Six Sigma

Not to be confused with Sigma 6.

The often used six sigma symbol

Six Sigma is a methodology to manage process variations that cause defects, defined as unacceptable deviation from the mean or target; and to systematically work towards managing variation to eliminate those defects. The objective of Six Sigma is to deliver high performance, reliability, and value to the end customer. It was pioneered by Bill Smith at Motorola in 1986 and was originally defined as a metric for measuring defects and improving quality; and a methodology to reduce defect levels below 3.4 Defects Per (one) Million Opportunities (DPMO). Six Sigma has now grown beyond defect control.

Six Sigma is a registered service mark and trademark of Motorola, Inc. Motorola has reported over US$17 billion in savings from Six Sigma to date.

Application & Success

AlliedSignal and General Electric became early adopters of Six Sigma, with GE reporting benefits of more than US $300 million during its first year of application. Their CEOs, Larry Bossidy and Jack Welch played a vital role in popularizing Six Sigma.

Starting with manufacturing, today Six Sigma is being used across a wide range of industries like banking, telecommunications, insurance, marketing, construction, healthcare, and software. Some non-manufacturing examples are given below:

Healthcare

North Carolina Baptist Hospital says, "The Six Sigma process improvement deployment at North Carolina Baptist Hospital is starting to show the kind of results that convert skeptics to believers." and "A Six Sigma process improvement team charged with getting heart attack patients from the Emergency Department into the cardiac catheterization lab for treatment faster slashed 41 minutes off the hospital's mean time" Six sigma lean can also be traced back to the Nazis.

Banking

Bank of America has used Six Sigma for credit risk assessment reduction, fraud prevention, and customer satisfaction improvement, etc. Bank of America's Six Sigma initiative resulted in benefits of more than US$2 billion; and increased customer satisfaction by 25%.

Insurance

Insurance companies have used Six Sigma for critical tasks like premium outstanding reduction and various cycle time reductions. For example, CIGNA Dental reports pending claim volume reduction by over 50% .

Construction

In engineering and construction of the Channel Tunnel Rail Link project in the UK, the Bechtel’s project team uncovered a way to save hundreds of job hours on one of the tunneling jobs.

The Institute of Quality Assurance has interesting success stories on Wipro, Citibank, and Motorola.

Military

The United States Navy has adopted Six Sigma as part of AIRSpeed[1], an overall set of practices designed to improve efficiency in aviation maintenance. The other components of AIRSpeed are Lean and Theory of Constraints.

The United States Air Force process improvement program based on Lean and Six Sigma is named Air Force Smart Operations 21 (AFSO21).

Programming

JPMorgan Chase & Co. tried combining Six Sigma with the computer programming methodologies of Extreme Programming (XP), and Capability Maturity Model Integration (CMMI). The result: the three systems did not mutually contradict, but reinforced each other well, leading to better development; see Extreme Programming (XP) Six Sigma CMMI.

Methodology

Six Sigma has two key methodologies – DMAIC and DMADV. DMAIC is used to improve an existing business process. DMADV is used to create new product designs or process designs in such a way that it results in a more predictable, mature and defect free performance. Sometimes a DMAIC project may turn into a DFSS project because the process in question requires complete redesign to bring about the desired degree of improvement.

DMAIC

Basic methodology consists of the following five phases:

• Define formally define the process improvement goals that are consistent with customer demands and enterprise strategy.
• Measure to define baseline measurements on current process for future comparison. Map and measure process in question and collect required process data.
• Analyze to verify relationship and causality of factors. What is the relationship? Are there other factors that have not been considered?
• Improve optimize the process based upon the analysis using techniques like Design of Experiments.
• Control setup pilot runs to establish process capability, transition to production and thereafter continuously measure the process and institute control mechanisms to ensure that variances are corrected before they result in defects.

DMADV

Basic methodology consists of the following five phases:

• Define formally define the goals of the design activity that are consistent with customer demands and enterprise strategy.
• Measure identify CTQs, product capabilities, production process capability, risk assessment, etc.
• Analyze develop and design alternatives, create high-level design and evaluate design capability to select the best design.
• Design develop detail design, optimize design, and plan for design verification. This phase may require simulations.
• Verify design, setup pilot runs, implement production process and handover to process owners.

Also see Design for Six Sigma quality. The most common acronym for Design for Six Sigma is DFSS.

Some people have used DMAICR (realize). Others contend that focusing on the financial gains realized through Six Sigma is counter-productive and that said financial gains are simply byproducts of a good process improvement.

Another additional flavor of Design for Six Sigma is the DMEDI method. This process is almost exactly like the DMADV process, utilizing the same toolkit, but with a different acronym. DMEDI stands for:

• Define
• Measure
• Explore
• Develop
• Implement

Roles Required for Implementation

Six Sigma identifies five key roles for its successful implementation.

• Executive Leadership includes CEO and other key top management team members. 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 are responsible for the Six Sigma implementation across the organization in an integrated manner. The Executive Leadership draws them from the upper management. Champions also act as mentor to Black Belts. At GE this level of certification is now called "Quality Leader".
• Master Black Belts, identified by champions, act as in-house expert coach for the organization on Six Sigma. They devote 100% of their time to Six Sigma. They assist champions and guide Black Belts and Green Belts. Apart from the usual rigor of statistics, their time is spent on ensuring integrated deployment 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. They operate under the guidance of Black Belts and support them in achieving the overall results.

Please note that in many successful modern programs, Green Belts and Black Belts are empowered to initiate, expand, and lead projects in their area of responsibility. The roles as defined above, therefore, conform to the antiquated Mikel Harry/Richard Schroeder model, which is far from being universally accepted.

Specific training programs are available to train people to take up these roles.

Examples of Some Key Tools Used

• Failure Modes Effects Analysis
• Cost Benefit Analysis
• CTQ Tree
• Customer Output Process Input Supplier Maps
• Customer survey
• Process Maps
• Run Charts
• Catapult Exercise on variability
• Histograms
• Stratification
• ANOVA Gage R&R
• Cause & Effects Diagram (a.k.a. Fishbone or Ishikawa Diagram)
• Homogeneity of Variance
• ANOVA
• Chi-Square Test of Independence and Fits
• General Linear Model
• Regression
• Correlation
• Design of Experiments
• Taguchi
• Control Charts
• 5 Whys
• Axiomatic design

Criticisms of Six Sigma

Origin

Robert Galvin did not really "invent" Six Sigma in the 1980s, but would more correctly be said to have applied methodologies that had been available since the 1920s and were developed by luminaries like Shewhart, Deming, Juran, Ishikawa, Ohno, Shingo, Taguchi and Shainin. The goal of Six Sigma, then, is to use the old tools in concert, for a greater effect than a sum-of-parts approach.

The use of "Black Belts" as itinerant change agents is controversial as it has created a cottage industry of training and certification which arguably relieves management of accountability for change; pre-Six Sigma implementations, exemplified by the Toyota Production System and Japan's industrial ascension, simply used the technical talent at hand — Design, Manufacturing and Quality Engineers, Toolmakers, Maintenance and Production workers — to optimize the processes.

The Term Six Sigma

Sigma (the lower-case Greek letter "s") is used to represent standard deviation (a measure of variation) of a population (lower-case 's', is an estimate, based on a sample). The term "six sigma process" comes from the notion that if you have six standard deviations between the mean of a process and the nearest specification limit, you will make practically no items that exceed the specifications. This is the basis of the Process Capability Study, often used by quality professionals. The term "Six Sigma" has its roots in this tool, rather than in simple process standard deviation, which is also measured in "sigmas". Criticism of the tool itself, and the way that the term was derived from the tool, often spark criticism of Six Sigma.

The widely accepted definition of a six sigma process is one that produces 3.4 defective parts per million opportunities (DPMO). http://www.isixsigma.com/dictionary/Six_Sigma-85.htm 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). So 3.4 DPMO corresponds to 4.5 sigmas, not six. Anyone with access to Minitab or QuikSigma can quickly confirm this by running a Capability Study on data with a mean of 0, a standard deviation of 1, and an upper specification limit of 4.5. So, how is this truly 4.5 sigma process transformed to a 6 sigma process? By arbitrarily adding 1.5 sigmas to the calcuated result, the "1.5 sigma shift" (SBTI Black Belt material, ca 1998). Dr. Donald Wheeler, one of the most respected authors on the topics of Control Charts, Capability Studies, and Designed Experiments, dismisses the 1.5 sigma shift as "goofy". (Wheeler, Donald J., Phd, The Six Sigma Practitioner's Guide to Data Analysis, p307, www.spcpress.com)

In a Capability Study, sigma refers to the number of standard deviations between the process mean and the nearest specification limit, rather than the standard deviation of the process, which is also measured in "sigmas". As process standard deviation goes up, or the mean of the process moves away from the center of the tolerance, the Process Capability sigma number goes down, because fewer standard deviations will then fit between the mean and the nearest specification limit. http://en.wikipedia.org/wiki/Cpk_Index The notion that, in the long term, processes usually do not perform as well as they do in the short term is correct. That requires that that Process Capability sigma based on long term data is less than or equal to an estimate based on short term sigma. However, the original use of the 1.5 sigma shift is as shown above, and implicitly assumes the opposite.

As sample size increases, the error in the estimate of standard deviation converges much more slowly than the estimate of the mean (see confidence interval). Even with a few dozen samples, the estimate of standard deviation often drags an alarming amount of uncertainty into the Capability Study calculations. It follows that estimates of defect rates can be very greatly influenced by uncertainty in the estimate of standard deviation, and that the defective parts per million estimates produced by Capability Studies often ought not to be taken too literally.

Estimates for the number of defective parts per million produced also depends on knowing something about the shape of the distribution from which the samples are drawn. Unfortunately, we have no means for proving that data belong to any particular distribution. We only assume normality, based on finding no evidence to the contrary. Estimating defective parts per million down into the 100’s or 10’s of units based on such an assumption is wishful thinking, since actual defects are often deviations from normality, which have been assumed not to exist.

The +/-1.5 Sigma Drift

Everyone with a Six Sigma program knows about the +/-1.5 sigma drift of a process mean, experienced by all processes. What this is saying is that if we are manufacturing a product that is 100 +/- 3 cm (97 - 103cm), over time, it may drift down to 98.5 – 104.5 or up to 104.5-101.5. Something that might be of concern to our customers. So where does the "+/-1.5" come from?

The +/-1.5 shift was introduced by Mikel Harry. Where did he get it? Harry refers to a paper written in 1975 by Evans, "Statistical Tolerancing: The State of the Art. Part 3. Shifts and Drifts". The paper is about tolerancing. That is how the overall error in an assembly is effected by the errors in components. Evans refers to a paper by Bender in 1962, "Benderizing Tolerances – A Simple Practical Probablity Method for Handling Tolerances for Limit Stack Ups". He looked at the classical situation with a stack of disks and how the overall error in the size of the stack, relates to errors in the individual disks. Based on "probability, approximations and experience", he suggests:

v= 1.5 SQRT (var X)

What has this got to do with monitoring the myriad of processes that people are concerned about? Very little. Harry then takes things a step further. Imagine a process where 5 samples are taken every half hour and plotted on a control chart. Harry considered the "instantaneous" initial 5 samples as being "short term" (Harry’s n=5) and the samples throughout the day as being "long term" (Harry’s g=50 points). Because of random variation in the first 5 points, the mean of the initial sample is different to the overall mean. Harry derived a relationship between the short term and long term capability, using the equation above, to produce a capability shift or "Z shift" of 1.5 ! Over time, the original meaning of "short term" and "long term" has been changed to result in "long term" drifting means.

Harry has clung tenaciously to the "1.5" but over the years, its derivation has been modified. In a recent note from Harry "We employed the value of 1.5 since no other empirical information was available at the time of reporting." In other words, 1.5 has now become an empirical rather than theoretical value. A further softening from Harry: "… the 1.5 constant would not be needed as an approximation".

Despite this, industry has fixed on the idea that it is impossible to keep processes on target. No matter what is done, process means will drift by +/-1.5 sigma. In other words, suppose a process has a target value of 10.0, and control limits work out to be, say, 13.0 and 7.0. "Long term" the mean will drift to 11.5 (or 8.5), with control limits changing to 14.5 and 8.5.

The simple truth is that any process where the mean changes by 1.5 sigma or any other amount, is not in statistical control. Such a change can often be detected by a trend on a control chart. A process that is not in control is not predictable. It may begin to produce defects, no matter where specification limits have been set.

World Class Quality means "On target with minimum variation" .

In summary, the term “Six Sigma” has its roots in a quality tool that can easily be misapplied by a naïve user and in the controversial 1.5 sigma shift.

Digital Six Sigma

In an effort to permanently minimize variation, Motorola has evolved the Six Sigma methodology to use information systems tools to make business improvements absolutely permanent. Motorola calls this effort Digital Six Sigma.

Statistics and robustness

Many mistakenly believe that the core of the Six Sigma methodology is statistics. This is not so. You can do a very acceptable Six Sigma project with only the most rudimentary statistical tools.

The core of the Six Sigma methodology is a data-driven, systematic approach to problem solving, and focus on customer impact. Statistical tools just happen to be useful along the way.

Six Sigma is not the answer to all problems. If you're writing poetry, it will probably be of little value. If you're working on business, engineering, or production processes it is practically always applicable and successful, when applied correctly. In this sense, the core methodology is remarkably general and robust.

Some professional statisticians justifiably criticize Six Sigma because the quality of statistical understanding that is propagated by practitioners is highly variable. Some programs are excellent, and some are much less so.

See also

• Design for Six Sigma
• Process Improvement
• Business Process
• Business Process Improvement
• Business Process Improvement Pattern
• Lean manufacturing

External links

• GE Six Sigma
• Motorola University