality-improvement process)".[62] The summary of the article is that Six Sigma is effective at what it is intended to do, but that it is "narrowly designed to fix an existing process" and does not help in "coming up with new products or disruptive technologies." Advocates of Six Sigma have argued that many of these claims are in error or ill-informed.[63][64]

Over-reliance on (statistical) tools

A more direct criticism is the "rigid" nature of Six Sigma with its over-reliance on methods and tools. In most cases, more attention is paid to reducing variation and searching for any significant factors and less attention is paid to developing robustness in the first place (which can altogether eliminate the need for reducing variation).[65] The extensive reliance on significance testing and use of multiple regression techniques increases the risk of making commonly-unknown types of statistical errors or mistakes. A possible consequence of Six Sigma's array of P-value misconceptions is the false belief that the probability of a conclusion being in error can be calculated from the data in a single experiment without reference to external evidence or the plausibility of the underlying mechanism.[66] One of the most serious but all-too-common misuses of inferential statistics is to take a model that was developed through exploratory model building and subject it to the same sorts of statistical tests that are used to validate a model that was specified in advance.[67] Another comment refers to the often mentioned Transfer Function, which seems to be a flawed theory if looked at in detail.[68] Since significance tests were first popularized many objections have been voiced by prominent and respected statisticians. The volume of criticism and rebuttal has filled books with language seldom used in the scholarly debate of a dry subject.[69][70][71][72] Much of the first criticism was already published more than 40 years ago. Refer to: Statistical hypothesis testing#Criticism for details. Articles featuring critics have appeared in the November–December 2006 issue of USA Army Logistician regarding Six-Sigma: "The dangers of a single paradigmatic orientation (in this case, that of technical rationality) can blind us to values associated with double-loop learning and the learning organization, organization adaptability, workforce creativity and development, humanizing the workplace, cultural awareness, and strategy making."[73] Nassim Nicholas Taleb consider risk managers little more than "blind users" of statistical tools and methods.[74] He states that statistics is fundamentally incomplete as a field as it cannot predict the risk of rare events - something Six Sigma is specially concerned with. Furthermore, errors in prediction are likely to occur as a result of ignorance for or distinction between epistemic and other uncertainties. These errors are the biggest in time variant (reliability) related failures.[75]

Stifling creativity in research environments

A BusinessWeek article says that James McNerney's introduction of Six Sigma at 3M had the effect of stifling creativity and reports its removal from the research function. It cites two Wharton School professors who say that Six Sigma leads to incremental innovation at the expense of blue skies research.[76] This phenomenon is further explored in the book Going Lean, which describes a related approach known as lean dynamics and provides data to show that Ford's "6 Sigma" program did little to change its fortunes.[77]
According to an article by John Dodge, editor in chief of Design News, use of Six Sigma is inappropriate in a research environment. Dodge states[78] "excessive metrics, steps, measurements and Six Sigma's intense focus on reducing variability water down the discovery process. Under Six Sigma, the free-wheeling nature of brainstorming and the serendipitous side of discovery is stifled." He concludes "there's general agreement that freedom in basic or pure research is preferable while Six Sigma works best in incremental innovation when there's an expressed commercial goal."

Lack of systematic documentation

One criticism voiced by Yasar Jarrar and Andy Neely from the Cranfield School of Management's Centre for Business Performance is that while Six Sigma is a powerful approach, it can also unduly dominate an organization's culture; and they add that much of the Six Sigma literature lacks academic rigor:
Probably more to the Six Sigma literature than concepts, relates to the evidence for Six Sigma’s success. So far, documented case studies using the Six Sigma methods are presented as the strongest evidence for its success. However, looking at these documented cases, and apart from a few that are detailed from the experience of leading organizations like GE and Motorola, most cases are not documented in a systemic or academic manner. In fact, the majority are case studies illustrated on websites, and are, at best, sketchy. They provide no mention of any specific Six Sigma methods that were used to resolve the problems. It has been argued that by relying on the Six Sigma criteria, management is lulled into the idea that something is being done about quality, whereas any resulting improvement is accidental (Latzko 1995). Thus, when looking at the evidence put forward for Six Sigma success, mostly by consultants and people with vested interests, the question that begs to be asked is: are we making a true improvement with Six Sigma methods or just getting skilled at telling stories? Everyone seems to believe that we are making true improvements, but there is some way to go to document these empirically and clarify the causal relations.[65]

Criticism of the 1.5 sigma shift

The statistician Donald J. Wheeler has dismissed the 1.5 sigma shift as "goofy" because of its arbitrary nature.[79] Its universal applicability is seen as doubtful.
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."[5][80] 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.[80] 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 is a confidence trick.[5]

See also

References

  1. Jump up ^ "The Inventors of Six Sigma". Archived from the original on 2005-11-06. Retrieved 2006-01-29.
  2. Jump up ^ Tennant, Geoff (2001). SIX SIGMA: SPC and TQM in Manufacturing and Services. Gower Publishing, Ltd. p. 6. ISBN 0-566-08374-4.
  3. Jump up ^ "The Evolution of Six Sigma". Retrieved 2012-03-19.
  4. Jump up ^ "six sigma".
  5. ^ Jump up to: a b c d e f g h i j k l Tennant, Geoff (2001). SIX SIGMA: SPC and TQM in Manufacturing and Services. Gower Publishing, Ltd. p. 25. ISBN 0-566-08374-4.
  6. Jump up ^ "Motorola University Six Sigma Dictionary". Archived from the original on 2006-01-28. Retrieved 2006-01-29.
  7. Jump up ^ "About Motorola University". Archived from the original on 2005-12-22. Retrieved 2006-01-28.
  8. Jump up ^ "Six Sigma: Where is it now?". Retrieved 2008-05-22.
  9. ^ Jump up to: a b c d e f De Feo, Joseph A.; Barnard, William (2005). JURAN Institute's Six Sigma Breakthrough and Beyond - Quality Performance Breakthrough Methods. Tata McGraw-Hill Publishing Company Limited. ISBN 0-07-059881-9.
  10. ^ Jump up to: a b Walshe, Kieran; Harvey, Gill; Jas, Pauline (15 November 2010). Connecting Knowledge and Performance in Public Services: From Knowing to Doing. Cambridge University Press. p. 175. ISBN 978-0-521-19546-1. Retrieved 2011-08-22.
  11. Jump up ^ "verizon".
  12. Jump up ^ "ISO 13053:2011". ISO.
  13. Jump up ^ Webber, Larry; Wallace, Michael (15 December 2006). Quality Control for Dummies. For Dummies. pp. 42–43. ISBN 978-0-470-06909-7. Retrieved 2012-05-16.
  14. Jump up ^ Harry, Mikel; Schroeder, Richard (2000). Six Sigma. Random House, Inc. ISBN 0-385-49437-8.
  15. Jump up ^ Harry, Mikel J.; Mann, Prem S.; De Hodgins, Ofelia C.; Hulbert, Richard L.; Lacke, Christopher J. (20 September 2011). Practitioner's Guide to Statistics and Lean Six Sigma for Process Improvements. John Wiley and Sons. pp. 30–. ISBN 978-1-118-21021-5. Retrieved 2011-11-15.
  16. ^ Jump up to: a b c Keller, Paul A.; Keller, Paul (16 December 2010). Six Sigma Demystified. McGraw-Hill Professional. p. 40. ISBN 978-0-07-174679-3. Retrieved 2011-09-20.
  17. Jump up ^ Webber, Larry; Wallace, Michael (15 December 2006). Quality Control for Dummies. For Dummies. pp. 292–. ISBN 978-0-470-06909-7. Retrieved 2011-09-20.
  18. Jump up ^ Coryea, R. Leroy; Cordy, Carl E.; Coryea, LeRoy R. (27 January 2006). Champion's Practical Six Sigma Summary. Xlibris Corporation. p. 65. ISBN 978-1-4134-9681-9. Retrieved 2011-09-20.
  19. Jump up ^ "Certification - ASQ". Milwaukee, Wisconsin: American Society for Quality. Retrieved 2011-09-09.
  20. Jump up ^ "Six Sigma Black Belt Certification | Global Outreach & Extended Education". Asuengineeringonline.com. Retrieved 2014-02-08.
  21. Jump up ^ Catalog. "Business Management (BUSM) | Catalog". Catalog.byuh.edu. Retrieved 2014-02-08.
  22. Jump up ^ "GSM OM 840 » Academics | Boston University". Bu.edu. Retrieved 2014-02-08.
  23. Jump up ^ "Professional Development Certificates from Cal State Fullerton". Csufextension.org. Retrieved 2014-02-08.
  24. Jump up ^ "Lean Six Sigma Green Belt Certification at Weatherhead School of Management". Weatherhead.case.edu. Retrieved 2014-02-08.
  25. Jump up ^ "Six Sigma Black Belt Certificate - Systems Engineering @ Cornell University". Systemseng.cornell.edu. 2012-04-03. Retrieved 2014-02-08.
  26. Jump up ^ http://ece.emory.edu/sixsigma/index.cfm
  27. Jump up ^ © 2014 Franklin University (2011-09-26). "Center For Professional Training & Development | Franklin University". Ce.franklin.edu. Retrieved 2014-02-08.
  28. Jump up ^ [1][dead link]
  29. Jump up ^ "Six Sigma | Leadership & Management | Georgia Tech Professional Education". Pe.gatech.edu. 2013-07-22. Retrieved 2014-02-08.
  30. Jump up ^ "JMU Six Sigma Certificate Program Online | Virginia | DC". Jmusixsigma.org. Retrieved 2014-02-08.
  31. Jump up ^ "Lean Six Sigma Training & Certification". Kent.edu. Retrieved 2014-02-08.
  32. Jump up ^ http://coes.latech.edu/engineering-technology-management/etm_greenbelt2.pdf
  33. Jump up ^ [2][dead link]
  34. Jump up ^ "Purdue Online Lean Six Sigma Program". Engineering.purdue.edu. Retrieved 2014-02-08.
  35. Jump up ^ [3][dead link]
  36. Jump up ^ [4][dead link]
  37. Jump up ^ "Six Sigma Certificate | Industrial and Systems Engineering | San José State University". Ise.sjsu.edu. Retrieved 2014-02-08.
  38. Jump up ^ http://www.usma.edu/pv/pointer%20view%20archive/07feb02.pdf
  39. Jump up ^ "GBO Payment | TCIE". Tcie.buffalo.edu. Retrieved 2014-02-08.
  40. Jump up ^ "Masters in Engineering Management | University of Colorado Boulder Engineering Management Program | Six Sigma Belt Certification | Lockheed Martin Engineering Management Program". Emp.colorado.edu. 2012-05-14. Retrieved 2014-02-08.
  41. Jump up ^ "UH Six Sigma Certificate Program - Houston, Texas". Scps.uh.edu. Retrieved 2014-02-08.
  42. Jump up ^ "ISD". Isd.engin.umich.edu. Retrieved 2014-02-08.
  43. Jump up ^ "USC Six Sigma Certificate Program - University of South Carolina". Saeu.sc.edu. Retrieved 2014-02-08.
  44. Jump up ^ "The University of Texas at Austin - Center for Lifelong Engineering Education". Lifelong.engr.utexas.edu. Retrieved 2014-02-08.
  45. Jump up ^ [5][dead link]
  46. Jump up ^ "Six Sigma Certification Requirements". Villanova.
  47. Jump up ^ "Indian Statistical Institute, Bangalore, Six Sigma Black Belt" (PDF).
  48. Jump up ^ "Indian Statistical Institute, Delhi, Six Sigma Master Black Belt".
  49. Jump up ^ "Indian Statistical Institute, Bangalore, Six Sigma Master Black Belt" (PDF).
  50. Jump up ^ "Indian Statistical Institute, Delhi, Six Sigma Black Belt".
  51. Jump up ^ "Indian Statistical Institute, Kolkata, MTECH -QROR, Masters Degree in Quality, Reliability and Operational Research, curricula covering six sigma up to MBB level".
  52. Jump up ^ Harry, Mikel J. (1988). The Nature of six sigma quality. Rolling Meadows, Illinois: Motorola University Press. p. 25. ISBN 978-1-56946-009-2.
  53. Jump up ^ Gygi, Craig; DeCarlo, Neil; Williams, Bruce (2005). Six Sigma for Dummies. Hoboken, NJ: Wiley Publishing, Inc. pp. Front inside cover, 23. ISBN 0-7645-6798-5.
  54. Jump up ^ El-Haik, Basem; Suh, Nam P. Axiomatic Quality. John Wiley and Sons. p. 10. ISBN 978-0-471-68273-8.
  55. Jump up ^ "R: A Language and Environment for Statistical Computing". R Foundation for Statistical Computing. Retrieved 2011-08-24.
  56. Jump up ^ Lopez, Emilio; Redchuk, Andres; Moguerza, Javier M. "SixSigma: Six Sigma Tools for Quality and Process Improvement". Retrieved 2011-08-24.
  57. Jump up ^ Roth, Thomas. "qualityTools: Statistical Methods for Quality Science". Retrieved 2011-08-24.
  58. Jump up ^ Scrucca, Luca. "qcc: Quality Control Charts". Retrieved 2011-08-24.
  59. Jump up ^ Recchia, Daniela R.; Barbosa, Emanuel P.; de Jesus Goncalves, Elias. "IQCC: Improved Quality Control Charts". Retrieved 2011-08-24.
  60. ^ Jump up to: a b c d Dusharme, Dirk. "Six Sigma Survey: Breaking Through the Six Sigma Hype". Quality Digest.
  61. Jump up ^ Paton, Scott M. (August 2002). Juran: A Lifetime of Quality 22 (8). pp. 19–23. Retrieved 2009-04-01.
  62. Jump up ^ Morris, Betsy (11 July 2006). "Tearing up the Jack Welch playbook". Fortune. Retrieved 2006-11-26.
  63. Jump up ^ Richardson, Karen (7 January 2007). "The 'Six Sigma' Factor for Home Depot". Wall Street Journal Online. Retrieved 2007-10-15.
  64. Jump up ^ Ficalora, Joe; Costello, Joe. "Wall Street Journal SBTI Rebuttal" (PDF). Sigma Breakthrough Technologies, Inc. Retrieved 2007-10-15.
  65. ^ Jump up to: a b "Six Sigma Friend or Foe" (PDF). Retrieved 2012-02-10.
  66. Jump up ^ "Twelve P value misconceptions" (PDF).
  67. Jump up ^ "important".
  68. Jump up ^ "y-FX".
  69. Jump up ^ Harlow, Lisa Lavoie; Stanley A. Mulaik; James H. Steiger, ed. (1997). What If There Were No Significance Tests?. Lawrence Erlbaum Associates. ISBN 978-0-8058-2634-0.
  70. Jump up ^ Morrison, Denton; Henkel, Ramon, ed. (2006) [1970]. The Significance Test Controversy. AldineTransaction. ISBN 0-202-30879-0.
  71. Jump up ^ McCloskey, Deirdre N.; Ziliak, Stephen T. (2008). The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives. University of Michigan Press. ISBN 0-472-05007-9.
  72. Jump up ^ Chow, Siu L. (1997). Statistical Significance: Rationale, Validity and Utility. ISBN 0-7619-5205-5.
  73. Jump up ^ Paparone, Dr. Christopher R. "Army Logistician (A Values-Based Critique of Lean and Six Sigma as a Management Ideology)". Almc.army.mil. Retrieved 2012-02-10.
  74. Jump up ^ The fourth quadrant: a map of the limits of statistics [9.15.08] Nassim Nicholas Taleb An Edge Original Essay
  75. Jump up ^ "Special Workshop on Risk Acceptance and Risk Communication" (PDF). Stanford University. 26–27 March 2007.
  76. Jump up ^ Hindo, Brian (6 June 2007). "At 3M, a struggle between efficiency and creativity". Business Week. Retrieved 2007-06-06.
  77. Jump up ^ Ruffa, Stephen A. (2008). Going Lean: How the Best Companies Apply Lean Manufacturing Principles to Shatter Uncertainty, Drive Innovation, and Maximize Profits. AMACOM (a division of American Management Association). ISBN 0-8144-1057-X.
  78. Jump up ^ Dodge, John (10 December 2007). "3M Shelves Six Sigma in R&D". Design News. Retrieved 2013-04-02.
  79. Jump up ^ Wheeler, Donald J. (2004). The Six Sigma Practitioner's Guide to Data Analysis. SPC Press. p. 307. ISBN 978-0-945320-62-3.
  80. ^ Jump up to: a b *Pande, Peter S.; Neuman, Robert P.; Cavanagh, Roland R. (2001). The Six Sigma Way: How GE, Motorola, and Other Top Companies are Honing Their Performance. New York: McGraw-Hill Professional. p. 229. ISBN 0-07-135806-4.

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