Six SigmaSix Sigma is a process improvement set of tools and strategies, originally developed by Motorola in 1986.[1][2] Six Sigma became well known after Jack Welch made it a central focus of his business strategy at General Electric in 1995,[3] and today it is used in different sectors of industry.[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.[5] 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","Orange Belts", etc...) who are experts in these very complex methods.[5] Each Six Sigma project carried out within an organization follows a defined sequence of steps and has quantified financial targets (cost reduction and/or profit increase).[5]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 defects per 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 byword for the management and engineering practices used to achieve it.

Historical overviewSix Sigma originated as a set of practices designed to improve manufacturing processes and eliminate defects, but its application was subsequently extended to other types of business processes as well.[6] In Six Sigma, a defect is defined as any process output that does not meet customer specifications, or that could lead to creating an output that does not meet customer specifications.[5]CEO Bob Galvin was always focused on improving the quality of Motorola products. Galvin found an ally in John F. Mitchell,[7][8][9] a young engineer on the rise to becoming Chief Engineer. Mitchell was seen as a demanding,[10][11] hands-on manager who cared for his co-workers[12][13] and insisted on team effort.[14] Mitchell believed in building quality into the engineering and manufacturing processes as a way of lowering costs and improving yield.[10] He also favored competition among product lines and distributors as a business discipline to both reduce costs and to promote quality improvement.[12]Mitchells early successes with quality control appeared with the introduction of a new digital transistorized Pager, and the formalization of improvised Mitchell Quality Tests.[15] Mitchell also used Shainin Methods and other tests[16] in his operations.[17] John F. Mitchell set the bar high for his engineers knowing they would respond.[18] By the early 1970s, as John F. Mitchell was on his ascendancy to General Manager, Communications Division in 1972, Motorola had established itself as second largest producer of electronic equipment behind IBM,[19] and as the world leader in wireless communication products, and had been battling Intel and Texas Instruments for the number one slot in Semiconductor sales. Motorola was also the largest supplier of certain parts and products to Japan's National Telegraph & Telephone Company, but at the same time, the Japanese were beginning to erode Motorola's lead in the Pager market.[20] The rapid successes and expansion of the Motorola Pager business created by John F. Mitchell, as cited above, led to competitive deficiencies in quality controls, notwithstanding the "Mitchell Testing."In the late 1970s, as John F. Mitchell was on the ascendancy to being named President & COO in 1980, he was joined by other senior managers, notably, CEO Bob Galvin, Jack Germain,[19][21] and Art Sundry,[14][15][22][23] who worked in John F. Mitchell's Pager organization to set the quality bar 10x higher. Sundry was reputed to have shouted "Our Quality Stinks"[20] at an organizational meeting attended by Galvin, John F. Mitchell and other Senior Executives; and Sundry got to keep his job.[20] But most importantly, the breakthroughs occurred when it was recognized that intensified focus and improved measurements, data collection, and more disciplined statistical approaches[23][24][25] John F. Mitchell's untiring efforts,[10][26] and support from Motorola engineers[14] and senior management, prevailed and brought Japanese quality control methods back to the USA,[27] and resulted in a significant and permanent change in culture at Motorola. "We ought to be better than we are," said Germain, director of Quality Improvement.[20] The culmination of Motorola quality engineering efforts occurred in 1986, with the help of an outside quality control consultant who joined Motorola, Bill Smith[28][29][30][31] when the Motorola University and Six-Sigma Institute[27] was founded. Two years later, in 1988, Motorola received the coveted Malcolm Baldrige National Quality Award[32] which is given by the United States Congress. Later, the Six Sigma processes subsequently were adopted at the General Electric Corporation. Jack Welch said: "Six Sigma changed the DNA of GE."[23][33] The Six Sigma process requires 99.99967% error free processes and products, (or 3.4 parts per million defects or less).[20] Without the Six Sigma process controls, it may not have been possible for John F. Mitchell to launch the Iridium satellite constellation, one of the most complex projects undertaken by a private company, which involved some 25,000 electronic components,[34] and took 11 years to develop and implement at a cost of $5 Billion.[34] Six Sigma processes resulted in $1617 Billion in savings to Motorola as of 2006.[23][35] A search of Safari Books Online reveals 1062 books written about Six Sigma.[23] with 532 published since 2009.[4]Six Sigma DoctrineLike its predecessors, 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, 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.[5] An increased emphasis on strong and passionate management leadership and support.[5] A special infrastructure of "Champions", "Master Black Belts", "Black Belts", "Green Belts", etc. to lead and implement the Six Sigma approach.[5] A clear commitment to making decisions on the basis of verifiable data and statistical methods, rather than assumptions and guesswork.[5]The term "Six Sigma" comes from a field of statistics known as process capability studies. Originally, it referred to the ability of manufacturing processes to produce a very high proportion of output within specification. Processes that operate with "six sigma quality" over the short term are assumed to produce long-term defect levels below 3.4 defects per million opportunities (DPMO).[36][37] Six Sigma's implicit goal is to improve all processes to that level of quality or better.Six Sigma is a registered service mark and trademark of Motorola Inc.[38] As of 2006[update] Motorola reported over US$17 billion in savings[39] from Six Sigma. 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.[40] 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.[41]In recent years[update], some practitioners have combined Six Sigma ideas with lean manufacturing to create a methodology named Lean Six Sigma.[42] 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".[42] Companies such as IBM and Sandia National Laboratories 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.MethodsSix 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.[41] DMAIC is used for projects aimed at improving an existing business process.[41] DMAIC is pronounced as "duh-may-ick" (). DMADV is used for projects aimed at creating new product or process designs.[41] DMADV is pronounced as "duh-mad-vee" ().[edit] DMAICThe DMAIC project methodology has five phases: Define the problem, the voice of the customer, 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.[43][edit] DMADV or DFSSThe DMADV project methodology, known as DFSS ("Design For Six Sigma"),[41] 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, create a high-level design and evaluate design capability to select the best design. Design details, optimize the design, and plan for design verification. This phase may require simulations. Verify the design, set up pilot runs, implement the production process and hand it over to the process owner(s).[edit] Quality management tools and methods used in Six SigmaWithin 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. 5 Whys Analysis of variance ANOVA Gauge R&R Axiomatic design Business Process Mapping Cause & effects diagram (also known as fishbone or Ishikawa diagram) Check sheet Chi-squared test of independence and fits Control chart Correlation Cost-benefit analysis CTQ tree Design of experiments Failure mode and effects analysis (FMEA) General linear model Histograms Pareto analysis Pareto chart Pick chart Process capability Quality Function Deployment (QFD) Quantitative marketing research through use of Enterprise Feedback Management (EFM) systems Regression analysis Rolled throughput yield Root cause analysis Run charts Scatter diagram SIPOC analysis (Suppliers, Inputs, Process, Outputs, Customers) Stratification Taguchi methods Taguchi Loss Function TRIZ

[edit] Implementation rolesOne key innovation of Six Sigma involves the "professionalizing" of quality management functions. Prior to Six Sigma, quality management in practice was largely relegated to the production floor and to statisticians in a separate quality department. Formal Six Sigma programs adopt a ranking terminology (similar to some martial arts systems) to define a hierarchy (and career path) that cuts across all business functions.Six Sigma identifies several key roles for its successful implementation.[44] 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 time to Six Sigma. They primarily focus on Six Sigma project execution, whereas Champions and Master Black Belts focus on identifying projects/functions for Six Sigma. Green Belts are the employees who take up Six Sigma implementation along with their other job responsibilities, 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.[45][edit] CertificationCorporations such as early Six Sigma pioneers 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.[41][46] Criteria for Green Belt and Black Belt certification vary; some companies simply require participation in a course and a Six Sigma project.[46] There is no standard certification body, and different certification services are offered by various quality associations and other providers against a fee.[47][48] 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.[46][49] 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.[46][48] Other providers offering certification services include the Juran Institute, Six Sigma Qualtec, Air Academy Associates and many others. 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.[36] 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. 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.[36]

Graph of the normal distribution, which underlies the statistical assumptions of the Six Sigma model. The Greek letter (sigma) marks the distance on the horizontal axis between the mean, , and the curve's inflection point. The greater this distance, the greater is the spread of values encountered. For the green curve shown above, = 0 and = 1. The upper and lower specification limits (USL and LSL, respectively) are at a distance of 6 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 1.5 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 least 6 away from the nearest specification limit.Role of the 1.5 sigma shiftExperience has shown that processes usually do not perform as well in the long term as they do in the short term.[36] 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.[36] To account for this real-life increase in process variation over time, an empirically-based 1.5 sigma shift is introduced into the calculation.[36][50] 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.[36]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).[36] 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.[36] 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.[36]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 ruleThe table[51][52] 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 levelDPMOPercent defectivePercentage yieldShort-term CpkLong-term Cpk

1691,46269%31%0.330.17

2308,53831%69%0.670.17

366,8076.7%93.3%1.000.5

46,2100.62%99.38%1.330.83

52330.023%99.977%1.671.17

63.40.00034%99.99966%2.001.5

70.0190.0000019%99.9999981%2.331.83

Software used for Six Sigma[edit] Statistics Analysis tools with comparable functions Arena ARIS Six Sigma Bonita Open Solution BPMN2 standard and KPIs for statistic monitoring JMP Mathematica MATLAB Microsoft Visio Minitab R language (The R Project for Statistical Computing[53]). Some contributed packages at CRAN contain specific tools for Six Sigma: SixSigma,[54] qualityTools,[55] qcc[56] and IQCC.[57] SDI Tools SigmaXL Software AG webMethods BPM Suite SPC XL STATA Statgraphics STATISTICAApplicationSix Sigma mostly finds application in large organizations.[58] 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.[58] 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.[58] This is due both to the infrastructure of Black Belts that Six Sigma requires, and to the fact that large organizations present more opportunities for the kinds of improvements Six Sigma is suited to bringing about.[58]In healthcareSix Sigma strategies were initially applied to the healthcare industry in March 1998. The Commonwealth Health Corporation (CHC) was the first health care organization to successfully implement the efficient strategies of Six Sigma.[59] Substantial financial benefits were claimed, for example in their radiology department throughout improved by 33% and costs per radiology procedure decreased by 21.5%;[60] Six Sigma has subsequently been adopted in other hospitals around the world.[61][62]Critics of Six Sigma believe that while Six Sigma methods may have translated fluidly in a manufacturing setting, they would not have the same result in service-oriented businesses, such as the health industry.[63]CriticismLack of originalityNoted 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."[64]Role of consultantsThe 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.[5]Potential negative effectsA 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 of consulting firm Qualpro (which espouses a competing quality-improvement process)".[65] 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.[66][67]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).[68] The extensive reliance on significance testing and use of multiple regression techniques include the risk of making commonly unknown types of statistical errors or mistakes. There are severe pitfalls inherent to the use of these methods and the misunderstandings are widespread. Since decennia these dangers have been pointed out, but are often not taken seriously or are simply ignored. The most serious consequence of this 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.[69] 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.[70][71][72][73] 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 NovemberDecember 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."[74]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.[75] 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.[76]Lack of systematic documentationOne 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:One final criticism, probably more to the Six Sigma literature than concepts, relates to the evidence for Six Sigmas 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.[68]Based on arbitrary standardsWhile 3.4 defects per million opportunities might work well for certain products/processes, it might not operate optimally or cost effectively for others. A pacemaker process might need higher standards, for example, whereas a direct mail advertising campaign might need lower standards. The basis and justification for choosing six (as opposed to five or seven, for example) as the number of standard deviations, together with the 1.5 sigma shift is not clearly explained. In addition, the Six Sigma model assumes that the process data always conform to the normal distribution. The calculation of defect rates for situations where the normal distribution model does not apply is not properly addressed in the current Six Sigma literature. This particularly counts for reliability-related defects and other problems that are not time invariant. The IEC, ARP, EN-ISO, DIN and other (inter)national standardization organizations have not created standards for the Six Sigma process. This might be the reason that it became a dominant domain of consultants (see critics above).[5]Criticism of the 1.5 sigma shiftThe statistician Donald J. Wheeler has dismissed the 1.5 sigma shift as "goofy" because of its arbitrary nature.[77] Its universal applicability is seen as doubtful.[5]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."[36][78] 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.[78] 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