Dr. Genichi Taguchi was a Japanese engineer and quality consultant who codified his consulting techniques into a formal methodology. This generic engineering tool, called the Taguchi method, is used for system studies. The purpose of these studies is to reduce system variability while simultaneously decreasing costs and increasing productivity.
The features of the Taguchi method include:
extensive use of experimental design
separation of factors by role (control and noise)
use of measures of variability as responses
dual objectives of process centering and noise minimization
use of loss functions for economic justification of each application
The following steps outline the Taguchi Design of Experiments method:
Identify what are the control factors and what are the noise factors. Noise factors are costly
and difficult to control, while an ideal control factor is easy to control precisely. Noise
factors can include environmental factors, component deterioration, and process variation.
Identify the levels for the control and noise factors.
Identify the responses of interest and determine a quality criterion for each response. Does
the system require that the response match a specified value, be as large as possible, or
approach zero?
Construct a design for the control factors (inner array) and a design for the noise factors
(outer array). The inner-array is selected based on the number of control factors. Typically,
interactions are assumed to be negligible, but if they are to be included, then a larger design
may be required. The outer array simulates the various conditions that the noise factors
would produce in reality. For each run in the inner array, all runs in the outer array are
carried out.
Conduct the design of experiments. Typically, you complete all the runs in the outer array
before proceeding to the next run of the inner array. The runs for the inner array and outer
array are (ideally) randomized separately.
Evaluate the performance statistic for each run of the inner array. These measures become
the responses for the inner array. The performance statistics include Mean(Y), StDev(Y) or
Ln(StDev), and Taguchi's signal-to-noise ratios. Some practitioners prefer to use Ln(StDev)
as a variance stabilizing transformation. Taguchi signal-to-noise ratios include Nominal is
Best, Larger is Better and Smaller is Better. Signal-to-noise ratios are always maximized.
From the Pareto of Deltas (Main Effects), Pareto of ANOVA SS (Sum-of-Squares) %
Contribution, Main Effects & Interaction Plots and Prediction Equation model, determine
the new set points for the control factors. Taguchi’s two step optimization first finds
control settings that maximize the SN Ratio (and/or minimize the StDev), then if available,
factors that move the mean to Target without affecting the SN Ratio.
Confirm that the new settings meet target, dispersion and loss criterion with follow-up
experimental runs.
Taguchi Orthogonal Arrays are a cookbook of designs that are similar to Full & Fractional-Factorial
and Plackett-Burman designs. For example, the L4 design is 2-level, 4 runs with up to 3 factors; L8
is 2-level, 8 runs with up to 7 factors; L9 is 3-level, 9 runs with up to 4 factors. Taguchi designs use
2-level coded values of 1, 2 instead of the orthogonal coding -1, +1 and 3-level coded values of 1, 2,
3 instead of -1, 0, +1.
Interactions are typically assumed to be negligible compared to main effects, but some designs
permit the analysis of all interactions or aliased interactions. Selection of aliased interactions is
more economical than all interactions, but they should be used with caution. Process knowledge,
engineering or theory are used to make the selection and assume that the chosen interaction is
dominant and the others are negligible. Aliased interactions are often associated with the largest
main effects. Confirmation runs should always be used to validate the model.
For further reading, see:
Basic:
Fowlkes, W.Y.; Creveling, C.M. (2006) Engineering Methods for Robust Product Design: Using
Taguchi Methods in Technology and Product Development, Prentice Hall.
Ross, P.J. (1996) Taguchi Techniques for Quality Engineering, 2nd Edition, McGraw-Hill, New York,
NY. Roy, R.K. (2010) A Primer on the Taguchi Method, 2nd Edition, Society of Manufacturing Engineers,
Dearborn, MI.
Advanced:
Taguchi, G.; Chowdhury, S.; Wu, Y. (2005) Taguchi's Quality Engineering Handbook, John Wiley,
Hoboken, NJ.
Overview of Taguchi DOE Templates
The Taguchi DOE templates are similar to the other SigmaXL templates: simply enter the inputs and resulting outputs are produced immediately.
Click SigmaXL > Design of Experiments > Basic Taguchi DOE Templates or SigmaXL > Templates
and Calculators > Basic Taguchi DOE Templates to access these templates:
Taguchi L4 (2 Level)
Two-Factor (with Two-Way Interaction)
Three-Factor
Taguchi L8 (2 Level)
Three-Factor (with Two-Way Interactions)
Four to Six-Factor (with Aliased Two-Way Interactions)
Seven-Factor
Taguchi L9 (3 Level)
Two-Factor (with Two-Way Interaction)
Four-Factor
Taguchi L12 (2 Level): Eleven Factor
Taguchi L16 (2 Level)
Five-Factor (with Two-Way Interactions)
Eight to Fourteen-Factor (with Aliased Two-Way Interactions)
Fifteen-Factor
Taguchi L18 (2/3 Level)
Three-Factor (with Two-Way Interactions)
Eight-Factor (with A*B Interaction)
Taguchi L27 (3 Level)
Three-Factor (with Two-Way Interactions)
Thirteen-Factor
Note: SigmaXL Basic Taguchi DOE templates do not include L32 (2 Level), L36 (2/3 Level), L54 (2/3 Level), designs with more than 3 Levels, or a signal factor for dynamic characteristics.
Template Features:
Levels are discrete categorical so may be numeric or text
Fill in the blanks template, charts automatically update
Predicted Response Calculator and Charts for Mean, Standard Deviation (or Ln Standard Deviation) and Signal-to-Noise Ratio
Available Signal-to-Noise Ratios:
Nominal is Best
Nominal is Best (Variance Only)
Nominal is Best (Mean Square Deviation with Target)
Larger is Better
Smaller is Better
Signal-to-Noise Ratios
Formula
SN: Nominal is Best
10*Log10(Ybar^2/S^2)
SN: Nominal is Best (Variance Only)
-10*Log10(S^2)
SN: Nominal is Best (Mean Square Deviation with Target)
-10*Log10(Sum((Y-T)^2)/n)
SN: Larger is Better
-10*Log10(Sum(1/Y^2)/n)
SN: Smaller is Better
-10*Log10(Sum(Y^2)/n)
Up to 27 Replications for Outer Array (i.e., support up to L27 Outer Array)
Pareto of Deltas (Effects) and ANOVA SS (Sum-of-Squares) % Contribution (for Main Effects and Two-Way Interactions)
Main Effects Plot and Interaction Plots (if applicable)
For designs with aliased interactions a drop-down list of available aliased interactions is provided. This is much easier to use than Linear Graphs
Column assignments to Orthogonal Array are optimized to ensure maximum design resolution
Template Notes:
Select desired Signal-to-Noise Ratio to maximize. The SN formula is displayed.
For Nominal is Best, "SN: Nominal is Best" is recommended for non-negative data. Use "SN: Nominal is Best (Variance Only)" if the data has a mixture of negative and positive values.
If selection is "SN: Nominal is Best MSD with Target", enter Target value (MSD denotes Mean Square Deviation); if Target = 0, this is equivalent to Smaller Is Better. For use of MSD in SN Ratio, see Ranjit Roy (2010) "A Primer on the Taguchi Method," Second Edition, Society of Manufacturing Engineers.
Larger is Better requires positive data. Smaller is Better requires non-negative data (target is zero).
Select desired Standard Deviation Response: StDev(Y) or Ln(StDev(Y)).
Enter Factor Names and Factor Levels. Levels are discrete categorical, so may be numeric or text
If applicable, select Aliased Interactions. Enter Run Number (if runs have been randomized) and Outer Array Response values
Selection of Aliased Interaction assumes that the chosen interaction is dominant and the others are negligible. It is often associated with the largest main effects. Confirmation runs should be used to validate model. Please refresh selection if message appears.
For Taguchi L8 Five to Six Factors and L16 Nine to Fourteen Factors, not all possible interactions are available in the drop-down list (they are aliased with main effects). If an interaction of interest is not available in any of the drop-down lists, please modify the Factor Names so that they are assigned to columns shown in the list and then select that interaction.
The typical default display of Yrep1 to Yrep9 accommodates an outer array up to L9. Unhide columns to display Yrep10 to Yrep27, which permits an outer array up to L27.
Delta is the difference between the maximum and minimum average response for the levels of each factor in the inner array. Two-way interactions are not included. ANOVA SS (Sumof-Squares) % Contribution includes two-way interactions.
To compute a predicted response, enter Actual Factor Setting using the drop-down selection. Factors are treated as categorical. If Factor Setting Coded is "FALSE", please refresh selection to match level settings. Note, Excel Solver cannot be used with this calculator.
The Interaction Plot X-axis/Legend factors may be switched by clicking on the chart, then select Excel Design > Switch Row/Column.
DOE Templates are protected worksheets by default, but this may be modified by clicking SigmaXL > Help > Unprotect Worksheet. Alternatively, you can click Excel File > Info > Unprotect or Home > Format > Unprotect Sheet.
Chart Y-axis scaling is automatic. To modify, double-click on the Y axis and adjust Minimum and Maximum.
The Orthogonal Array or Dummy Coding may be analyzed using Multiple Regression Analysis, adding and removing terms from the model as necessary. Terms that are removed will be used to estimate error for p-values. In particular, regression analysis of 3 Level designs with interactions (L9 Two Factor, L18 Three Factor and L27 Three Factor) should use Dummy Coding
Dummy Coding uses Level 1 as the reference value, so Level 1 does not appear in the array. The Predicted Output calculator formula coefficients and ANOVA Sum-of-Squares (SS) % Contribution are computed using Dummy Coding regression. This is consistent with SigmaXL's use of Dummy Coding regression for categorical factors in other tools.
Do not modify any other part of the template.
Caution: The use of Cell Autocomplete with Flash Fill in Excel 2016 or higher may result in a crash (this is a known Microsoft issue). If this occurs, please turn off Automatic Flash Fill (File > Options > Advanced, uncheck "Automatically Flash Fill" under "Enable Autocomplete for cell value").
If there are further stability issues, please turn off Automatic Recalculate (Formulas > Calculation Options, Select Manual). Use "Calculate Now" to refresh calculations after entry of Factor Names, Levels, Outer Array data or as needed.
