An Accidental Statistician

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An Accidental Statistician Page 20

by George E P Box


  Humans have a two-sided brain specifically designed to carry out such continuing deductive-inductive conversations. While this iterative process can lead to a solution of a problem, you should not expect the nature of the solution, or the route by which it is reached, to be unique.7

  Your subconscious mind goes on trying to figure things out when you are not aware of it. When something really new occurs to you, it doesn't usually happen when you are sitting down and working at your desk. You might be in the shower or taking a walk, and you suddenly get an idea that solves, or at least helps to solve, the problem. I like working with someone else. The sum of our efforts has always been greater than the parts. Bouncing ideas around with a colleague, discussing, arguing—all catalyze the process of learning and discovery.8

  Bisgaard9 defined innovation as the complete process of development and eventual commercialization of new products and services, new methods of production or provision, new methods of transportation or service delivery, new business models, new markets, or new forms of organization. Thus, innovations can occur in marketing, investment, operations, and management techniques as well as in manufacturing and services.

  Breakthrough innovation and incremental innovation are commonly used terms. Breakthrough innovations are often associated with new products or services and incremental innovations with improvements in current services or products.

  The importance of innovation has sometimes been neglected. Although there are many famous historic examples where innovation was paramount, we pick just one. At the end of World War II, Japanese industry was in ruins. If you visit the Toyota museum in Japan, you will be shown their first car, an exact copy of a Volkswagen. There were many modes of innovation that subsequently brought Toyota cars to world attention. Three of these were (1) previously unknown standards of quality control, (2) new designs developed with the help of thousands of statistically designed experiments, and (3) an attitude toward the workforce based on the idea that they were all one family dedicated to making a good product, with the workers treated fairly by management. Toyota also introduced many other important ideas, such as lean manufacturing. Unfortunately U.S. manufacturers were slow to adopt these concepts. I will go into detail about these facets of Japanese innovation in the next chapter.

  The deductive-inductive iteration described earlier is one route to innovation. More generally, some important initiatives that can lead to successful innovation are:

  1. Inductive-deductive iteration

  2. Lateral thinking

  3. Cross-functional discussion

  4. Analogy

  5. Leadership

  In using these ideas, we should not ask which is best but be prepared to employ them all.

  With de Bono's lateral thinking, one solves a problem not by working further down the established inductive-deductive path but by finding a new direction.10 The disadvantage of the inductive-deductive route is that the scheme you arrive at may have already occurred to competing scientists and engineers who have similar education and work with the same set of scientific principles. This is less likely to happen with lateral thinking.

  The lateral thinking concept is easier to demonstrate than to define. A simple example of lateral thinking concerns the quandary of a person who has to organize a tennis championship. Supposing that there are 47 contenders, how many matches would be necessary to come up with a winner in a single elimination tournament? The answer could be obtained by enumeration, but it can be reached much more easily by thinking not about the winners but about the losers. There have to be 46 losers, so this is the number of needed contests.

  A good statistical example of de Bono's lateral thinking occurred at a Princeton seminar where Merve Muller discussed a way of generating normal deviates by piecewise approximation of the normal curve. This was complicated and messy, and it seemed that there should be a simpler way. This led me to the following question: “What is it in the normal distribution that is uniformly distributed?” For two independent normal deviates, the angle of the radius vector and the log of its length are distributed uniformly and independently. So this provides a way of generating pairs of random numbers. (The less-than-two-page note containing this result11 has been cited almost 1,400 times on Google Scholar.)

  These applications of lateral thinking are not earth shattering, but the idea can be. This was demonstrated, for example, by Charles Darwin. Everyone could see how wonderfully a multitude of living things fitted exactly into our environment, so it seemed obvious that this must be the result of magnificent intelligent design that individually fashioned every living thing and only a super power could accomplish. Darwin, thinking laterally, realized that all that was needed was reproduction and natural selection.12

  Another example of lateral thinking was R.A. Fisher's use of n-dimensional geometry. This led, at once, among other things, to the distribution of the correlation coefficient, to degrees of freedom, orthogonality, the additive property of independent sums of squares, the analysis of variance, the idea of sufficiency, the development of regression analysis, and a better understanding of Gauss's method of least squares.

  Lateral thinking is counterintuitive and will usually be resisted. It is easy to understand this. We have all been trained to think as if the inductive-deductive mode was the only way to solve problems. Thus, at first Darwin's ideas were contested, as were Fisher's.

  The discovery process can also be greatly catalyzed by group discussion, especially if the group contains people from different disciplines. Adair has discussed how teams should be formed and run in order to be most effective.13 Scholtes et al. described the many aspects that can make this method effective.14

  Discussion groups are important not only in themselves but also as a necessary adjunct to the other approaches. Thus, for example, de Bono's “six thinking hats” method can be regarded as either a means to facilitate lateral thinking or as a way to facilitate discussion within groups.15

  It is important for there to be openness and trust on teams; otherwise, potentially useful ideas may not be suggested. Many point out that with an experienced team, there is little distinction between work and play.

  Characteristics of successful teams were evident in the “Monday Night Beer Session” held for years in my home. As noted, students and faculty came from many different departments, and sometimes from industry, to discuss problems and ideas in an atmosphere of open exchange. The sessions were, in the eyes of many who attended, an invaluable learning experience.

  Another approach that can prove useful in innovation is the use of analogy. As an example, at ICI one way to improve processes was by running designed experiments, but experiments on the full scale were expensive and disruptive, and small-scale experiments could be misleading. A graphical representation of the imaginary evolution of a species of lobster was used to illustrate to company executives at ICI the idea of evolutionary operation. This statistical procedure made it possible to generate information on how to improve a product during actual manufacture. Under evolutionary operation, small changes close to normal operating conditions are continually repeated. One is then able to move process factors toward better settings during routine manufacture. This procedure also has the capacity of following moving maxima.

  All of these efforts will fail without appropriate leadership. It is true that many people helped Thomas Edison develop the light bulb, many sailors helped Admiral Lord Nelson win the battle of Trafalgar, and no doubt many engineers and scientists helped Steve Jobs develop the iPhone. Nevertheless, these happenings would not have occurred (at least not at that time) without these leaders. One reliable guide to effective leadership is that of Scholtes.16

  A few years ago, I got a letter from India. The writer said he was a student who very much wanted to study under my guidance. I wrote back explaining that I had retired and no longer supervised Ph.D. students. But he responded that that didn't matter as far as he was concerned; he just wanted to be with me. He was given a three-year
visa and enrolled in the Industrial Engineering Program at the University. He was quick to learn and very helpful.

  Suren had been granted a temporary visa, but I had not realized that he faced a serious problem. He needed to borrow money to pay his fees at the University in dollars, but on an Indian salary, it would take most of his life to pay off. But happily he got a job in the Quality Control Department of the Kohler Company in Wisconsin. The company was very impressed with his work, and they asked the U.S. immigration authorities to provide him with some sort of a document allowing him to stay. Suren went from strength to strength at Kohler, and they used their influence to get him permanent residence, which will allow him to pay off his loan easily.

  In 2010, we wrote a paper together introducing a fundamental change in quality control charting.17 This was published in the journal Quality Engineering and received the Brumbaugh Award for the best paper appearing in that year in any of American Society for Quality's journals.

  The iteration between practice and theory and the innovation of new ideas is a never-ending process, and sometimes well-established ideas need to be re-thought. An example of this is quality control charts. These were originally developed by Shewhart in the 1930s. The underlying process model had been one where the data was assumed to vary about a fixed mean with deviations that were random. But the fact is that no system behaves in this way. In real processes, the mean and the size and nature of the variation about the mean are not fixed. In our paper, Suren and I pointed out that a more realistic model is provided by the nonstationary integrated moving average (IMA). The reason why this model is of central importance was first explained by John F. Muth in 1960. This leads to an exponentially weighted average quality control chart that can represent reality with much greater closeness.

  1 W.G. Hunter, Generation and Analysis of Data in Non-Linear Situations, Ph.D. dissertation, University of Wisconsin, Madison, 1963.

  2 C. Fung, “Some Memories of Bill Hunter,” Sep. 2009, retrieved from http://williamhunter.net/email/conrad_fung.cfm.

  3 Luis Arimani de Pablos, Daniel Peña Sanchez de Rivera, Javier Tort-Martorell Llabres, and Alberto Prat Bartes worked extremely hard on the first edition, and Xavier Tomas Morer and Ernesto Barrios Zamudio did the same for the second.

  4 W.G. Hunter, “101 Ways to Design an Experiment, or Some Ideas About Teaching Design of Experiments,” CQPI Technical Report No. 413, June 1975.

  5 Parts of this section appeared in the article, “The Importance of Practice in the Development of Statistics,” Technometrics, Vol. 26, No. 1, Feb. 1984, pp. 1–8.

  6 It is heartening that this particular happening even withstood the scientific test of repeatability, for at about the same time and with similar practical inspiration, sequential tests were discovered independently in Great Britain by George Barnard. Nor was this the end of the story. Some years later, Ewan Page, then a student of Frank Anscombe, while considering the problem of finding more efficient quality control charts, was led to the graphical procedure using the sequential idea of plotting the cumulative sum of deviations from the target value. The concept was further developed by Barnard who introduced the idea of a V mask to decide when action should be taken. The procedure is similar to a backward-running, two-sided sequential test. Cusum charts have since proved to be of great value in the textile and other industries. In addition, this graphical procedure had proved its worth in the “post mortem” examination of data where it can point to the dates on which the certain critical events may have occurred. This sometimes leads to discovery of the reason for the events.

  7 G.E.P. Box, J.S. Hunter, and W.G. Hunter, Statistics for Experimenters: Design, Innovation and Discovery, John Wiley and Sons, Hoboken, NJ, 2005.

  8 This discussion of innovation is taken in part from the article, “Innovation in Quality Engineering and Statistics,” by G.E.P. Box and W. Woodall, Quality Engineering, Vol. 21, 2012, pp. 20–29.

  9 S. Bisgaard, “The Future of Quality Technology: From a Manufacturing to a Knowledge Economy and from Defects to Innovations,” (2005 Youden Address) ASQ Statistics Division Newsletter, Vol. 24, No. 2, 2006, pp. 4–8. Available at http://www.asq.org/statistics/. Reprinted in Quality Engineering, Vol. 24, No. 1, 2012, pp. 29–35.

  10 E. de Bono, Lateral Thinking, Harper and Row, New York, 1970; and Lateral Thinking: A Textbook of Creativity, Viking, New York, 2009.

  11 G.E.P. Box and M.E. Muller, “A Note on the Generation of Random Normal Deviates,” Annals of Mathematical Statistics, Vol. 29, No. 2, 1958, pp. 610–611.

  12 Alfred Russel Wallace (1823–1913) proposed a theory of evolution based on natural selection independent of Darwin's. Although Darwin has overshadowed Wallace, the two were in regular communication and supported one another in their research.

  13 J. Adair, Leadership for Innovation: How to Organize Team Creativity and Harvest Ideas, Kogan Page Limited, London, 1990.

  14 P.R. Scholtes, B.L. Joiner, and B.J. Streibel, The Team Handbook, 3rd ed., Oriel Inc., Madison, WI, 2003.

  15 E. de Bono, Six Thinking Hats, Little Brown and Company, Boston, 1985.

  16 P.R. Scholtes, The Leader's Handbook: Making Things Happen, Getting Things Done, McGraw-Hill, New York, 1998.

  17 G.E.P. Box, and S. Narasimhan “Rethinking Statistics for Quality Control,” Quality Engineering, Vol. 22, No. 2, 2010, pp. 60–72.

  “The race is over! … ‘Everybody has won and all must have prizes.’”

  Chapter Thirteen

  The Quality Movement

  Bill Hunter and I were very interested in the quality movement from its earliest days, and Bill was closely involved in bringing its techniques to the city of Madison. In 1969, Bill had spent a year in Singapore on a Ford Foundation grant that supplied sophisticated computers and professional expertise to Singapore Polytechnic, where Bill worked with faculty and students. While there, he also worked with another professor to teach an evening seminar on quality techniques for full-time workers in vital positions in Singapore (e.g., those who oversaw the harbor, refuse collection, etc.). He would later teach a similar course in Madison. Bill also traveled to Japan and Taiwan where he visited factories using quality improvement programs.

  In the 1970s and 1980s, people in the United States were starting to realize that the Japanese were building cars and other products that were far superior to theirs. This was a spectacular change because before the war, Japanese manufactures had been inferior. Immediately after the Second World War, Japanese industry had been in ruins, and the United States was anxious to help Japan get back on its feet. As part of this effort, two leading experts from the United States, Dr. W. Edwards Deming and Dr. Joseph M. Juran went to Japan to lecture on quality control. Although this subject had largely originated in the West, it had been only sparingly used there. By contrast, in Japan these concepts were taken very seriously and the teachings were spread widely throughout Japanese industry. In fact, education on the principles of quality control was undertaken as a national project of the highest importance. (Figure 13.1)

  Figure 13.1 Bill Hunter and me.

  But as I have said, there was another factor. In the West, directors and managers seemed to believe that they already knew all there was to know about manufacturing and selling their product. The workers were thought of as disposable underlings who were there to carry out instructions. In particular, this has been the convenient rationale that has justified salaries for upper management that were spectacularly higher than those received by the workers. The Japanese philosophy, on the other hand, was that production was a joint effort in which everyone was personally involved and ideas for improvement were welcomed, rewarded, and celebrated wherever they came from. Their management was paid at a more reasonable level, and the result was that a prodigious number of ideas came from the people who were actually making the product. The methods used for quality improvement were not only those taught by their American mentors, but also those coming from Japanese workers and Japanese experts, such as Professor K
aoru Ishikawa. Because workers developed many new ideas of their own, there was a high level of morale throughout the organization.

  One other important concept for quality improvement, which I addressed before, was the use of statistical experimental design conceived in the 1920s by Sir Ronald Fisher for improvements in agriculture. As I mentioned, Fisher showed that it was much better to vary several factors at a time. Fisher's approach was known in Japan as “Taguchi Methods,” named for engineering professor Genichi Taguchi. Thousands of designed experiments had been run in Japan to design optimal systems for automobiles.

  In 1980, NBC broadcast a special program featuring Dr. Deming that was called If Japan Can, Why Can't We? On the show, Deming explained to an American audience that Japan's industrial success in the post-war period relied on statistical methods that would benefit U.S. companies. In Japan, Deming noted, statistical control had led to consistently good quality in a multitude of production processes. Good quality led, in turn, to better control of costs. Moreover, statistical thinking guided everyone in the Japanese production process, from line workers to executives.

  The effect of these innovations in Japan was dramatic, and they were applied not only to automobiles. Sometime in the middle of the 1980s, I remember seeing a slide that asked, “What do these things have in common?” On the slide were pictures of automobiles, cameras, and every kind of technological gadget. The answer was that for each of these products, the United States had lost 50% of its market to the Japanese in the previous five years. In particular, of course, the U.S. automobile industry had been astonished and embarrassed by the clever designs and narrow tolerances of their Japanese competitors.

 

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