Featured Product
This Week in Quality Digest Live
Quality Insider Features
Henning Piezunka
Businesses and leaders influence the kinds of ideas they receive without even realizing it
Having more pixels could advance everything from biomedical imaging to astronomical observations
Chris Caldwell
Significant breakthroughs are required, but fully automated facilities are in the future
Dawn Bailey
Helping communities nurture the skilled workforce of the next generation
Leah Chan Grinvald
Independent repair shops are fighting for access to vehicles’ increasingly sophisticated data

More Features

Quality Insider News
Easy to use, automated measurement collection
A tool to help detect sinister email
Funding will scale Aigen’s robotic fleet, launching on farms in spring 2024
3D printing technology enables mass production of complex aluminum parts
High-end microscope camera for life science and industrial applications
Three new models for nondestructive inspection
Machine learning identifies flaws in real time
Developing tools to measure and improve trustworthiness

More News

Matthew Barsalou

Quality Insider

The Legacies of Genichi Taguchi

The statistician demonstrated the advantages of designing quality into a product

Published: Thursday, March 21, 2013 - 09:55

Genichi Taguchi passed away in Tokyo on June 2, 2012, at the age of 88. He started his career by studying textile engineering with the expectation of entering his family’s kimono business, but was drafted into Japan’s Imperial Navy during World War II. He became interested in statistics after the war and worked with such well-known figures in statistics as C. R. Rao, Walter A. Shewhart, and Ronald A. Fisher. He also worked at the Institute of Statistical Mathematics and made many contributions to industrial experimentation.

After years of consulting in industrial experimentation, Taguchi joined a Japanese research organization called the Electrical Communication Laboratory in 1950. His work contributed to the development of phone system components that were so successful they beat out the well-established Bell Labs for a contract. During this time Taguchi developed what would become robust engineering. This was followed by several decades of statistics-related work. In 1982 Taguchi became involved in training executives at Ford Motor Co. By 1983 he was the executive director of the Ford Supplier Institute that later became the American Supplier Institute, which continues to encourage the use of Taguchi’s methodology today.

Introduction to the Taguchi Methods

According to Taguchi’s Quality Engineering Handbook (Wiley-Interscience, 2004), Taguchi’s method differs from what the United States terms “quality engineering.” His method, variously known as “the Taguchi method,” “the Taguchi paradigm,” or “Taguchi quality engineering” in both Europe and the United States, is “robust engineering based on the following three procedures: (1) orthogonal array, (2) SN ratio, and (3) loss function.”

Taguchi’s DOE methodology has inspired many DOE practitioners who use his methodology, and much discussion and controversy regarding it. Some writers, such as Ranjit K. Roy in Design of Experiments Using the Taguchi Approach (Wiley-Interscience, 2001) and the American Supplier Institute’s James O. Wilkins Jr. report successes using Taguchi’s DOE methodology; others, such as George E. P. Box, Søren Bisgaard, and Dorian Shainin and Peter Shainin, take a more critical view.

Taguchi’s design of experiments (DOE) uses orthogonal arrays. In DOE, “orthogonal” means the columns of arrays are balanced, and “balanced” means the number of levels in the columns are equal. Balancing ensures that there are an equal number of all possible combinations of factors.

The signal-to-noise (SN) ratio is a key element of analyzing DOE conducted using Taguchi’s orthogonal arrays. The SN ratio is the reciprocal of the variance of the measurement error, and it uses the logarithm of the standard deviation to separate dispersion and location effects in DOE. This is in contrast to other methods of DOE that use the more conventional analysis of variance (ANOVA) for analyzing experimental results.

Taguchi’s loss function can be illustrated with the example of a low-quality automotive component (see figure 1). The component may be produced within specification, but with a large standard deviation that will result in some customers receiving good parts, and other customers receiving parts that will present a problem. Those customers with a problem will need to take the time to bring their vehicles to a dealer. The dealer will need to have a large staff of mechanics if many vehicles are returned due to problematic components. The dealer loses money by employing a staff dedicated to fixing problems that could have been prevented, and society as a whole experiences a loss when many people miss work to take their vehicles to a dealer for repairs. Taguchi’s solution is to design quality into a product as early as possible during the engineering phase.

Figure 1: The Taguchi loss function

According to Genichi Taguchi, Subir Chowdhury, and Shin Taguchi in Robust Engineering (McGraw-Hill Professional, 1999), robustness is “the state where the technology, product, or process performance is minimally sensitive to factors causing variability (either in the manufacturing or user’s environment) and aging at the lowest unit manufacturing cost.” Robust components minimize the loss in the loss function because the process is at the center of the curve in the Taguchi loss function.

The difference between producing parts in specification, but with variation between the upper and lower specification limits, can be dramatic. Taguchi presents the case of Ford vs. its one-time partner Mazda. Both companies produced the same transmissions using the same specifications, and the transmissions were assembled into vehicles at the same North American plant. The Ford-built transmissions generated more warranty issues, higher costs, and lower customer satisfaction, so Ford disassembled and studied transmissions assembled by Ford and Mazda. Both sets of transmissions were in specification; however, the Mazda transmissions were all built to the nominal value, and the Ford transmissions had a high degree of variability. Although Ford-assembled transmissions were in specification, the deviations from nominal could be a problem when the tolerances stack up or are on opposite sides of the specification. Ford had a zero defects policy that achieved in-specification parts that produced warranty costs, despite being in specification. Mazda used robust engineering to produce parts that were not only in specification but also displayed little variation about the nominal.

Criticism of Taguchi’s methodology

Many writers have criticized Taguchi’s methodology. Same take an especially harsh tone. For example, Shainin and Shainin conclude that Taguchi’s methods are used by “unsophisticated firms.” In Quality or Else (Mariner Books, 1993), Lloyd Dobyns and Clare Crawford-Mason describe how quality guru Philip Crosby disregarded Taguchi by claiming that a doctorate in mathematics is required to understand Taguchi, and that Crosby believes Taguchi’s methodology has been implemented because quality professionals believe, “If it’s incomprehensible in Japanese, it must be good for you.” Unfortunately, such unquantified criticism adds little to the debate on Taguchi methods.

Much criticism of Taguchi is well-presented and clearly explained. For example, Bisgaard considers Taguchi’s contributions to DOE, such as signal-to-noise ratios, to be both inefficient and more complicated. Bisgaard thinks Taguchi’s methods would have value if they offered a simpler alternative to more conventional methods; however, they are neither better nor easier. The SN ratio depends on separating dispersion and location effects using a log transformation; unfortunately, a log transformation is not always appropriate. The data may not require a transformation, or some other transformation method may be more appropriate. Although he offers praise for some of Taguchi’s contributions to the field of quality engineering, Box refers to Taguchi’s use of ANOVA as “reckless.”

Another part of Taguchi’s DOE is the use of linear graphs for assigning factors in the experiment. Bisgaard reanalyzed several experiments described by Taguchi, and his conclusions were different than Taguchi’s. The reanalysis resulted in more accurate results with less effort. Box reanalyzed an experiment that was presented at a symposium on Taguchi methods. The experiment used an L-16 orthogonal array, which Box believes to have been both more complicated than necessary and incomplete. Box’s reanalysis only identified two factors as being significant, in contrast with the eight factors originally identified by the study that used an SN ratio in place of a conventional ANOVA. Box and Conrad Fung also reanalyzed an experiment performed and documented by Taguchi and Yuin Wu. Box and Fung concluded the results achieved by Taguchi and Wu using an orthogonal array did not lead to the optimal solution. Box and Conrad A. Fung used more conventional DOE to arrive at a better solution. Bisgaard considers Taguchi’s methods of DOE to be “better than doing nothing at all”; which is not a convincing argument for using a methodology when there are many alternatives available.

Taguchi’s legacy

Although he is critical of Taguchi’s DOE, Bisgaard recognizes the enormous contributions Taguchi has made to industry by generating interest in DOE and demonstrating the economic advantages of designing quality into a product. One of Taguchi’s valuable contributions is “robust design” and the method of achieving it, which is called “parameter design.” Bisgaard illustrates this with the example of a design for an automobile that functions well in both high temperature and high humidity and low temperature and low humidity. The vehicle is robust in regards to the operating environment, and parameter design is used to achieve this robustness. In parameter design, experiments are used to identify the ideal design so that the product is not sensitive to variation. Bisgaard suggests adding Taguchi’s valuable contributions to the body of knowledge while discarding his less useful contribution—Taguchi’s orthogonal arrays for DOE.

Like Bisgaard, Box praises Taguchi’s contributions in helping engineers realize the need to minimize variance, and produce designs that are not sensitive to the operating environment and are not harmed by variation in the components. He also praises Taguchi for getting more people interested in using DOE, and he encourages taking Taguchi’s ideas on engineering seriously while discarding his method of DOE.

Another of Taguchi’s contributions to the field of quality is his loss function. Taguchi and Don Clausing illustrated the loss function with Sony televisions produced in Tokyo and San Diego. The televisions had the same specification of 10 for a measure of color density. The lower tolerance was seven, and the upper tolerance was 13. Anything between the tolerance limits was acceptable; unfortunately, customers became more unsatisfied as the actual value moved above or below the nominal. The televisions from Tokyo were produced directly at the nominal value of 10; the San Diego televisions were produced with values throughout the tolerance range. The San Diego televisions were in specification, but still resulted in higher costs due to unsatisfied customers. The Taguchi loss function is a valuable concept that should be added to the quality body of knowledge together with robust engineering and parameter design.


Some DOE is superior to no DOE; however, practitioners must ensure that the methods used offer more advantages than simply being “better than nothing.” There are many types of DOE available, including full factorial, fractional factorial, response surface methodology (RSM), evolutionary operation (EVOP), Latin square, Box-Behnken, Plackett-Burman, and Greco-Latin square designs. To achieve Taguchi’s ideal of a robust design that both minimizes loss and is insensitive to variation, the optimal design should be used. Such a product can result in both customer satisfaction and the economic advantage resulting from high quality produced at an economical cost.


About The Author

Matthew Barsalou’s picture

Matthew Barsalou

Matthew Barsalou is a statistical problem resolution master black belt at BorgWarner Turbo Systems Engineering GmbH. He is an ASQ-certified Six Sigma Black Belt, quality engineer, and quality technician; a TÜV-certified quality manager, quality management representative, and quality auditor; and a Smarter Solutions-certified lean Six Sigma Master Black Belt. He has a bachelor’s degree in industrial sciences, and master’s degrees in engineering, business administration, and liberal studies with emphasis in international business. Barsalou is author of Root Cause Analysis, Statistics for Six Sigma Black Belts, The ASQ Pocket Guide to Statistics for Six Sigma Black Belts, and The Quality Improvement Field Guide.



I would suggest not to ignore Keki R. Bothe's "World Class Quality - DOE made easier, more cost-effective than SPC", AMA, 1988, and Walter Masing's "Handbuch Qualitaets-management", Hanser, 2007, edited by Tilo Pfeiler & Robert Schmitt. Thank you.


In my own quality work, I thought Taguchi's Loss Function concept was the most useful of his ideas.  In one plant we had a top salesman who used to come lecture us about the need for "Uniformity, Uniformity, Uniformity."  My version with plant production personnel was, "Run to Target, Stay in Control".

And this leads me to a long standing question, who said "Variation is the Enemy of Quality"?  I have heard it attributed to both Deming and Taguchi but neither man's foundation has been able to verify the source.

And while I agree that "Variation is the Enemy of Quality"; I also say "Uniformity is the Enemy of Knowledge"

Thanks for the article.

William H. Pound, PhD

Fundamentals of Taguchi

Thanks you for the article. However, I do not agree with the statement :  “robust engineering based on the following three procedures: (1) orthogonal array, (2) SN ratio, and (3) loss function.” as an indication of the essence of Taguchi.

To me, the true importance of Taguchi lies in two things: Off line Quality Control and Robustness. In other words: we have to make sure that long term process capability has been secured at the moment we start with the new product / process. The things mentioned in the quotes are means, methods, techniques, but not the essentials. As an example: orthogonal arrays are nothing special at all, they are either fractional factorials or Plackett-Burmann designs. Robustness can be studied with full factorials as well if that is what you want. But introducing noise (that you will see during the lifetime of your process or product) in the off line testing, allows you to take measures to counteract their effect and thus to improve long term capability before the process even started to produce. This preventive  testing / thinking is vital in understanding Taguchi and in my view much more important than the three elements in the quote.Kind regards,

Willy Vandenbrande 

Taguchi comments

Thank you for the comments. I don’t know if you remember me, you administered two of my ASQ certification exams a few years ago.

The Taguchi quote is just that, a direct Taguchi (and co-authors) quote. Unless I am mistaken, that is how Taguchi described robust engineering.

I believe my point was that we should use Taguchi’s concept of designing quality and robustness into a product and I hope the examples I used have made that clear.

I have written a different Taguchi related article that will appear in the April edition of the German magazine Qualität und Zuverlässigkeit and it may interest you. In it I referenced your “Make Love Not War: Combining DOE and Taguchi.”

Best regards,

Matthew Barsalou


Hello Matthew,

Yes, now I remember. Small world :) Did you pass the exams?On Taguchi I think we general mean the same thing. And I am a strong advocate for integrating good ideas from different methods in stead of trying to fight each other and pointing out weaknesses.  

Thanks again for the article and for the reference. If at all possible, I would be interested in receiving a copy of your article (pdf would be fine).




Small world

Hello Willy,

Yes, I passed both exams.

I think we are in agreement. I would like to have one solution for all problems, but I am highly skeptical of anybody who offers one. I think a tool kit approach is best.

I still have your email address. I’ll email you a copy after the article is published.