Permutation Methods: A Distance Function Approach

Ranjit Roy has written this book to cover the material of his earlier book, A Primer on the Taguchi Method, at a simpler level. This simpli cation is to allow people without a college education or formal statistical training (as well as others) to learn robust design. The simpli cation is thorough; Roy spends two sentences each de ning systems and tolerance design (which admittedly get much less coverage than parameter design in robust design books), but then states that they will not be covered. But this simpli cation does not mean that this is a slim volume. Roy feels that the best way to teach is to provide many applications examples. He also uses a heavily directed approach that often works well with students with less education. The introduction has a one-paragraph summary of each chapter. Each chapter starts with a goal and ends with a summary, review questions with answers, and exercises with answers. A one-page collection of symbols and abbreviations reduces frantic page  ipping. Included are a number of discussions about topics (like the number of levels you should use) that are often shortchanged elsewhere as being obvious, the catch being that the obviousness is often only apparent after a painful experience. A downside to this approach is that the student is assumed to live in a simpler world than I do. There is no mention in the index, nor could I  nd anything in the book, on the need for randomization, blocking, or dealing with outliers and missing data, or the consequences of not doing so. Similarly, there is no discussion of the dif culty in analyzing historical data due to correlation between factors, which I  nd very helpful in persuading students that they need to design experiments at all. Roy brie y mentions extrapolation, but does not discuss its risks. He does put more emphasis on the importance of interactions than many followers of Taguchi, which I  nd commendable. In addition, Roy proposes using an overall evaluation criterion in the common case of more than one response to deal with. Unfortunately, Roy shares Taguchi’s enthusiasm for using a small set of designs, L arrays. This is admittedly simple; if one has x factors with y levels, then one uses a L-z design, as given in Chapters 5 and 6. But this is the simplicity of a shoe store with only a few sizes. The back lling begins in Chapter 8, where it is admitted that one may need “advance(d) experiment design” to deal with situations like interaction. This means unlearning previous material, which could have been avoided if it had been dealt with from the beginning. Further, labeling it an advanced topic tempts weaker students to think this is some  ne point that can be safely slept through, undercutting Roy’s expression of the importance of interactions. He is unenthusiastic about interactions: “After all, if you had any control over (an interaction), you would rather not have it” (p. 243). On the contrary, although interactions make life more complicated, they often lead to a better or more stable product, as in buffering. The subsequent two chapters deal with surgically altering standard L arrays when the number of factors or levels differs from the standard L arrays. This is complicated, and one would think that such designs are not as good as ones designed from scratch with the right number of factors and levels. Like Taguchi, Roy is selective when checking for statistical signi cance. On the one hand, F tests are used to determine which factors are signi cant in the analysis of variance. On the other hand, in the door closing force example on page 43, station 2 has a slightly smaller mean square deviation from nominal, 5.142, than the  rst station, 5.25, and so Roy judges the former to be superior. But is this difference statistically signi cant, particularly given the small sample sizes of 6 and 9? Neither the means nor the variances are statistically signi cantly different at the p D 010 level. I don’t think we can tell to a reasonable certitude whether station 2 is better, and the student should know that this boss-infuriating answer is common. Roy differs from Taguchi in  nding computers to be a useful adjunct and has written a software package (Qualitek-4) for this. Included with the text is a CD-ROM that contains all of the examples and exercise solutions in the text and a Qualitek-4 “Full Featured Working Model—Demo. ” There seems to be some tension between the front and back half of the quoted phrase. As the text makes clear, demo is the operant phrase; one can analyze only eight run (L8) designs using the disk. A complete copy of Qualitek-4 costs roughly the same as a retail copy of Minitab. The program will run on a PC486 under Windows 3.1, which suggests possible problems when one converts to Windows XP. If one  nds the price steep, is worried about the continued operability of the program, or wishes to use a different package, then the book’s usefulness will be noticeably reduced, because it spends considerable time stepping screen-by-screen through the program. ( In fairness, I haven’t  gured out how to solve the if-you-don’t-show-softwarethey-won’t-use-the-statistics-but-if-it’s-not-the-software-they-use-they-won’tuse-the-statistics-anyway conundrum either). On the other hand, those who do use the software, particularly the less sophisticated students targeted by this book, will like the screen-by-screen walkthrough. If one wishes to check out the demo  rst, it can be found at www.rkroy. com. Stylistically, I disagree with some of Roy’s salesman-like enthusiasms; for example: “A formal course or background in statistics is not required. Readers interested in application of the technique will grasp the methods easily, regardless of background” (p. 2). The “easily” part has not been my experience for high school graduates with no statistical training. Again, “As long as you perform the experiments as planned and analyze the results correctly, you may expect an improvement most of the time (over 95% )” (p. 433). That’s a higher batting average than I see; not infrequently, the result of well-run and well-analyzed experiments is “none of these factors matter. ” This is a valuable  nding but not an improvement. Sometimes Roy seems overly dogmatic: “The new discipline demands that all decisions regarding the experimental studies be reached by consensus in a formally convened meeting of project team members. It requires that the democratic decisions be preferred to individual expertise or experience” (p. 15). I’ve never had the power to impose such a rule, but in any case, I think that a fair amount of delegation and deference to speci c expertise is a good idea. Finally, there is some implication, like the “16 Steps” in the subtitle, that a procedure has been supplied that will virtually ensure success if it is exactly followed in detail. There is a strong human psychological yearning for such certainty (witness some investing guides), but nonetheless it is a mirage. To summarize, this book provides a simple introduction to robust design, mostly in line with Taguchi’s original approach but with several improvements, including more emphasis on interactions and the usefulness of computers. Its most appropriate audience is students with less education and little background in statistics, for whom the book’s numerous examples and the repeated coats of paint from the goals-material-summary-review questionsexercises format will be most helpful.