Introduction to Taguchi Methods

Abstract

We have seen how, using fractional-factorial designs, we can obtain a substantial amount of information efficiently. Although these techniques are powerful, they are not necessarily intuitive. For years, they were available only to those who were willing to devote the effort required for their mastery, and to their clients. That changed, to a large extent, when Dr. Genichi Taguchi, a Japanese engineer, presented techniques for designing certain types of experiments using a “cookbook” approach, easily understood and usable by a wide variety of people. Most notable among the types of experiments discussed by Dr. Taguchi are two- and three-level fractional-factorial designs. Dr. Taguchi’s original target population was manufacturing engineers, but his techniques are readily applied to many management problems. Using Taguchi methods, we can dramatically reduce the time required to design fractional-factorial experiments.

Appendix

Example 13.10 Electronic Component Production in R

For this illustration, let’s assume the same electronic components study described in Example 3.8. Recall that our target value is 1.600 volts and the tolerance is ±0.350 volts. We have six factors , each at two levels, in a L₈ design with six (clean) main effects . In this example, we also consider four replicates per treatment combination, but we will use a different dataset, shown in Table 13.17. The assignment of factors to columns was arbitrary and is the same as what was used in Table 13.13.

Table 13.17 Dataset for electronic-components study

For this analysis, we will use the qualityTools package in R. Using the taguchiChoose() function, we can get a matrix of all possible Taguchi designs available in this package, as follows:

> taguchiChoose()

1	L4_2	L8_2	L9_3	L12_2	L16_2	L16_4
2	L18_2_3	L25_5	L27_3	L32_2	L32_2_4	L36_2_3_a
3	L36_2_3_b	L50_2_5	L8_4_2	L16_4_2_a	L16_4_2_b	L16_4_2_c
4	L16_4_2_d	L18_6_3

Choose a design using e.g. taguchiDesign("L4_2")

We are interested in L8_2, that is, a design for four to seven two-level factors . Using the taguchiDesign() function, we can select this option and set the number of replicates per treatment combination:

> design <- taguchiDesign("L8_2", randomize=FALSE, replicates = 4) Warning messages: 1: In `[<-`(`*tmp*`, i, value = <S4 object of class +"taguchiFactor">) : implicit list embedding of S4 objects is deprecated 2: In `[<-`(`*tmp*`, i, value = <S4 object of class +"taguchiFactor">) : implicit list embedding of S4 objects is deprecated 3: In `[<-`(`*tmp*`, i, value = <S4 object of class +"taguchiFactor">) : implicit list embedding of S4 objects is deprecated 4: In `[<-`(`*tmp*`, i, value = <S4 object of class +"taguchiFactor">) : implicit list embedding of S4 objects is deprecated 5: In `[<-`(`*tmp*`, i, value = <S4 object of class +"taguchiFactor">) : implicit list embedding of S4 objects is deprecated 6: In `[<-`(`*tmp*`, i, value = <S4 object of class +"taguchiFactor">) : implicit list embedding of S4 objects is deprecated 7: In `[<-`(`*tmp*`, i, value = <S4 object of class +"taguchiFactor">) : implicit list embedding of S4 objects is deprecated

We can then set the names and levels of each factor. Recall that the second column will not be assigned to any effects; we will call it X. Next, we create a vector with the responses and incorporate it in the design:

> names (design) <- c("FacA", "X", "FacB", "FacC", "FacD", +"FacE", "FacF") > values(design) <- list(FacA=c(1,2), X=c(1,2), FacB=c(1,2), +FacC=c(1,2), FacD=c(1,2), FacE=c(1,2), FacF=c(1,2)) > y <- c(1.358, 1.433, 1.526, 1.461, 1.444, 1.402, 1.573, +1.528, 1.365, 1.450, 1.546, 1.490, 1.461, 1.403, 1.576, +1.519, 1.387, 1.5, 1.55, 1.472, 1.49, 1.411, 1.558, +1.492, 1.339, 1.441, 1.563, 1.455, 1.476, 1.424, 1.543, +1.554) > response(design) <- y > summary(design) Taguchi SINGLE Design Information about the factors :

	A	B	C	D	E	F	G
value 1	1	1	1	1	1	1	1
value 2	2	2	2	2	2	2	2
name	FacA	X	FacB	FacC	FacD	FacE	FacF
unit
type	numeric	numeric	numeric	numeric	numeric	numeric	numeric

	StandOrder	RunOrder	Replicate	A	B	C	D	E	F	G	y
1	1	1	1	1	1	1	1	1	1	1	1.358
2	2	2	1	1	1	1	2	2	2	2	1.433
3	3	3	1	1	2	2	1	1	2	2	1.526
4	4	4	1	1	2	2	2	2	1	1	1.461
5	5	5	1	2	1	2	1	2	1	2	1.444
6	6	6	1	2	1	2	2	1	2	1	1.402
7	7	7	1	2	2	1	1	2	2	1	1.573
8	8	8	1	2	2	1	2	1	1	2	1.528

Only the first replicate was shown for demonstration purposes.

We can generate an effect plot (Fig. 13.12) using the following commands:

> par(mar=rep(4,4)) > effectPlot(design,fun=mean, response="y", points=FALSE, +col=2, pch=16,lty=3, axes=TRUE)

Fig. 13.12

Effect plots for Taguchi design in R