Sigma Magic Help Version 17

Taguchi Design

Overview

The Taguchi method involves conducting a series of experiments using an orthogonal array to systematically vary the signal factors' levels and observe the system's performance. The optimal combination of factor levels that minimizes the variability and is less sensitive to noise can be determined by analyzing the experimental results.

The Taguchi method is widely used in experimental design and quality improvement to achieve robust and reliable products or processes. It is beneficial in industries such as manufacturing, where variations in production processes can impact product quality.

This tool can be added to your active workbook by clicking on Stats and then selecting Design of Experiments > Taguchi Design.

Inputs

Click on Analysis Setup to open the menu options for this tool. The Analysis Setup has several tabs that can help create and analyze the Taguchi Design of Experiments. The available tabs are:

Option	Description
Create	Create a new Taguchi design and update to the worksheet
Options	Additional options for the create design
Data	Import any data available in tables onto the worksheet
Analyze	Specify how you want to analyze the design
Plots	Specify the plots to create for the analysis
Verify	Check your inputs to see if there are any errors

Create

Create can create a new Taguchi design and save the design to your worksheet. Note that any existing data on the worksheet may be overwritten when you create a new design. A sample screenshot of the create design menu is shown below.

1	Num Factors: Specify the number of factors in your design. You can create designs for up to 15 factors. The number of factors you can choose depends on the levels you pick for your design.
2	Design: Select the design (typically a Latin square design). The available Latin square designs depend on the number of factors you specified earlier. The available designs are as follows: Option Description L4 Design 2 levels of up to 3 factors L8 Design 2 levels of up to 7 factors L8 Design two levels of up to 4 factors, four levels of up to 1 factor L9 Design 3 levels of up to 4 factors L12 Design 2 levels of up to 11 factors L16 Design 2 levels of up to 15 factors L16 Design two levels of up to 12 factors, four levels of up to 1 factor L16 Design two levels of up to 9 factors, four levels of up to 2 factors L16 Design two levels of up to 6 factors, four levels of up to 3 factors L16 Design two levels of up to 3 factors, four levels of up to 4 factors L16 Design 4 levels of up to 5 factors L18 Design two levels of up to 1 factor, three levels of up to 7 factors L25 Design 5 levels of up to 6 factors L27 Design 3 levels of up to 13 factors L32 Design 2 levels of up to 31 factors
3	Signal Factors: Specify if you have signal factors in your design. Signal factors refer to the controllable factors or variables that the experimenter can adjust or set to optimize a process or system. These factors are also known as control factors or design parameters. The Taguchi method aims to identify the optimal combination of levels for these signal factors that will result in a robust and reliable product or process. The available options are: Option Description No In a static Taguchi experiment, the levels of the factors (both signal and noise) are fixed during the experiment. These experiments are suitable when the factors do not change over time. The objective is to find the optimal factor levels under constant conditions. Yes In dynamic Taguchi experiments, the levels of one or more factors are allowed to change during the experiment. Dynamic Taguchi experiments are employed when the system or process under investigation is subject to changes in conditions. The objective is to find robust settings that perform well across varying conditions.
4	Num Noises: Specify the number of noise levels (these are runs across the outer array) used to estimate mean and standard deviation. You can have up to 16 levels for the noise factors. If you have any noise variables, consider running a fractional factorial type design to limit the total noise levels to 16.
5	Factor Name: Specify a name for the factor. Make sure the names are unique across all factors and do not contain special characters.
6	Factor Type: Specify the type of factor under consideration. The available options are: Option Description Numeric The factor levels are variable and can take any value. For example, variables like temperature, pressure, etc. Text The factor levels are fixed and can only take specific values. For example, the presence or absence of a catalyst.
7	Num Levels: Specify the total number of levels for each factor. The number of levels available in the dropdown box depends on the design you selected. For example, if you have an L4 design, only two levels are possible for all factors, while if you pick an L8 design, you can have either two or four levels for some factors.
8	Levels: Specify the values of the levels. For example, if you have temperature as a factor and conduct the experiments at 100 and 150 degrees, then the two levels will be 100 and 150, respectively.
9	Help Button: Click on this button to open the help file for this topic.
10	Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.
11	Create Design: If this is your first time using this template, click this button to format it. You can also update the worksheet format any time, but remember that you may lose any data entered on this worksheet. Once you are happy with the template layout, you must enter any required data on the worksheet. When the data entered into the worksheet is complete, you can click on Analysis Setup and then Compute Outputs to generate analysis results.
12	Analyze Design: Click on this button to save all changes and compute the outputs for this analysis. Review the results of your analysis and make changes to your inputs if required to update analysis results.

Once you enter the inputs and press OK, the worksheet creates the Taguchi design. You must conduct each test and upload the results in the response columns (Y1, Y2, Y3, etc.).

Options

This tab contains additional options for the created design that may not be used as much. A sample screenshot of the options menu is shown below.

1	Randomize Runs: Randomizing runs in a Design of Experiments (DOE) study is a common practice that helps control the effects of uncontrolled variables or external factors that could otherwise introduce bias or confounding into the experimental results. By randomly assigning experimental runs to different conditions or factor levels, researchers can distribute the effects of uncontrolled variables evenly across the experimental conditions. This helps reduce uncontrolled factors' impact on the observed responses and ensures that their effects are averaged out. Randomization increases the robustness of the experimental design. Introducing variability through randomization makes the results less sensitive to specific conditions or orders, making the findings more generalizable to a broader range of situations. The available options are: Option Description No Do not randomize the design. The design is generated in the standard order. Yes Randomize the design. This is a recommended setting to ensure better results.
2	Random Seed: Specify the seed to use for the random number generator. This option is enabled only if you are randomizing the runs. Use the same random seed to generate the same random numbers each time. A random Seed of 0 implies that a new random seed is used each time. If you want to use a random seed, ensure it is an integer greater than zero.
3	Specify Columns: By default, the values of the levels are derived from a Latin square. The columns are assigned from left to right. For example, an L8 Latin square with two levels has seven columns. Hence, you can assign up to 7 factors. However, we only have three factors, A, B, and C, for an experiment. These factors are assigned to columns 1, 2, and 3 (from left to right). The factors on the left vary slowly, and those on the right vary faster. So, if you have an expensive factor to change the levels, you would want to assign it to a leftmost column. Secondly, the factor assignments constitute a particular level of resolution and confounding. If you have factors you don't want to be confounded, you can use a different set of columns instead of 1, 2, or 3. For example, you can assign columns 1 to A, 3 to B, and 5 to C. This assignment pattern could have a different confounding pattern. Depending on your problem and requirements, you can specify a set of columns for your analysis.

Data

You can directly enter the data on the worksheet or import any data stored in tables onto the worksheet. This tab helps you import data from tables onto the worksheet. A sample screenshot of the data menu is shown below.
For example, if you have two factors, A and B, and are using an L8 design, you will have eight runs for this experiment. Hence, your table needs eight rows of data for the response variable. Corresponding to your three noise levels, you must run each experiment under three different noise levels: N1, N2, and N3. Corresponding to each noise level, you will receive a response variable (Y) value. That information must be stored in a table, which can be imported onto your worksheet. An example of the type of data stored in tables is shown in the following figure under columns Y1, Y2, and Y3.

1	Search Data: The available data displays all the columns of data that are available for analysis. You can use the search bar to filter this list and speed up finding the right data for analysis. Enter a few characters in the search field, and the software will filter and display the filtered data in the Available Data box.
2	Available Data: The available data box contains the list of data available for analysis. If your workbook has no data in tabular format, this box will display "No Data Found." The information displayed in this box includes the row number, whether the data is Numeric (N) or Text (T), and the name of the column variable. Note that the software displays data from all the tables in the current workbook. Even though data within the same table have unique column names, columns across different tables can have similar names. Hence, it is crucial that you not only specify the column name but also the table name.
3	Select Button: Click on this button to select the data for analysis. Any data you choose for the analysis is moved to the right. To select a column, click on the columns in the Available Databox to highlight them and then click on the Select Button. A second method to choose the data is to double-click on the columns in the list of Available Data. Finally, you can drag and drop the columns you are interested in by holding down the select columns using your left mouse key and dragging and dropping them in one of the boxes on the right.
4	Required Data: The code for the required data specifies what data can be specified for that box. An example code is N: 2-4. If the code starts with an N, you must select only numeric columns. If the code begins with a T, you can select numeric and text columns. The numbers to the right of the colon specify the min-max values. For example, if the min-max values are 2-4, you must select a minimum of 2 columns of data and a maximum of 4 columns in this box. If the minimum value is 0, then no data is required to be specified for this box.
5a	Add or View Data: Click on this button to add more data to your workbook for analysis or to view more details about the data listed in the available data box. When you click on this button, it opens the Data Editor dialog box, where you can import more data into your workbook. You can also switch from the list view to a table view to see the individual data values for each column.
5b	View Selection: Click on this button to view the data specified for this analysis. The data can be viewed in a tabular format or a graphical summary.

Analyze

The analyze tab contains menu options that can specify how you want to analyze the data collected and draw conclusions. A sample screenshot of the analyze menu is shown below.

1	Metric: Currently, only one response variable can be selected for this analysis.
2	Objective: Specify the objective of this study. The available options are: Option Description Lowest is Best In Taguchi experiments, especially in the context of quality improvement, the concept of "lower is better" or "lowest is best" is common. This is particularly true when dealing with characteristics representing a deviation from a target value or a nominal condition. For example, if you are experimenting to minimize the amount of variation, defects, or errors in a process, you might consider a quality characteristic where lower values are preferred. In such cases, the goal is to minimize the response variable, and achieving a lower value is considered an improvement. Nominal is Best When you mention "Taguchi objective nominal is best," it could be referring to the idea that in Taguchi experiments, the goal is often to optimize a response or outcome variable by adjusting the factors or variables to their nominal levels. The nominal level typically represents the standard or target value for each factor. Largest is Best In some cases, the "largest is best" criterion is used in Taguchi experiments. This occurs when the objective is to maximize a particular performance or response variable. Instead of minimizing a deviation from a target value, the goal is to achieve the highest possible value for the response variable. For example, if you are experimenting to maximize the strength of a material, the "largest is best" criterion would apply. In this case, the goal is to identify the factor settings that result in the highest strength values.
3	Reference Point: In Taguchi's experimental design, a "reference" is often used to represent a target or standard value for a particular factor or parameter. The reference value serves as a baseline or nominal setting that the experimenter aims to achieve or maintain during optimization. The idea is to compare the performance or quality of the system under different experimental conditions to the reference value. Taguchi experiments are designed to identify factor settings that minimize variation or deviation from the reference, leading to a more robust and reliable system. For example, if you are conducting a Taguchi experiment to optimize a manufacturing process, the reference values could represent the target specifications for factors such as temperature, pressure, or speed. The goal is to find the combination of factor settings that brings the system as close to these reference values. Using a reference point, Taguchi's methods help achieve robustness and reliability in the face of variations and external factors. The focus is on optimizing the mean or average performance and minimizing variability around the reference, making the system less sensitive to uncontrollable factors. Understanding and setting appropriate reference values are crucial for the success of Taguchi experiments, as they guide the experimenter in identifying the optimal factor settings that lead to improved performance and reduced variability. Note that references can only be specified for dynamic Taguchi designs. If you specify the Signal Factor as Yes on the Create tab, you can specify whether you have reference points in your design. If a reference point is selected, the best-fit line will pass through it. If no reference point is selected, the best-fit line is determined based on the specified data. It is not forced to go through a specific point.
4a	Signal (X): If you have specified that a reference point is to be used, you can specify the X and Y values. The X value refers to the Signal value through which the best-fit line is to pass. For example, if X = 0 and Y = 0, the best-fit line will pass through the origin.
4b	Response (Y): If you have specified that a reference point is to be used, you can specify the X and Y values. The Y value refers to the Response value through which the best-fit line is to pass. For example, if X = 0, Y = 10, the best-fit line will pass through the intercept value 10 when X = 0.
5	Terms Available: The terms available are the factors for which the design was created. Currently, only the linear terms can be included in our model. Hence, if we have three factors, they are represented as A, B, and C.
6	Select Button: The select button can move the factors from the Terms Available list box to the Terms Included list box. All the terms specified in the Terms Included list will be analyzed, and the model will include these terms. For example, suppose you know that factor B is unnecessary or insignificant. In that case, you can only build a model with terms A and C. By default; we would like to include all terms in our model to determine which factors are essential and which are not for our response variable. You can use the double right arrow (>>) to move all terms from the left to the correct box. You can use the double left arrow (<<) to remove all terms from the terms included list box. Use a single right arrow (>) or a single left arrow (<) to move a single term from the left to proper to left boxes.
7	Terms Included: Displays the list of factors that must be included in the final model.

Plots

These are optional settings that are used to annotate the charts. You can specify these options if you are not happy with the default options used by the software. A sample screenshot of the plots menu is shown below.

0	Pick Charts: Select the charts you would like to display for this analysis. Click on the checkbox for Mean plots if you want to generate the plot of the mean values. Click on the checkbox for Stdev plots to plot the results for standard deviation values. Click on the checkbox for SN Ratio plots to plot the results for the Signal to Noise ratios.
1	Title: The system will automatically pick a title for your chart. However, if you want to override that with your title, you can specify a title for your chart here. Note that this input is optional.
2	Sub Title: The system will automatically pick a subtitle for your chart. However, if you want to override that with your subtitle, specify a subtitle for your chart here. Note that this input is optional.
3	X Label: The system will automatically pick a label for the x-axis. However, if you would like to override that with your label for the x-axis, you can specify a different label here. Note that this input is optional.
4	Y Label: The system will automatically pick a label for the y-axis. However, if you would like to override that with your label for the y-axis, you can specify a different label here. Note that this input is optional.
5	X Axis: The system will automatically pick a scale for the x-axis. However, if you would like to override that with your values for the x-axis, you can specify them here. The format for this input is to determine the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum x-axis scale is set at 10, and the maximum x-axis scale is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the x-axis increment is set at 2. Note that this input is currently disabled, and you cannot change this setting.
6	Y Axis: The system will automatically pick a scale for the y-axis. However, if you would like to override that with your values for the y-axis, you can specify them here. The format for this input is to determine the minimum, increment, and maximum values separated by a semi-colon. For example, if you specify 10;20, the minimum y-axis scale is set at 10, and the maximum y-axis is set at 20. If you specify 10;2;20, then, in addition to minimum and maximum values, the y-axis increment is set at 2. Note that this input is optional.
7	Horizontal Lines: You can specify the values here if you want to add a few extra horizontal reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 12;15, two horizontal lines are plotted at Y = 12 and Y = 15, respectively. Note that this input is optional.
8	Vertical Lines: You can specify the values here if you want to add a few extra vertical reference lines on top of your chart. The format for this input is numeric values separated by semi-colon. For example, if you specify 2;5, two vertical lines are plotted at X = 2 and X = 5, respectively. Note that this input is optional.

Verify

If you click the Verify button, the software will perform some checks on the data you entered. A sample screenshot of the dialog box is shown in the figure below. The software checks if you have correctly specified the input options and entered the required data on the worksheet. The results of the analysis checks are listed on the right. If the checks are passed, they are shown as green-colored checkmarks. If the verification checks fail, they are shown as a red-colored cross. If the verification checks result in a warning, they are shown in the orange exclamation mark. Finally, any checks that are required to be performed by the user are shown as blue info icons.

1	Item: The left-hand side shows the major tabs and the items checked within each section
2	Status: The right-hand side shows the status of the checks.
3	Overall Status: The overall status of all the checks for the given analysis is shown here. The overall status check shows a green thumps-up sign if everything is okay and a red thumps-down sign if any checks have not passed. Note that you cannot proceed with generating analysis results for some analyses if the overall status is not okay.

Outputs

When all inputs have been entered, click on OK to generate the outputs. Click on Compute Outputs to update the output calculations. A sample screenshot of the worksheet is shown below. The analysis reports each factor's impact on the mean value and the standard deviation value. The objective of the Taguchi design is to select those factors that have a large impact on the standard deviation to control or minimize the variation and then select the remaining factors to control the mean value.

Taguchi Menu Bar

For Taguchi worksheets, an additional menu bar is displayed on the top main menu bar, as shown in the following screenshot: If you don't see this menu bar when you are on a Taguchi DOE worksheet, you can display it by clicking the Refresh button (#1 shown in the screenshot). The making predictions (#2) button is added to the top menu bar. Once you have built your model, you can use the Make Predictions button to make predictions for different input settings. For example, if you have analyzed a design and determined optimal settings for the inputs that result in a robust design, you can use this button to predict the model outputs at these settings.

Make Predictions

If you would like to make predictions using the developed Taguchi DOE model, you can use the Make Predictions menu on the top menu bar. The figure below shows a sample screenshot of the results of the Make Predictions menu.

1	Model: The model analyzed in the current worksheet is displayed in this section. Note that if no model has been studied yet, you cannot make predictions using this dialog box. You will need first to generate a model using the Analysis Setup and Compute Outputs buttons. You can use a model to make predictions only when a model has been developed and saved to the worksheet.
2	Date: The date shows the date the model was developed and saved to the worksheet. Note that once a model has been saved, it can be used for predictions. You don't need to use Compute Outputs to update the model. You can share this worksheet with other users, and they can enter their inputs and generate the predicted model outputs using the model equation.
3	Inputs: Specify the input values you want to use to make the prediction. You will need to specify all the model inputs to make a prediction. A blank value of input will be taken as a value of 0.
4	Predict Button: Click on the >> button to make the prediction. This will use the model equation and the inputs you have specified to generate the model outputs.
5	Outputs: The outputs from the model are displayed in this section. The outputs typically contain the mean value of the response, the standard deviation of the response, and the signal-to-noise ratio value. Currently, the outputs are only displayed in this dialog box and not on the worksheet. You will need to manually copy the solution to your worksheet if you would like to save this value.
6	Cancel Button: Click on this button to close this dialog box.

Notes

Here are a few pointers regarding this analysis:

• You are currently limited to 15 factors in this analysis.
• Signal factor analysis is currently disabled.

Examples

The following examples are in the Examples folder.

• Create a Taguchi design for three factors. The data for the exercise is given in the file. (Taguchi 1.xlsx).
• Analyze the Taguchi design based on the results given in the data file. Determine which factor you will use to make the design insensitive to noise. (File: Taguchi 1.xlsx).

---

© Rapid Sigma Solutions LLP. All rights reserved.