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Why Meaningful Relevant Data is Critical to Six Sigma

admin — Mon, 17 May 2010 16:13:51 +0000

Before being introduced to Six Sigma, many managers consider it a mysterious approach to process efficiency that cannot be properly measured. Indeed, there are plenty of business management strategies that emerge and are successful for awhile based upon fad rather than delivering practical results. By contrast, this methodology is firmly grounded in data and statistical analysis.

The foundation of this approach is built upon the collection and evaluation of numbers. Every step of the deployment, from the identification of the initiative’s objective to long term performance tracking, relies upon numbers. Below, I’ll explain how data is used throughout a Six Sigma assignment.

The Core Of Process Improvement

The purpose of the methodology is to improve business processes. In order to do that, the project team must identify variances and study their individual and collective impacts on waste. The only reliable way to make those improvements is by collecting data and measuring it against existing baselines.

The dedication of Six Sigma initiatives to a quantitative approach not only helps to ensure improvements, but it also sets the stage for ongoing measurement. Every process has a tendency to accrue waste over time. By establishing baselines and measuring future results by them, that waste can be kept at bay. Ultimately, that improves product cycle times, deliverability, and revenue while lowering operational expenses.

Identifying And Eliminating Waste

A Six Sigma project begins with identifying opportunities for an organization to limit waste and variances that exist in a given process. Part of that procedure includes isolating inputs and outputs. Those variables are isolated in order that the project team can collect metrics that might lead to future improvements.

During the assignment, the metrics collected from the inputs and outputs are compared to predefined benchmarks. At this point, the project team has two responsibilities. First, they must identify the presence of defects and errors within the process. Second, they must review the gathered metrics and determine each variable’s impact on Critical To Quality (CTQ) factors.

Note how the metrics are vital to the success of the entire initiative. Without them, the organization’s current performance and the errors and defects which may exist within cannot be properly analyzed.

Designing Solutions

The next phase of a Six Sigma initiative relies heavily on the data collected from the previous steps. The project team will develop solutions which, when implemented, will hopefully lead to process related improvements. These solutions are not designed in a vacuum; they rely upon the gathered metrics.

The project team will review each of the key variables to determine the effects of making changes to them. While there is some experimentation involved, designing solutions which can eliminate waste and variances depends upon rigorous statistical analysis.

Measuring Results

Once the Six Sigma team’s solutions have been implemented, they must be monitored in order to track their success. Data will be collected from each of the inputs and outputs identified earlier in the project to determine whether the solutions are having the intended effect.

It is possible that the project team’s changes will lead to improvements in the process, yet not completely eliminate errors, defects, and waste. This is the reason data is so important to success. The process metrics must be reviewed and analyzed until waste has been eliminated. Then, once that has been accomplished, they must be perpetually monitored to ensure waste does not creep in again.

Those who are familiar with the Six Sigma methodology will not be surprised to hear that data is essential to the success of a project. It both guides the initiative and provides a platform on which to objectively measure results.

First seen on http://pete.lawnygolf.com/2010/05/15/why-data-is-critical-to-six-sigma/

Download the Six Sigma Handbook Third Edition

admin — Mon, 23 Nov 2009 11:46:45 +0000

The authoritative classic–revised and updated for today’s Six Sigma practitioners

Whether you want to further your Six Sigma training to achieve a Black or Green Belt or you are totally new to the quality-management strategy, you need reliable guidance. The Six Sigma Handbook, ThirdEdition shows you, step by step, how to integrate this profitable approach into your company’s culture.

Co-written by an award-winning contributor to the practice of quality management and a successful Six Sigma trainer, this hands-on guide features:
- Cutting-edge, Lean Six Sigma concepts integrated throughout
- Completely revised material focused on project objectives
- Updated and expanded problem-solving examples using Excel and Minitab
- A streamlined format that puts proven practices at your fingertips

The Six Sigma Handbook, Third Edition is the only comprehensive reference you need to make Six Sigma work for your company. The book explains how to organize for Six Sigma, how to use customer requirements to drive strategy and operations, how to carry outsuccessful project management, and more. Learn all the management responsibilities and actions necessary for a successful deployment, as well as how to:
- Dramatically improve products and processes using DMAIC and DMADV
- Use Design for Six Sigma to create innovative products and processes
- Incorporate lean, problem-solving, and statistical techniques within the Six Sigma methodology
- Avoid common pitfalls during implementation

Six Sigma has evolved with the changing global economy, and The Six Sigma Handbook, Third Edition is your key to ensuring that your company realizes significant gains in quality, productivity, and sales in today’s business climate.

560 pages

Six Sigma Handbook Third Edition

McGraw-Hill Professional;
3 edition (September 21, 2009)
ISBN: 0071623388
PDF 9.6Mb

Download it from http://rapidshare.com/files/310019896/McGraw-Hill_-_The_Six_Sigma_Handbook_3rd_Edition__2009_.zip or

http://www.10xdownloads.com/servers.asp?pb=2&PID=2bc60e94-1b70-4fdc-9f6f-d525c70aaf4f&jstyle=3&q=The%20Six%20Sigma%20Handbook,%203rd%20Edition

Six Sigma and Minitab A complete Toolbox Guide for All Six Sigma Practitioners

admin — Wed, 11 Nov 2009 11:29:08 +0000

Six Sigma and Minitab

Six Sigma and Minitab: A complete toolbox guide for all Six Sigma practitioners (2nd edition) by Quentin Brook

In completing my final week of black belt training, my esteemed master black belt, George Woodley. Thanks George.

Description

The long awaited 2nd edition of this bestselling pocket guide on Six Sigma contains a range of new tools and techniques including new Lean material and Improve tools. In addition it has been updated for Minitab 15 (whilst still compatible with versions 13 and 14). Cutting through Six Sigma s strange terminology and consultancy speak, this guide delivers Six Sigma in a down to earth, logical and user friendly format. Minitab: For each tool, this guide details how to enter the data into Minitab, interpret the results and avoid the common pitfalls. Interactive: All the data files and templates are available online. Routemaps: A logical flow is provided through each DMAIC phase. Who should use this book? Six Sigma Trainees: Both during and after training, this guide provides an invaluable reference text to those who are actually implementing Lean Six Sigma improvement projects. Six Sigma Project Sponsors and Managers: For those who are accountable for deploying Six Sigma or sponsoring Six Sigma projects, and who might not have been fully Six Sigma trained, this guide will provide an overview of the tools and techniques that your project teams are trained in.

Here are some customer reviews we spotted on Amazon.

I really like how this “toolbox” book is put together. It is quick and to the point in a compact format. It shows what minitab tests can be used within each phase of the DMAIC process. I recommend it for the person who already has at least a bit of an understanding of the Six Sigma philosophy. It is the kind of book you will use for minitab reference over and over again.

This book is my go-to resource for DMAIC processes. It provides simple explanations of the tools and outcomes and is the reference material I always recommend to new belts.

Really good book for anybody using Minitab in Six Sigma or just plain statistics. Not too superficial (like many ‘Management Books’) and not too many silly examples (like some ‘Text Books’). Really useful. After reviewing it we bought one copy for each Black Belt at our company.

I do agree, however, that the new listed price is $49.99 given that much of Minitab’s documentation is now complete and freely available on their website.

Spiral-bound: 240 pages

Publisher: QSB Consulting (October 23, 2006)

Language: English

ISBN-10: 0954681320

ISBN-13: 978-0954681326

Also, if you’re looking for a great Master Black Belt, mentor, statistician, I highly recommend George Woodley. George learned Six Sigma at Motorola, taught SPC at Ford but to name a few of his stints. Check out his website at http://qualityforall.net

Design of Experiments DOE Planning and Some Basic Terms

admin — Wed, 04 Nov 2009 17:26:58 +0000

Design of Experiment

DOE Planning

Don’t be like a DOE in the headlights (yes this is a subtle attempt at Six Sigma humor).

Before embarking on a DOE you must first determine what you are trying to accomplish

What kind of information or data do you have to run the experiment?

Approximations

Before beginning a DOE: Do you have a clear objective or charter?

This is an experiment; therefore, it’s not 100% reliable. Your results will be approximated – like a simulation.

The reason the results are approximations is that you may not understand or have enough information to be certain but you need to make a decision.

Realism

Is the experiment realistic?

Will you be mixing different types of data (continuous, discrete) in ways that don’t reflect reality or the real world?

Will you be simulating things that aren’t realistic?

Are the materials and resources available to perform an experiment?

– Is the setting with aircraft, military equipment, ball-point pens, condoms?

– Are you performing the experiment on a team or work shift at the end of the quarter?

Terms and Definitions

Balanced design

Each experimental level for any one factor is repeated the same number of times for all possible combinations involving the levels of the other factors.

Blocking variable

A factor n an experiment that has an undesired influence on the response

Center points

Repeats or replicates run at the center or midpoint of all quantitative factor levels. Center points are often run at current factor levels. Used to detect accuracy of linear fit.

Confounding

One or more effects that can not unambiguously be attributed to a single factor or interaction.

Designed experiment

The simultaneous study of the impact of multiple process factors on the response variable.

Experimental error

Variation in the sum of squares after all significant sources of variability have been accounted for.

Factors

One of the controlled or uncontrolled variables whose influence on the response is being studied. May be variable or classification data.

Interaction

The combined effect of two or more factors that is observed which is in addition to the main effect of each factor individually.

Level

The values or the factor being studied usually high (+) and low(-) or (+1) to (-1)

Main effect

Change in the average response observed during a change from one level to another for a single factor

Orthogonal

Balanced designs. Each factor is statistically independent from the others. Enhances the ability to detect and quantify interactions.

Pure Error

Variation in the sum of squares that can only be estimated by true repeat or replicate runs.

Repetition

Performing several experimental runs consecutively using the same treatment combinations (one setup)

Replication

The number of runs or replicates. How many times was the experiment run.

Test run

A single combination of factors that yields one or more observation of the response

Treatment

A single level assigned to a single factor during an experimental run

Treatment combination

An experimental run using a set of the specific levels or each input variable.

Unbalanced design

The experimental levels of any one factor is not repeated the same number of times for all combinations of levels of the other factors.

Introduction to Six Sigma Statistics

admin — Mon, 19 Oct 2009 17:04:26 +0000

I thought I’d bring in some key points here before embarking on a serious Design of Experiment, or multiple regression analysis. I’ve come across several black belt candidates in training (like myself), who get too caught up with the statistical side of things (or Minitab) and forget the basics. I thought

1. Learn the scales of measure

Nominal
It is in the name
Marital status, Phone numbers

Ordinal
Relative, unequal value ranking
Race finish, opinion poll response

Interval
Equal intervals are equal differences
Calendar year, Fahrenheit temperature

Ratio
Proportional amount of difference
Has a real zero value
Annual income, Kelvin temperature

2. Learn the measures of central tendency

Mean: Arithmetic average of a set of values
• Reflects the influence of all values
• Strongly Influenced by extreme values
Mode: The most frequently occurring value
Median: Midpoint in a string of sorted data, where 50% of the observations, or values, are below and 50% are above
• Does not necessarily include all values in calculation
• Is “robust” to extreme scores
• Organize the data from low values to high when determining the Median

3. Learn the measures of dispersion

Range: the distance between the extreme values of a data set (Highest – Lowest)
The range is more sensitive to outliers than the variance

Variance: the Average Squared Deviation of each data point from the Mean

Standard Deviation: the Square Root of the Variance
measure of the average deviation about the mean

4. Understand the different types of data

Variable (quantative) and Continuous Data (Decimal subdivisions are meaningful)
o Time (seconds)
o Pressure (psi)
o Conveyor Speed (ft/min)
o Rate (inches

Attribute (qualitative)
o Categories
o Good/Bad (Pass/Fail)
o Machine 1, Machine 2, Machine 3
o Shift number
o Counted things (# of Errors in a document, # units shipped, etc.)

Convert Attribute to Continuous wherever possible. Here are some examples of attribute data converted to continuous data:

– Count of defects to ‘% defects’
– Y/N late to ‘average days late’
– Leaks/No leaks to ‘rate of leaks on a continuous scale’
– Success or failure of electrical parts to ‘voltage flow of good parts’

5. Descriptive Statistics

Consists of basic statistics and graphical techniques used to summarize data
Measures of central location
Measures of spread (dispersion)
Evaluation of symmetry & skewness
Typical graphical techniques
- Histograms
- Boxplots
- Dotplots
- Normal probability plots

6. Be able to identify different data distributions

Why does it matter? If you’re treating non-normal data as normal, you’ll get a totally different p-value for your data set, thereby overstating or understating your prediction or analysis.

Normal Distribution (Bell Curve)

The “Normal” Distribution is a distribution of data which has certain consistent properties (the mean, median and mode are equal in value)

These properties are very useful in our understanding of the characteristics of the underlying process from which the data were obtained

Most natural phenomena and man-made processes are distributed normally, or can be represented as normally distributed

The Normal Distribution is a continuous distribution which is symmetrical and extreme values are less likely than moderate values (unimodal)

An example would be measuring heights of people or the length of a table. In either case the measurement is continuous and can be broken down into finer increments

t-distribution

The t distribution assumes samples are drawn from a normal distribution but the population variance, s2, is not known… The shape of the t-distribution varies as the sample size, n, changes. The distribution becomes more narrow as the sample size becomes larger. As n becomes very large, the critical value corresponding to the area under the curve approaches the Normal distribution’s Z value

Poisson Distribution

Appropriate as a model of number of defects or nonconformities in a unit of product
X is number of defects found in a per unit basis
– Per unit area, per unit volume, per unit time, etc.
– Area X is a discrete, positive integer
– Area for opportunity is a finite region of space, time or product

When the average is high, the distribution can be approximated by the normal distribution

When the average is low, the distribution is skewed to the right

F Distribution

A continuous distribution formed from the ratio of variances calculated from two independent samples drawn from Normal Distributions

Chi-square Distribution

A continuous distribution used in statistical hypothesis testing and confidence interval estimation for many different applications, including inferences about a population variance

7. Know about samples and population sizes

Population is every possible observation (census)

Samples are subsets of populations

Data is obtained using samples because we seldom know the entire population

Descriptive statistics apply to any distribution
- Sample or population

Population statistics are desired, but often not available

Samples from a population can be used to ‘infer’ or approximate population parameters

8. Know the Statistics and Reporting Tools

By far the most used Six Sigma tools is Microsoft Excel. Excel provides most of the day to day uses required to manage most Six Sigma projects. Please note though that Excel must be accompanied by other Microsoft tools such as Word, PowerPoint, and Outlook for email. In other words, the Six Sigma Black or Green belt candidate should always ensure that he or she has the latest version of Microsoft Office installed.

Also, check with your IT department or on the Microsoft Excel disc for the “Data Analysis Pack” that will allow you, through Excel to perform:

– Anova
– Correlations
– Covariances
– Descriptive Statistics
– Exponential Smoothing
– F-Tests and Two-Samples for Variances
– Fourier Analysis
– Histograms
– Various t-tests

However, the ultimate tool for Six Sigma Black Belts is MiniTab. Minitab will get you going where Excel leaves you hanging.

– Minitab will go into profound levels of englightenment with
– Measurement System Analysis
– Multivariate Analysis
– Anova
– Regression Analysis
– Statistical Process Control
– Reliability/Survival Analysis
– And other great simulations

Don’t forget to check out Minitab’s powerful reporting tools that will provide the following graphical reports:

– Dotplots / Histograms / Normal Plots
– Run charts / Time Series
– Pareto Diagrams
– Stratification (2nd Level Pareto)
– Boxplots
– Scatter Plots
– Checksheets / Concentration Diagrams

Now you should be ready to go run your multi-var charts, multiple regression, 2k full-factorial regression, and last but not least, your Design of Experiment. We’ll keep data transformations to another paper.

Please don’t hesitate to drop us a line at admin@sixsigmaz.com if you have any questions or concerns.

Measurement System Analysis for Beginners

admin — Wed, 14 Oct 2009 16:43:20 +0000

Hey there fellow Six Sigma Black Belt candidates in training. I thought I’d share with you my short thoughts on MSA. Even though I’ve written about this before, I included this summary. It simply answers the basic questions as to what Measurement System Analysis is and when to use it. For more, I highly recommend that you install Minitab and go through the tutorials.

A Measurement System Analysis is a six sigma tool to ensure that your measurement system is accurate

From the gages or measurement equipment

– Multimeters

– Fax machines synchronized to the same time

– Vernier calipers

– Thermometers

To the employees or operators

– Ensure there is no bias among different operators

– Ensure they can repeat and obtain the same measurements

– Ensue that operators can obtain the same measurements among each other

To the parts that make up a product

– Are they within specification tolerance?

– If so, is this still good enough?

When Should You Conduct an MSA?

Before any significant process improvement evaluation or initiative takes place

What are the MSA Key Proportions?

%R&R

– Contribution of variation of Repeatability and Reproducibility

% P/T

– Contribution of variation with respect to the Precision to its Tolerance

A goal is to keep these ratios under 10% contribution to variation which helps us isolate component or part variation

Measurement System Analysis Statistics

Variance of the MS is expressed as:

s²ms = s²rpt + s²rpd

Where s is the sigma mean of the samples collected

The total variation is equal to the process variation plus the measurement system variation and is expressed as:

s²total = s²ms + s²process

Where s is the sigma mean of the samples collected

Determing how to go about your MSA

Some key questions that need to be answered before conducting a flawed MSA:

What types of data are available? Normal or non-normal? Continuous, discrete, or attribute? If attribute, please conduct an attribute MSA to determine attribute agreement (hence the Kappa statistic)

Is the analysis and data available in such a way that you can determine accuracy (repeatability) and precision (reproducibility).

Also, how will the measurements be conducted on samples? That is, will the data be considered as destructive or non-destructive?

The difference between destructive and non-destructive is that in a non-destructive test, each sample is measured more than once by more than one operator, whereas, in a destructive test, each sample is only measured once by an operator as the sample is no longer available or destroyed by the test. An example of a destructive test, not always yielding destructive results, would be the analysis of aircraft landings.

Analyzing Your MSA

Did you obtain reliable data?

Did you obtain at least ten samples, measured two to times by at least two to three operators
Did you ensure randomization of the sample population and operator readings?
Did you include samples representing typical process variation (some good parts, some bad parts?) –
If not your Gage R&R will be inaccurate and show to perform poorly as compared to your parts variation

You should be able to:

Determine the next steps to take – do we improve the process or change the specifications?
Obtain 5 distinct categories – indicating good resolution

The MSA Six Pack

The following screenshot is provided courtesy of Minitab*

gage r&r

The Kappa Statistic is the proportion of agreement between inspectors (or operators) after the probability of chance has been removed.

The Kappa Statistic is used when you have attribute data

– Pass/Fail

– Go/No Go

– Hot/Cold

– Etc.

*Minitab copyright – “Portions of the input and output contained in this publication/book are printed with permission of Minitab Inc. All material remains the exclusive property and copyright of Minitab Inc. All rights reserved.”

How to Explain the Six Sigma Approach in a Minute or Less

admin — Fri, 02 Oct 2009 16:11:25 +0000

Six Sigma (sometimes referred to in short as 6 Sigma or 6S) is a data driven approach to facilitate the best non-emotional, non-impulsive decision that will satisfy the customer’s requirements without increasing costs or variation.

Applying Six Sigma methods will help you understand business impacts of arising problems and your subsequent decisions and understanding. 6S also brings clear understanding of the Voice of the Customer and drives the Customer Voice into your product designs.

6s also enables and empowers you to reduce variation by detecting occurrences of defects from a process or product. Some ways that this is done is by reducing complexity and better understanding the entire value chain, smoothing and streamlining the flow of value from our suppliers through you to your customers.

One of the strengths of Six Sigma is the application of SPC or Statistical Process Control. This doesn’t mean you need to understand complex math, arithmetic, or statistics. You will be gradually introduced to basic quality and statistics tools, however. SPC is where much of the data-driven decisions are based on.

The methods of Lean thinking provide an efficient way to reduce operational waste, save time, save cost, and extend capacity of valuable resources.

Minitab’s Latest Quality Companion Software Update Adds Value Stream Mapping

admin — Thu, 01 Oct 2009 13:26:02 +0000

State College, PA (Vocus/PRWEB ) October 1, 2009 — Minitab Inc. today released Quality Companion 3.2, an update to its software for managing and executing quality improvement projects.

This update introduces new functionality, including a powerful tool for Value Stream Mapping (VSM), a primary technique used in Lean Six Sigma initiatives. A free, 30-day trial version is available at www.QualityCompanion.com. The update is free to registered users of Quality Companion 3.

VSM helps businesses define the steps required to produce a product or service that meets customer expectations, find improvement opportunities and pinpoint sources of waste. Quality Companion’s VSM tool makes it easy to track important variables such as inventory, takt time, and cycle time, among others, to help improve manufacturing, supply chain, service-related, healthcare, software development, or product development processes.

Quality Companion by Minitab® is designed to manage improvement projects from start to finish, and has been embraced by organizations as diverse as Xerox, the U.S. Postal Service and BHP Billiton.

Quality Companion’s Project Roadmap™ helps plot a clear course of action to execute quality improvement projects. Adding Companion’s built-in “soft” tools, such as process mapping, brainstorming and reporting, creates a detailed plan for the entire project–and the means to complete each step.

Quality Companion also includes more than 100 form templates, including C&E Matrix, FMEA and Project Charter, all of which are easily customized to fit any organization.Quality Companion even offers on-demand guidance, with built-in Coaches that give expert advice from experienced Lean Six Sigma professionals.
When a project ends, Companion maintains the entire project in one easy-to-manage file, making it simple to archive and review in the future.

Quality Companion 3.2 also integrates with latest release of the Quality Companion Dashboard, a utility that aggregates and displays details of all projects in a single view to help you evaluate your progress and success, and can serve as a launch pad for projects.

The Dashboard is free, so executives and others who don’t use Quality Companion can use it to monitor the progress of their organization’s entire improvement program. Colleagues who don’t use Companion can also review projects with the free Quality Companion Viewer, which provides read-only access to project files.

About Minitab
Minitab Inc. is one of the world’s leading developers of statistical and process improvement software. Thousands of distinguished companies use Minitab software, including Toshiba, DuPont, Boeing, Royal Bank of Scotland, Nestlé and Wyeth Pharmaceuticals.

Minitab Statistical Software has been used in virtually every major Six Sigma initiative around the world, and is used to teach statistics in over 4,000 colleges and universities. Quality Companion® is used worldwide to plan and execute Six Sigma projects. Both products are backed by outstanding services, including training, e-learning opportunities, and free technical support.

Minitab Inc., headquartered in State College, Pa., operates offices in the United Kingdom, France and Australia and has additional representatives throughout the world.

For more information or materials, including screen shots, logos and other graphics, contact Eston Martz in Minitab’s Media Relations office: PublicRelations(at)minitab.com.

Introduction to Design of Experiments

admin — Mon, 21 Sep 2009 16:54:23 +0000

The Basic Concepts Underlying DOE

Six Sigma stresses making alterations in existing business processes for improving overall efficiency. To make effective alterations, it is important to first understand the various aspects of business processes so that the cause and effect relationship between various processes can be determined. However, this is easier said than done because most business processes comprise of multiple sub processes, which themselves are quite complicated.

Making alterations in a simple business process having just two to three sub-processes is easy, but the task becomes quite difficult when alterations are to be made in a business process having more than ten sub-processes. The level of difficulty goes on increasing with an increase in the number of sub-processes. This is where DOE is beneficial as it can easily crawl through vast amounts of data that is generated as part of the six-sigma implementation process. This data is meant for understanding the cause and effect relationship between various processes and sub-processes, but since the amount of data generated is quite huge, advanced tools such as DOE are used.

Why Is DOE Necessary?

DOE analyses the data and generates quantifiable results, which are then used for defining the type of experiments or alterations that are to be conducted for achieving Six Sigma quality levels. Conducting pre-tests or experiments is necessary in Six Sigma because the organizational efficiency and productivity are at stake while the implementations are going on. If Six Sigma concepts and methodologies are not implemented properly, it can seriously affect the company’s bottom-line and lead to redundancies.

Another thing is that organizations cannot hope to achieve desired results just by conducting wayward and misguided experiments or alterations. DOE is effective because it helps Six Sigma professionals in selecting the most suitable experiment designs that in turn would help in achieving the desired results. In the absence of DOE, it would be quite difficult to ascertain the type of experiments that are to be conducted.

Other Uses And Benefits

DOE can also be used for understanding the root cause of variations in a business process. Business processes are designed for delivering exactly the same quality and quantity, irrespective of what they are being used for, be it for manufacturing a product or rendering a service. However, maintaining this level of consistency is not always possible because the efficiency of business processes can be affected by various variable factors that are quite difficult to decipher.

This is where DOE can help because it can analyze vast amounts of data related to the variations and generate results that can be used for pointing out the root cause of variations. Once the variations have been eliminated, it would become quite easy for Six Sigma professionals to successfully carry out the implementations. DOE is thus an inseparable part of Six Sigma implementations in any type of industry.

Tony Jacowski is a quality analyst for The MBA Journal. Aveta Solution’s Six Sigma Online offers online six sigma training and certification classes for lean six sigma, black belts, green belts, and yellow belts.

Short Biography on Genichi Taguchi

admin — Mon, 21 Sep 2009 10:32:46 +0000

Taguchi realized that the best opportunity to eliminate variation is during design of a product and its manufacturing process

Genichi Taguchi

Gen’ichi Taguchi (born January 1, 1924 in Tokamachi, Japan) is an engineer and statistician. From the 1950s onwards, Taguchi developed a methodology for applying statistics to improve the quality of manufactured goods. Taguchi methods have been controversial among some conventional Western statisticians but others have accepted many concepts as valid extensions to the body of knowledge.

Life

Taguchi was raised in the textile town of Tokamachi where he initially studied textile engineering with the intention of entering the family kimono business. However, with the escalation of World War II, in 1942, he was drafted into the Astronomical Department of the Navigation Institute of the Imperial Japanese Navy.

After the war, in 1948, he joined the Ministry of Public Health and Welfare where he came under the influence of eminent statistician Matosaburo Masuyama who kindled his interest in design of experiments. He also worked at the Institute of Statistical Mathematics, during this time, and supported experimental work on the production of penicillin at Morinaga Pharmaceuticals, a Morinaga Seika company.

In 1950, he joined the Electrical Communications Laboratory (ECL) of the Nippon Telegraph and Telephone Corporation just as statistical quality control was beginning to become popular in Japan under the influence of W. Edwards Deming and the Japanese Union of Scientists and Engineers. ECL was engaged in a rivalry with Bell Labs to develop cross bar and telephone switching systems and Taguchi spent his twelve years there in developing methods for enhancing quality and reliability. Even at this point, he was beginning to consult widely in Japanese industry, with Toyota being an early adopter of his ideas.

During the 1950s, he collaborated widely and in 1954-1955 was visiting professor at the Indian Statistical Institute where he worked with R. A. Fisher and Walter A. Shewhart.

On completing his doctorate from Kyushu University in 1962, he left ECL, though he maintained a consulting relationship. In the same year he visited Princeton University under the sponsorship of John Tukey who arranged a spell at Bell Labs, his old ECL rivals. In 1964 he became professor of engineering at Aoyama Gakuin University, Tokyo. In 1966 he began a collaboration with Yuin Wu who later emigrated to the USA and, in 1980, invited Taguchi to lecture. During his visit there, Taguchi himself financed a return to Bell Labs where his initial teaching had made little enduring impact. This second visit began a collaboration with Madhav Phadke and a growing enthusiasm with his methodology in Bell Labs and elsewhere, including Ford Motor Company, Xerox and ITT.

Since 1982, Genichi Taguchi has been an advisor to the Japanese Standards Institute and executive director of the American Supplier Institute, an international consulting organization.

Contributions

Loss functions

Taguchi’s reaction to the classical design of experiments methodology of R. A. Fisher was that it was perfectly adapted in seeking to improve the mean outcome of a process. As Fisher’s work had been largely motivated by programs to increase agricultural production, this was hardly surprising. However, Taguchi realized that in much industrial production, there is a need to produce an outcome on target, for example, to machine a hole to a specified diameter or to manufacture a cell to produce a given voltage. He also realized, as had Walter A. Shewhart and others before him, that excessive variation lay at the root of poor manufactured quality and that reacting to individual items inside and outside specification was counter-productive.

He, therefore, argued that quality engineering should start with an understanding of the cost of poor quality in various situations. In much conventional industrial engineering the cost of poor quality is simply represented by the number of items outside specification multiplied by the cost of rework or scrap. However, Taguchi insisted that manufacturers broaden their horizons to consider cost to society. Though the short-term costs may simply be those of non-conformance, any item manufactured away from nominal would result in some loss to the customer or the wider community through early wear-out; difficulties in interfacing with other parts, themselves probably wide of nominal; or the need to build-in safety margins. These losses are externalities and are usually ignored by manufacturers. In the wider economy the Coase Theorem predicts that they prevent markets from operating efficiently. Taguchi argued that such losses would inevitably find their way back to the originating corporation (in an effect similar to the tragedy of the commons) and that by working to minimize them, manufacturers would enhance brand reputation, win markets and generate profits.

Such losses are, of course, very small when an item is near to nominal. Donald J. Wheeler characterized the region within specification limits as where we deny that losses exist. As we diverge from nominal, losses grow until the point where losses are too great to deny and the specification limit is drawn. All these losses are, as W. Edwards Deming would describe them, …unknown and unknowable but Taguchi wanted to find a useful way of representing them within statistics. Taguchi specified three situations:

Larger the better (for example, agricultural yield);
Smaller the better (for example, carbon dioxide emissions); and
On-target, minimum-variation (for example, a mating part in an assembly).

The first two cases are represented by simple monotonic loss-functions. In the third case, Taguchi adopted a squared-error loss function on the grounds:

It is the first symmetric term in the Taylor series expansion of any reasonable, real-life loss function, and so is a “first-order” approximation;
Total loss is measured by the variance. As variance is additive it is an attractive model of cost; and
There was an established body of statistical theory around the use of the least-squares principle.

The squared-error loss function had been used by John von Neumann and Oskar Morgenstern in the 1930s.

Though much of this thinking is endorsed by statisticians and economists in general, Taguchi extended the argument to insist that industrial experiments seek to maximize an appropriate signal to noise ratio representing the magnitude of the mean of a process, compared to its variation. Most statisticians believe Taguchi’s signal to noise ratios to be effective over too narrow a range of applications and they are generally deprecated.

Off-line quality control

Taguchi realized that the best opportunity to eliminate variation is during design of a product and its manufacturing process (Taguchi’s rule for manufacturing). Consequently, he developed a strategy for quality engineering that can be used in both contexts. The process has three stages:

System design;
Parameter design; and
Tolerance design.

System design

This is design at the conceptual level involving creativity and innovation.

Parameter design

Once the concept is established, the nominal values of the various dimensions and design parameters need to be set, the detail design phase of conventional engineering. Taguchi’s radical insight was that the exact choice of values required is under-specified by the performance requirements of the system. In many circumstances, this allows the parameters to be chosen so as to minimize the effects on performance arising from variation in manufacture, environment and cumulative damage. This is sometimes called robustification.

Tolerance design

With a successfully completed parameter design, and an understanding of the effect that the various parameters have on performance, resources can be focused on reducing and controlling variation in the critical few dimensions (see Pareto principle).

Design of experiments

Taguchi developed much of his thinking in isolation from the school of R. A. Fisher, only coming into direct contact in 1954. His framework for design of experiments is idiosyncratic and often flawed but contains much that is of enormous value. He made a number of innovations.

Outer arrays

Unlike the design of experiments work of R. A. Fisher, Taguchi sought to understand the influence that parameters had on variation, not just on the mean. He contended, as had W. Edwards Deming in his discussion of analytic studies, that conventional sampling is inadequate here as there is no way of obtaining a random sample of future conditions. In R. A. Fisher’s work, variation between experimental replications is a nuisance that the experimenter would like to eliminate whereas, in Taguchi’s thinking, it is a central object of investigation.

Taguchi’s innovation was to replicate each experiment by means of an outer array, possibly an orthogonal array that seeks deliberately to emulate the sources of variation that a product would encounter in reality. This is an example of judgment sampling. Though statisticians following in the Shewhart-Deming tradition have embraced outer arrays, many academics are still skeptical.

Later innovations in outer arrays resulted in ‘compounded noise’. This involves combining a few noise factors to create two levels in the outer array. First, noise factors that drive output lower and second, noise factors that drive output higher. This still emulates the extremes of noise variation but with fewer test samples required.

Management of interactions

Many of the orthogonal arrays that Taguchi has advocated are saturated allowing no scope for estimation of interactions. This is a continuing topic of controversy. However, this is only true for ‘control factors’ or factors in the ‘inner array’. By combining an inner array of control factors with an outer array of ‘noise factors’, Taguchi’s approach provides full information on control-by-noise interactions. His concept is that those are the interactions of most interest in achieving a design that is robust to noise factor variation. In this sense, the Taguchi approach provides more complete interaction information than typical fractional factorial experiments.

Followers of Taguchi argue that the designs offer rapid results and that interactions can be eliminated by proper choice of quality characteristic and by transforming the data. That notwithstanding, a confirmation experiment offers protection against any residual interactions. If the quality characteristic represents the energy transformation of the system, then the likelihood of control factor by control factor interactions is greatly reduced since energy is additive.

Analysis of experiments

Taguchi introduced many methods for analyzing experimental results including novel applications of the analysis of variance and minute analysis. Little of this work has been validated by Western statisticians.

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