Electronic Design

# What's All This Taguchi Stuff, Anyhow? (Part II)

<i>Electronic Design</i> extends an open invitation to Dr. Taguchi or any of his proponents wishing to respond in print to Bob's comments.

Once upon a time, some engineers at Nippon Electric Corp. (NEC) had designed some voltage regulators for television sets to put out + 115 V dc at 600 mA.1 But because the regulators were built of inexpensive ±5% components, a few of the circuits sometimes had an output variance as bad as +25 or -25V, so they could not be trimmed to 115 V using the adjustment pot. Then Genichi Taguchi proposed to help them by using the new "Taguchi method" to optimize their circuit and improve the yield ("What's All This Taguchi Stuff, Anyhow?," June 25, 1992, p. 83). He used NEC's basic circuit shown in Figure 1, and the equations and the initial values of components in Figure 2.

He also used his proprietary "Taguchi method," with orthogonal arrays,2 to help "optimize" the circuit and get the output voltage to have less variation without using expensive, tight-tolerance components. And he succeeded.

My, he really made a big improvement. Instead of an output variance of ±25V, Taguchi achieved a variance of ±1.5V. If some of the resistors had a bad tolerance, that didn't cause the output to err excessively. Very good. And even if the Reference Voltage had a tolerance of 5 or 10%, the circuit was so well optimized that the output was still more accurate than 2%. Great! But—hey—wait a minute! Does that make any sense? Ah, let's set this question aside until later.

In his 1979 book, Introduction to Off-Line Quality Control, Dr. Taguchi observed that this 115-V regulator was an excellent example of how to use his techniques to get low variability.3 After all, Taguchi said, "I define quality as the losses a product imparts to society from the time the product is shipped."4 If your products don't have quality, you're robbing from widows and orphans. And if you can use low-cost components to achieve high quality, then you have used Taguchi method wisely. That's much better than the common engineering practice in the United States of "throwing money at the problem."5

Furthermore, observes Taguchi, the wise way to engineer a circuit such as a voltage regulator is to trim one resistor to achieve a substantially flat slope by working on a parabolic curve in the region where it gets flat.6 If your circuit has a positive sensitivity with a steep positive slope, you may find that a mere 100-Ω resistance shift of one certain 200-Ω resistor can make a terrible 22-V change in the output. Once again you are imparting losses to society. But if you set this resistor at 350Ω, minor variations in resistor value have virtually no effect (see Figure 3).

Ah—now—which resistor is that? And in what circuit is that? Can Dr. Taguchi please explain? (Dr. Taguchi has been demurring.) But, he says, after you use the resistor to trim the output to where the slope is zero, you can then specify a higher or lower beta on one of the transistors to force the Vout back to 115 V. (Which transistor? Dr. Taguchi has no comment.)

One of the instructors who teaches, among other things, the Taguchi method, Professor Thomas Barker, from the Center for Statistics and Quality Control at the Rochester Institute of Technology, expanded still further in his book:7 He says we should take advantage of this type of circuit that has low sensitivity to variations in one part of its curve. We should select a transistor with higher hFE (higher than 10 or 20, as high as 40, but not any higher or the sensitivity will get worse again), until the slope or gradient of (DVout) vs. (DhFE) is flat. Then trim a resistor to get the output back to 115 V dc. Which transistor should one select? Which transistor should one select? Which resistor should one then trim? In what circuit? I have asked Professor Barker several times, but he has never supplied an answer.

Now, isn't that funny? Dr. Taguchi proposes that we should select the resistor to get a flat slope of Vout vs. resistance, and then tweak the transistor's beta to hit the target for Vout. Professor Barker claims to be teaching the Taguchi method, yet in his book he teaches to select a transistor for medium gain to get a flat slope of Vout vs. gain, and then trim a resistor to get the desired Vout. Which one is right?? Can they both be right?? Let's go back and look at that circuit....

The original NEC circuit had an 11.2-V Zener at z(11), and z(5)/z(6) = 10. The noise gain of 11 caused the output to be around 115 V, although with the usual variations due to the component tolerances. The original component values are shown in the chart in Figure 2. But the "optimal" values of the components are also shown in Figure 1—the ones provided by the Taguchi method's "optimization." As you can see, I have pencilled in the "optimal" resistor values right beside the resistors so we can see what's happening, whereas Dr. Taguchi put them on another page where it's hard to see what's going on.

NOW I can see what is going on. If Vin is 138 V, and Vout is 115 V, then z(1) = 656 Ω, which means it has to have about 20 V across it, and about 30 mA going through it. Okay, but where does that current go? The base of TR1 doesn't draw even 1 mA. So, can the current go through z(4)?? Hardly. The value of 33k won't permit 30 mA to go through it. THEREFORE, this circuit as presented cannot work; the output voltage would be 133 V. There must be an error somewhere.

Let's take a quick look at the equations for Vout. The value of z(4) wasn't included in any equation. So, perhaps it was a minor error to assume that setting an arbitrary value of 33 k for z(4) would not cause any harm. Let's propose that z(4) now has a lower value, 10Ω or 100 Ω, to give the circuit a chance to regulate. That's still consistent with the equations and their intent.

If 30 mA flows through z(1), TR3 can now sink this current. If Vout is about 115 V, TR3 will be at about the right level to draw that 30 mA through z(8) and through the reference diode z(11), a 1.12-V Zener.

Hey—what's the story? Can a 1.12-V Zener work in this circuit? Are you sure that's not a misprint?? Well, there's a Zener reference, z(11). But remember—Dr. Taguchi stated that he wanted the output voltage to be 115 V, "robust" and invariant of tolerances of the reference voltage. He wanted Vout to be 115 V invariant of the resistor values or tolerances. In fact, he said he wished the output to be 115 V invariant of the values of the voltage divider, and even invariant of the setting of the adjustment pot (refer to z(5), z(6), and z(7) that "trims" Vout. And that's the result he got in the optimization provided by his method.

Okay—what is going on here? The output voltage of 115 V is alleged to have a tight tolerance and is invariant of any of the component values? HOW CAN THAT BE?? The answer is easy: Dr. Taguchi asked the computer to optimize this circuit with a nominal input voltage of 138 V, and the computer gave him a circuit whose output depends ONLY on the input voltage—the Vout is just 83% of Vin. If the input voltage moves 10 V, the output will also move 8 V, but no resistor or Zener values have any significant effect on Vout. (There is a fine-print disclaimer saying that the output voltage, with a fixed input of 138 V dc, is the only parameter being optimized; all other characteristics, such as line regulation, aren't considered).8 I built this circuit, and after I changed z(4) to a low value, the output went right to 116 V—so long as the input was at 138 V.

Dr. Taguchi and his friends have established "robustification" as a highly desirable procedure whereby a desired output is "robust," largely immune to parameter changes.9 In this case, Taguchi wished to have the output invariant to any resistor changes—but he neglected to say that he still wanted it to REGULATE! He forgot to check to see if the "optimal" circuit would still keep a constant output vs. changes in Vin. So he got what he asked for. And he did not check the answer. Needless to say, this kind of "optimization" is great for filling in a chapter of a book, but not so good for making TV sets that work.

Taguchi claims in his book that there are some resistors that have a steep effect on Vout, but the best circuit that achieves the much-desired "robustness" has excellent invariance to resistor values.10Well, there's no place in the NEC circuit for a mere 250- or 350-Ω resistor to have the effect that Taguchi claims. I wonder WHAT the Taguchi circuit could REALLY BE? EXACTLY where did he connect his 350-Ω resistor? I have made pointed inquiries, but have yet to get any answer.

Professor Barker also takes note of Taguchi's "optimal" regulator and its fantastic robustness. He claims that in the best version of the regulator, improving the beta from 20 to 40 will increase the output voltage and then cause a decrease of the sensitivity to beta. But, increasing the beta past 40 will cause a further degradation of sensitivity. I wonder what circuit he's been using? I've been asking for years, since January 1990, and still haven't gotten an answer. Maybe it's just a "hypothetical" or imaginary circuit? With merely some "conceptual" robustness against all resistor variations?

I mean, if an engineer wants to propose a hypothetical circuit, that is OK; I do that all the time. But I cannot then use the hypothetical circuit to prove that I'm a better, smarter circuit designer with superior design techniques. If I can make my hypothetical circuit jump through conceptual hoops, nobody else can critize me because there actually is no real circuit like this....

Look, gentlemen, you can't have a circuit that has perfect accuracy despite all sorts of tolerances, which you achieved by adding in wishful components that reject all of the conceptual imagined variations. It's time now to admit that there never was a regulator circuit that had all of these advantages. It's time to admit that Dr. Taguchi exercised his computer to "optimize" a circuit until it did not regulate at all. A 10-V change of Vin would cause 8 V of shift on the output. A ripple of 20 V on the main filter gives a totally unacceptable ripple of 16 V on the output—IF you build it.

These Taguchi experts hope you will follow their tortuous reasoning, which is if you can make a circuit more "robust" against one thing, then that should likewise make the circuit more "robust" and insensitive to other parameters. A perfect, truly "robust" design will make the output invariant of "everything."11

LOOK HERE GUYS, the output voltage has to depend on SOMETHING. If it doesn't depend on one thing, it has to depend on something else! You can't live on wishful thinking forever.

Meanwhile, the righteous Taguchi experts heap insults on honest engineers: American engineers try to solve a problem by "throwing money at it."12 They "gold-plate" the invention with "the most costly components.13 Well, I think that cutting down the Error Budget by spending a few pennies to buy a couple of 2% resistors for z(5) and z(6) is a lot better than heaping on bovine manure to confuse the situation, with complicated matrices and huge equations. Everybody knows that a 10% tolerance of a regulator's reference voltage will cause a 9 or 10% shift of Vout, and anybody who tries to pretend it won't cause a shift has probably designed an un-regulator.

Still, Taguchi insists that a regulator that ages and goes out of tolerance can cause the whole TV set to be thrown away.14 Don't look now, Dr. Taguchi, but the whole reason for putting in an adjustment pot at z(7) is so you can tweak the Vout and get the set back into spec without a big "loss to society." Taguchi is the one who doesn't understand the situation.15

Please note—Dr. Taguchi and Prof. Barker did not just observe that the regulator circuit was the beneficiary of some very good "optimization." They embellished the situation by claiming they knew the secret of how to achieve such good results, which is by selecting the value of one component so that the circuit was less sensitive to variation in that component. Unfortunately, they never checked to find out why the "variation" was so "good"—why changes in the reference voltage did not cause changes in the output voltage. They never checked to see that the circuit was NOT WORKING. They never built the circuit.

Furthermore, by using fancy matrices and orthogonal arrays and computer programs, they obscured the actual procedure of optimization. They trusted the computers to give them a perfect answer, so they didn't have to think about the process or understand the answer. Their computer took away their reasoning, and the optimization process gave them no insights. I'd never put up with that. I'd never let my engineers do that.

Now, anybody can make a mistake. But after you ask your computer to do something for you, you check it. If the computer designed an optimum that's absurd, you stop and go back and redesign. But, apparently, Dr. Taguchi was so confident that a 16X improvement in tolerance was the natural result of his "Taguchi method," he never checked his results.

Too many people who trust their computers seem to be neglecting to do a sanity check these days... So much for the "widget amplifier," or more correctly, the "widget regulator" that took me several years to figure out why it seemed to be too good to be true.

(Note: Don't try to use Taguchi's equations from Figure 2 to compute what that circuit is really doing, because those equations have erroneous terms in them—heaven knows where they came from—and they give answers that can be off by 6% to 16%. I know, because I tried to derive these and I couldn't. So I derived the true equations, which are rather different from these. Available on request to anybody who's nut about regulators...)

Next, I'd like to present some brief comments by an Expert who works for one of the Fortune 500 Companies (who prefers to remain anonymous). I talked to the Expert shortly after my original column came out.16 He said that as a collaborator with Dr. Taguchi, he was obliged to point out that Taguchi himself doesn't say you must neglect and ignore "the parameters that are not under our control"; Taguchi can and does sometimes take those into account.

I observed that the video lecturer who taught me, a Professor from a major Eastern technical school, was quite clear and adamant about this. So it seemed strange that that Professor claimed he was teaching us "the Taguchi method" if it was in contradiction to what Taguchi believes and teaches. The Expert also observed that Taguchi doesn't insist on using the absolute minimum of tests, but is willing to add tests to check for drifts and noises and other potential errors. Again, I wondered why the Professor called it "the Taguchi method" if his teachings were in diametric opposition to those of Taguchi himself.

The Expert observed that a number of people claim to teach "the Taguchi method," and some of them do teach things that Taguchi doesn't agree with. I replied that it's unfortunate that people seem to be putting words into Dr. Taguchi's mouth, yet he doesn't repudiate those other people's teachings, even when they have permission from Taguchi's American Supplier Institute to use the "the Taguchi method" trademark.

So it seems that some of the accusations I made in my earlier column, that I disliked the methods of Genichi Taguchi, were misplaced. I should state that other people who claim to be teaching "the Taguchi method" are apparently responsible for some of the ideas that horrified me. I'm sorry I accused Dr. Taguchi of teaching all those unacceptable ideas, which apparently belong to other people.

However, now that I have been able to pin down the facts, I find that Dr. Taguchi has showed some truly bad judgment in claiming glorious advantages for circuits that don't work at all. Also, some of his other optimization schemes show terrible errors. He uses his large orthogonal arrays in another book17 to prove that the output voltage of a voltage regulator has just a small variation with z(4). But z(4) isn't even represented in his equations. Maybe his computer got sloppy when evaluating that huge array of numbers?

He designed an "efficient" regulator to put out 600 mA at 220 V, with a 1000-Ω current-limit resistor that dissipates over 2000 W. 18 And it all runs on a 138-V dc supply without any switching mode. Really, with a straight face, he presents this as an optimized design...

So while I must concede that some of my complaints against Dr. Taguchi were misdirected, I have found that every page I do understand, in every "Taguchi" book that I have seen, is full of mathematical errors, engineering blunders, and intellectual fiascoes. (Diamond's book, Design of Experiments, is one of the few exceptions—I find it quite good, per my recommendation in the June 25, 1992 column).19

So I conclude that in this field, if anybody claims you must heed HIM because H E is teaching you "THE Taguchi method," hold onto your wallet tight and watch out for mathematical or philosophical errors. As with any teacher, you should be thoughtful and skeptical. If any "expert" proposes to teach you something, you should check it out with reality. Make sure it makes sense. Question authority, no matter who the teacher is. In this particular field, since there are several strong and contradictory claims, be aware that your skepticism may be justified.

One of my friends steered me to a recent story by Jim Smith and Mark Oliver—"Statistics: The Great Quality Gamble,"20 which criticizes various aspects of statistical analysis, including a subsection on "Taguchi: Too good to be true?" It deals with people and insights in the workplace—experience and intuition, contrasted with over-confidence and over-reliance on statistical analysis. It includes the quote, "He who works with statistical methods alone won't be here in three years," said by Bill Deming, the dean of the Quality movement.

Another friend pointed out an article by Eugene Sprow, "What Hath Taguchi Wrought?"21 It comments on Taguchi's methods from a rather different viewpoint, so if you're a statistician or a manufacturing engineer, you might like to read that to see where other experts think Taguchi's ideas are good, and where not so advantageous.

I hope you will agree with me that the outcome of all this debate will be beneficial: Every engineer should be aware that books or classes claiming to teach "the new Miracle Method" may indeed be telling you something too good to be true. Any book, any teaching, deserves to be considered skeptically.22 Every engineer should think, every reader should THINK. Should they trust Pease, or Taguchi, or any other teacher? I hope they will study and trust those people who show they deserve to be trusted. And we all deserve to be greeted with skepticism when we start making erroneous or foolish statements. QUESTION AUTHORITY!

All for now./Comments invited!
RAP / Robert A. Pease / Engineer

Mail Stop C2500A
National Semiconductor,
P.O. Box 58090,
Santa Clara, CA 95052-8090

(The opinions expressed herein are those of the writer and do not necessarily reflect the views of National Semiconductor Corporation.)

P.S. I did receive a pleasant response from Dr. Taguchi concerning my questions about the "optimized regulator" (personal correspondence, Oct. 27, 1992). He did not have any comments on voltage regulators, or "optimal values" that caused circuits to not regulate, nor on sensitivities to changes in 200-Ω resistor. He just stated, "We are not interested in any actual results because quality engineering deals with only optimization." Unfortunately, if the actual result is a circuit that doesn't work, I can't consider the optimization anything but useless... or, worse than useless.—RAP

1. Genichi Taguchi and Yuin Wu, Introduction to Off-Line Quality Control; Central Japan Quality Control Association, Nagaya, Japan, 1979; p. 41. (This is surely Nagoya, but the book says Nagaya.)

2. Ibid., p. 42-47.

3. Ibid., p. 9-14.

4. Ibid., p. 1. NOTE, I did not misquote Dr. Taguchi. I'm not the one who made up "I define quality as the loss to society..."; Taguchi said this.

5. Thomas Barker, Engineering Quality by Design; Marcel Dekker, NY & Basel, with ASQC Press, Milwaukee, 1990; p. 13.

6. Taguchi, p. 30-31.

7. Barker, p. 12-16.

8. Taguchi, p. 42. "Also, characteristics other than the output voltage are not discussed."

9. Barker, p. 136.

10. Taguchi, p. 31.

11. I'm sure I read this somewhere.... such as:

11a. Phillip J. Ross, Taguchi Techniques for Quality Engineering; McGraw-Hill, 1988; p. 177. "Making a circuit robust against one noise makes it robust against other noises also." Or:

11b. Thomas Barker, "The Quality Paradox," course notes from Center for Quality and Applied Statistics, College of Engineering, RIT; p. 7. "This empirical observation leads to an informal 'axiom' that says that if I can robustify a function for one type of noise, I can robustify it for any other type of noise."

12. Barker, p. 13.

13. Ibid., p. 104.

14. Taguchi, p. 9.

15. Ibid., p. 10, "This is the reason why such an act is more immoral than the actions of a thief."

16. Robert A. Pease, "What's All This Taguchi Stuff, Anyhow?," Electronic Design, June 25, 1992; p. 83-84.

17. Genichi Taguchi, System of Experimental Design; Kraus International Publications, White Plains N.Y., with American Supplier Institute, Dearborn, Mich., 1988; p. 379-389.

18. Ibid., p. 382.

19. Robert A. Pease, "What's All This Statistical Stuff, Anyhow?," Electronic Design, March 14, 1991; p. 97-98.

20. Jim Smith and Mark Oliver, "Statistics: The Great Quality Gamble," Machine Design, Oct. 8, 1992; pp. 77-81.

21. Eugene E. Sprow, "What Hath Taguchi Wrought?," Journal of Manufacturing Engineering, Vol. 108, No. 4, April 1992; pp. 57-60.

22. Robert A. Pease, "What's All This Critical Thinking Stuff, Anyhow?," Electronic Design, June 27, 1991; p. 119-120.