Genichi Taguchi and Taguchi Methods - Practical, Rapid Quality Cohort 2, Wooshik Jung Taguchi methodology is concerned with the routine optimisation of product and process prior to manufacture, rather than emphasizing the achievement of quality through inspection. Instead concepts of quality and reliability are pushed back to the design stage where they really belong. The method provides an efficient technique to design product tests prior to entering the manufacturing phase. However, it can also be used as a trouble-shooting methodology to sort out pressing manufacturing problems. Here are some of the major contributions that Taguchi has made to the quality improvement world: 1. The Loss Function - Taguchi devised an equation to quantify the decline of a customer's perceived value of a product as its quality declines. Essentially, it tells managers how much revenue they are losing because of variability in their production process. It is a powerful tool for projecting the benefits of a quality improvement program. Taguchi was the first person to equate quality with cost. 2. Orthogonal Arrays and Linear Graphs - When evaluating a production process analysis will undoubtedly identify outside factors or noise which cause deviations from the mean. Isolating these factors to determine their individual effects can be a very costly and time consuming process. Taguchi devised a way to use orthogonal arrays to isolate these noise factors from all others in a cost effective manner. 3. Robustness - Some noise factors can be identified, isolated and even eliminated but others cannot. For instance it is too difficult to predict and prepare for any possible weather condition. Taguchi therefore referred to the ability of a process or product to work as intended regardless of uncontrollable outside influences as robustness. He was pivotal in many companies' development of products and processes which perform uniformly regardless of uncontrollable forces; an obviously beneficial service.

Continuing our series on the leaders that have made a significant impact to the quality movement, lean manufacturing, and six sigma, we’ve featured Sakichi Toyoda, Walter Shewhart, and Armand Feigenbaum, and today we feature Genichi Taguchi.
Perhaps Taguchi is best known for his influence on modern day website optimization, better known as A/B Testing or Multivariate Testing, which we’ll discuss shortly. Overall, his application of statistics for business specific problems is his greatest contribution with broad influence.
Genichi Taguchi History
Genichi Taguchi stressed quality right from the design stage and not just as an inspection. In short, he believed quality was related to process design. Dr Genichi Taguchi was born in 1924 in Japan. Initially, he served the Astronomical Department of the Navigation Institute of the Imperial Japanese Navy during the Second World War. Later, he joined the Ministry of Public Health and Welfare and the Institute of Statistical Mathematics. It was here that he worked with the eminent Japanese statistician Matosaburo Masuyama and gained vital insights into statistical analysis.
His expertise in statistics garnered him an opportunity to work with reputed pharmaceutical company Morinaga Seika and its sister company, Morinaga Pharmaceuticals. Taguchi then joined the Nippon Telegraph Electrical Communications Laboratory. Here, he was entrusted with the task of enhancing the productivity of the Research and Development (R & D) department. To achieve this objective, Taguchi trained the engineers to improve productivity through effective and simple techniques. Initially, Taguchi visited many Japanese companies to study different operating procedures. He would later educate the engineers on what he had learned. Eventually, he developed his own techniques, and his visits to companies helped him propagate his techniques. He stayed at the Nippon Telegraph Electrical Communications Laboratory for over 12 years
Soon, Japanese companies like Toyota adopted Taguchi’s techniques because they foresaw its great advantages. In 1951, he published a book that introduced the concept of orthogonal arrays. In his quest for a methodology for high quality, he met two legendary statisticians at the Indian Statistical Institute – R. A. Fisher and Walter A. Shewhart. After his interactions with them, he published a book on Design of Experiments in 1957.
Genichi Taguchi Contributions
Taguchi’s contributions have made its way into almost every facet of business. Unfortunately, few know about them while actively practicing what he either invented or had a large influence on. Here are a few of Taguchi’s contributions.
Taguchi Quality Loss Function
In 1970, Taguchi devised a new concept in quality called the Quality Loss Function. He published two more books this year, along with the third edition of Design of Experiments.
Unlike the western definition of quality, Taguchi defined quality loss, as “loss imparted by the product to society from the time the product is shipped.” The loss factor encompasses two losses: 1. Loss at the company end due to financial set-up, time, man-hours, productivity, rework, scrap, warranty cost, equipment downtime cost and loss of customer trust. 2. Loss at the customer end due to substandard product delivery, financial setbacks, distrust of customers, shared value deprecation, wasted time and project delays.
Taguchi Loss Function was developed on the premise that the greater the variation of a value from the standard, the greater the costs incurred. Taguchi Loss Function suggests that organizations must settle for options that cost the least. Organizations should thus make decisions after conducting a cost analysis and understanding all implications. It also suggests that the lowest cost decision is not always the best one for the organization. This decision depends on organizational priorities
In its most basic form, Taguchi Loss Functions shows us the cost to the firm when we deviate from the standard. Below is an image of the Taguchi Loss Function:

Take a simple example of a tire manufacturer. This firm produces tires and a key component of high quality tires is the thickness of the rubber, for it induces safety and comfort and stability. The firm has statistically arrived at a “standard” tire thickness.
To apply the Taguchi Loss Function, suppose the firm produces tires whose thickness are less than standard or tires whose thickness is more than standard. In either case, there is a cost as indicated by the function above.
Design of Experiments (DOE)
Taguchi is also known for his contribution to multivariate testing, otherwise known as Design of Experiments or DOE. In a Design of Experiment, the central question is this:
How many different conditions do you need to experience to be able to reliably ascertain whether “A” is better than “B” or not?
As such, a Design of Experiment is centered around Factors, Responses, and Runs. We are interested in how a Factor affects a Response and we do in several Levels or Runs.
Here are 2 examples where Design of Experiments can be applied:
Taguchi Experiment: Microwave Popcorn
What is the best method to prepare microwave popcorn? The Response you want is this: the best outcome is the bag with the most popped corn kernels.
Below are the Factors: * How long to cook the popcorn (between 3 and 5 minutes) * What level of power to use on the microwave oven (between settings 5 and 10) * Which brand of popcorn to use (Top Secret or Orville Redenbacher)
A/B Testing (Multivariate Testing)
Another application of Taguchi’s Design of Experiments is for testing elements of a website landing page that lead to the desired outcome, whether the outcome or conversion is defined as a sale, email sign-up, click through to the next page, etc.
In general, the steps to test the elements of a landing page are similar to the steps above: 1. Select elements on the landing page that we believe will influence sign-up 2. Create alternatives for each element 3. Create test “recipes” that combine these elements according to the Taguchi Methodology 4. Set up and run a concurrent multi variable test.
Here’s an example experiment: * Headline Graphic on left, right, top of page Font selections in Body text, and varying sizes Color schemes in the footer and header Validation logos like Truste, BBB, Visa, Mastercard, American Express, Discover Card, etc.
The elements on a landing page are Factors. The number of times and variations you run a Taguchi Test are the Runs. And, the outcome or Response is Conversion.
Conclusion
We owe much to Genichi Taguchi. Without knowing it, much of what we do today in terms of our statistical approach to “what is better a or b or c or d” can be credited to Genichi Taguchi.

Born 1924
Genichi Taguchi is a Japanese quality expert, known for the Quality Loss Function and for methodologies to optimise quality at the design stage – “robust design”. Taguchi received formal recognition for his work including Deming Prizes and Awards.
Genichi Taguchi considers quality loss all the way through to the customer, including cost of scrap, rework, downtime, warranty claims and ultimately reduced market share.
Genichi Taguchi's Quality Loss Function
The Quality Loss Function gives a financial value for customers' increasing dissatisfaction as the product performance goes below the desired target performance.

Equally, it gives a financial value for increasing costs as product performance goes above the desired target performance. Determining the target performance is an educated guess, often based on customer surveys and feedback.
The quality loss function allows financial decisions to be made at the design stage regarding the cost of achieving the target performance.
Quality through Robust Design Methodology
Taguchi methods emphasised quality through robust design, not quality through inspection. Taguchi breaks the design process into three stages: 1. System design - involves creating a working prototype 2. Parameter design - involves experimenting to find which factors influence product performance most 3. Tolerance design - involves setting tight tolerance limits for the critical factors and looser tolerance limits for less important factors.
Taguchi’s Robust Design methodologies allow the designer through experiments to determine which factors most affect product performance and which factors are unimportant.

The designer can focus on reducing variation on the important or critical factors. Unimportant or uncontrollable “noise” factors have negligible impact on the product performance and can be ignored.

Robust Design of Cookies
This is easier explained by example. If your business makes cookies from raw ingredients, there are many possible factors that could influence the quality of the cookie - amount of flour, number of eggs, temperature of butter, heat of oven, cooking time, baking tray material etc.
With Genichi Taguchi’s Robust Design methodologies you would set up experiments that would test a range of combinations of factors - for example, high and low oven temperature, with long and short cooking time, 1 or 2 eggs, etc. The cookies resulting from each of these trials would be assessed for quality.
A statistical analysis of results would tell you which are the most important factors, for example oven temperature affects cookie quality more than the number of eggs.

With this knowledge you would design a process that ensures the oven maintains the optimal temperature and you would be able to consistently produce good cookies.

Rise to fame
Dr Genichi Taguchi was born in 1924. After service in the Astronomical Department of the Navigation Institute of the Imperial Japanese Navy in 1942-45, he worked in the Ministry of Public Health and Welfare and the Institute of Statistical Mathematics, Ministry of Education. He learned much of experimental design techniques and the use of orthogonal arrays from the prize-winning Japanese statistician Matosaburo Masuyama whom he met whilst working at the Ministry of Public Health and Welfare. This also led to his early involvement as a consultant to Morinaga Pharmaceuticals and its parent company Morinaga Seika.
In 1950 he joined the newly founded Electrical Communications Laboratory of the Nippon Telephone and Telegraph Company with the purpose of increasing the productivity of its R and D activities by training engineers in effective techniques. He stayed for more than 12 years, during which period he began to develop his methods.
Whilst working at the Electrical Communications Laboratory, he consulted widely amongst Japanese industry. Accordingly, Japanese companies began applying Taguchi methods extensively from the early 1950s, including Toyota and its subsidiaries. His first book, which introduced orthogonal arrays, was published in 1951.
In 1954-5 Taguchi was visiting Professor at the Indian Statistical Institute. During this visit he met the famous statisticians R A Fisher and Walter A Shewhart.
In 1957-8 he published the first version of his two-volume book on Design of Experiments. His first visit to the United States was in 1962 as Visiting Research Associate at Princeton University, during which time he visited the AT & T Bell Laboratories. At Princeton, Taguchi was hosted by the eminent statistician John Tukey who arranged for him to work with the industrial statisticians at Bell Laboratories. In 1962 he was awarded his PhD by Kyushu University.
In 1964 Taguchi became a Professor at Aoyama Gakuin University in Tokyo, a position he held until 1982. In 1966 Taguchi and several co-authors wrote Management by Total Results which was translated into Chinese by Yuin Wu. At this stage, Taguchi's methods were still essentially unknown in the West, although applications were taking place in Taiwan and India. In this period and throughout the 1970s most applications of his methods were on production processes, the shift to product design being in the last decade.
In the early 1970s Taguchi developed the concept of the Quality Loss Function. He published two other books in the 1970s and the third (current) edition of Design of Experiments. By the late 1970s Taguchi had an impressive record in Japan having won the Deming application prize in 1960 and Deming awards for literature on quality in 1951 and 1953.
In 1980 Taguchi was invited by Yuin Wu, who had emigrated to the United States, to give a presentation at his company. By this time Taguchi was director of the Japanese Academy of Quality. During his visit he arranged to revisit AT & T Bell Laboratories at his own cost where he was hosted by Madhav Phadke. Despite communication problems, successful experiments were run that established Taguchi methods within Bell Laboratories.
Following his 1980 visit to the United States, more and more American manufacturers implemented Taguchi's methodology. Despite an adverse reaction among American statisticians at the methods, and possibly at the way they were being marketed, major US companies became involved in the methods including Xerox, Ford and ITT.
In 1982 Taguchi became an advisor at the Japanese Standards Association. In 1984 he again won the Deming award for literature on quality. In 1986 he was awarded the Willard F Rockwell Medal by the International Technology Institute. With one or two notable exceptions, such as Lucas, his methods had made little impact on Europe until the Institute of Statisticians organised the first conference on the methods in 1987 in London. The UK Taguchi Club (now the Quality Methods Association) was formed later that year.
Taguchi's message
Taguchi methodology is concerned with the routine optimisation of product and process prior to manufacture, rather than emphasizing the achievement of quality through inspection. Instead concepts of quality and reliability are pushed back to the design stage where they really belong. The method provides an efficient technique to design product tests prior to entering the manufacturing phase. However, it can also be used as a trouble-shooting methodology to sort out pressing manufacturing problems.
In contrast to Western definitions, Taguchi works in terms of quality loss rather than quality. This is defined as 'loss imparted by the product to society from the time the product is shipped'. This loss includes not only the loss to the company through costs of reworking or scrapping, maintenance costs, downtime due to equipment failure and warranty claims, but also costs to the customer through poor product performance and reliability, leading to further losses to the manufacturer as his market share falls. Taking a target value for the quality characteristic under consideration as the best possible value of this characteristic, Taguchi associates a simple quadratic loss function with deviations from this target.
This loss function shows that a reduction in variability about the target leads to a decrease in loss and a subsequent increase in quality.
With this conception a loss will occur even when the product is within the specification allowed, but is minimal when the product is on target. (If the quality characteristic or response is required to be maximised, eg strength, or minimised, eg shrinkage, then the loss function becomes a half-parabola.) The loss function may be used to evaluate design decisions on a financial basis to decide whether additional costs in production will actually prove to be worthwhile in the market place.
Taguchi methodology can be applied off-line in design or on-line in production.
Taguchi breaks down off-line quality control into three stages:
1. System design.
2. Parameter design.
3. Tolerance design.
System design is the genius of creating a design concept or 'up and limping' prototype. In the past we have been good at this in the West.
Parameter design is the crucial step - this is where the Japanese excel at achieving high quality levels without an increase in cost. The nominal design features or process factor levels selected are tested and the combination of product parameter levels or process operating levels least sensitive to changes in environmental conditions and other uncontrollable (noise) factors is determined.
Finally, tolerance design is employed to reduce variation further if required, by tightening the tolerance on those factors shown to have a large impact on variation. This is the stage at which, by utilising the loss function, more money is spent if necessary buying better materials or equipment, emphasising the Japanese philosophy of invest last not invest first.
The potential for these methods within UK and world industry is large. Typically, designs and line calibrations are in reality far from optimal. Much manufacturing folklore is based on the need to 'twiddle' important parameters or settings. Typically we do not understand the correct settings although we do have our prejudices.
Taguchi methodology is fundamentally a prototyping method that enables the engineer or designer to identify the optimal settings to produce a robust product which can survive manufacturing time after time, piece after piece, in order to provide the functionality required by the customer.
There are perhaps two major features of the advantage of Taguchi methodology. Firstly, it was developed by, and is largely used by engineers rather than statisticians. This removes most of the communication gap and the problems of language traditionally associated with many statistical methodologies. In addition, it means that it is tailored directly to the engineering context. The consequence of this is that the importance of noise variables which disrupt production must be considered in addition to the control variables introduced. Optimising a product corresponds not only to getting its quality characteristics on target but also to minimising variability away from that target on a piece-to-piece or time-to-time basis. This is the connection with Statistical Process Control (SPC).
Taguchi may be used to narrow the spread of the quality characteristics distribution and to identify variables to build control on. SPC may then be used to keep quality characteristics on target by making use of the known spread about the target value. Essentially this is the other novel feature of Taguchi methodology: the use of the so-called Signal-To-Noise ratio to choose the control setting that minimises the sensitivity to noise. In addition to this the methods are fundamentally evolutionary.
One major feature, however, is the codifying by Taguchi of the so-called Orthogonal Arrays. These are designs for experiments which were largely previously identified by others but are codified by Taguchi in such a way that an engineer automatically has a route to the minimum number of prototypes necessary for experimentation. The numbers are kept deliberately small by sacrificing all the interaction information that may be present in the design (or almost all of it) since information about interactions can subsequently be found in typical industrial applications by evaluating one more prototype - that corresponding to the predicted optimum setting (the confirmatory trial). This is the difference between industrial application and the agricultural context on which most of the Western statistical methods which foreran Taguchi were based. In agriculture, responses are slow so that leaving out prototype combinations and sacrificing interactions would necessitate an extra year in the agricultural cycle in order to be able to verify that the predicted prototype combination really was best. In the industrial setting responses are usually fast, so that it is possible to go back immediately and try out one additional prototype. Interactions can, however, be incorporated into Taguchi methodology and he presents a simple graphical codification of these (the linear graphs) to enable the analyst to introduce them systematically and easily. However, only limited numbers can be conveniently introduced without leading to great increase in prototype or experimental sizes.
Further readings:
Bendell, A (ed) - Taguchi Methods, London, Elsevier Science Publishers Ltd, 1989.
Bendell, Tony et al (ed) - Taguchi Methods: Applications in World Industry, Bedford, IFS Publications, 1989.
Bendell, Tony et al - Taguchi Methodology Within Total Quality Bedford, IFS Publications, 1990.
Taguchi, G - Introduction to Quality Engineering, Tokyo, Asian Productivity Organization, 1986.
Taguchi, G - Systems of Experimental Design, Unipub/Kraus International Publications and American Supplier Institute, 1978.