Dr. Genichi Taguchi
Dr. Taguchi built on the work of Plackett and Burman by combining
statistics and engineering to achieve rapid improvements in product
designs and manufacturing processes.
His efforts led to a subset of screening experiments commonly
referred to the Taguchi Techniques or the Taguchi Method®.
Major Premises of Taguchi Techniques
Taguchi calls common cause variation the “noise.”
Noise factors are classified into three categories: Outer Noise,
Inner Noise, and Between Product Noise.
Taguchi’s approach is not to eliminate or ignore the noise
factors; Taguchi techniques aim to reduce the effect or impact of
the noise on the product quality.
Quality Loss Function
The Loss Function can help put the cost of deviation from target
The loss represents a summation of rework, repair, warranty cost
plus customer dissatisfaction, bad reputation, and eventual loss of
market share for the manufacturer.
Signal to Noise Ratio
Taguchi's emphasis on minimizing deviation from target led him to
develop measures of the process output that incorporate both the
location of the output as well as the variation. These measures are
called signal to noise ratios.
The signal to noise ratio provides a measure of the impact of
noise factors on performance. The larger the S/N, the more robust
the product is against noise.
Calculation of the S/N ratio depends on the experimental
Derivation of Taguchi Matrices
Taguchi matrices are derived from classical Full Factorial arrays.
As with Plackett-Burman designs, Taguchi designs are based on the
assumption that interactions are not likely to be significant.
Taguchi designs have been developed to study factors at
two-levels, three-levels, four-levels, and even with mixed levels.
The levels in Taguchi matrices have historically been reported as
Level 1 and Level 2 for two-level experiments.
These levels are no different than the Low (-) Level and the High
(+) Level used in Full Factorial designs and by Plackett and Burman.
For more than two levels, experimenters typically use Level 1,
Level 2, Level 3, etc. for Taguchi designs.
Types of Taguchi Designs
A series of Taguchi designs for studying factors at two-levels are
Two-level designs include the L4, L8, and L16 matrices.
The L4 design studies up to 3 factors.
The most popular Taguchi designs are the L8 and L16 that study up
to 7 and 15 factors respectively.
The L4, L8, and L16 designs are geometric designs based on the 22,
23, and 24 Full Factorial matrices respectively. They are based on
the Full Factorials so that interactions can be studied if desired.
Non-geometric Taguchi designs include the L12, L20, and L24
designs that can study up to 11, 19, and 23 factors respectively.
- There are other two-level Taguchi Matrices, both geometric and
non-geometric, designed to study even more factors, but it is rare
that larger numbers of factors can be studied in a practical,
feasible, or cost-effective manner.
Analysis of Interactions
While Taguchi views interactions as noise factors and most likely
not significant, he does offer techniques to evaluate the impact of
two-way interactions on responses.
Taguchi provides two techniques to explore interactions in a
The linear graph is a graphical tool that facilitates the
assignment of factors and their interactions to the experimental
Some experimenters find the interaction tables developed from the
linear graphs to be easier to use.
Matrices with Outer Arrays
The use of outer arrays provides a means to separate the impact of
the process or product factors from the noise factors.
The standard matrix is used as an inner array to study the
process/product factors and an outer array for evaluating one or two
noise factors is added.