Sigma Magic Help Version 17

Design of Experiments (DOE)

Overview

Design of Experiments (DOE) can be used to create an experimental design and then analyze the responses to develop a model between the input(s) and the output. There are several types of designs one can use to perform experiments. The following flowchart shows the experiments you can run using Sigma Magic software. You should run a Full factorial design for up to 6 factors and a Fractional factorial design if you have more than six factors. Adding center points to check if your model is linear is a good idea. If your model is not linear, consider running a General factorial design with more than two levels or create a response surface design. You can also run the experiments sequentially. First, you run the Fractional factorial design with many factors and narrow the list to the most important ones. Next, you can run a Full factorial design with center points added. Based on the results of the analysis, you can run either a general factorial or a response surface design.

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

Inputs

Click on Analysis Setup to open the menu options for this tool.

Create Design

A sample screenshot of the create design menu is shown below.

1	Num Factors: You can analyze up to 15 factors in this software.
2	Design Type: Specify the type of design you want to create. The following options are available: Option Description Full factorial Create a Full factorial design. You should use a Full factorial design for up to six factors. Fractional factorial Create a Fractional factorial design. Use a Fractional factorial design if you have more than six factors. General factorial Use a General factorial design when you have more than two levels for one or more factors. Typically used for models with text factors. Response Surface Use a response surface design if you want to build a non-linear model with continuous factors. Plackett-Burman Use a Plackett-Burman design for your factors. Plackett-Burman designs are usually Resolution III designs where we can analyze many factors with minimal runs.
3	Factors: Specify the details of your design in this frame. The number of factors you selected will display the input rows in this frame.
4	Variable Name: Specify a name for each of your variables. Make sure the names are unique and don't involve special characters.
5	Variable Type: Specify the type of factor. The available options are: Option Description Numeric Used for continuous factors where the factor can take any value. Text Used for discrete factors where the factor can take only specific levels.
6	Levels: Specify the number of levels for each factor. We can only have two levels for 2-level factorial designs such as full factorial, fractional factorial, response surface, and Plackett-Burman designs. However, for a general factorial, we can have up to 10 levels for each factor.
7a	Low Level: Specify the low level for each factor. If you specify numeric type, then all levels must be numeric.
7b	High Level: Specify the high level for each factor. If you specify text type, the levels could be numeric or text. No interpolation is made between these values, even if you specify numeric levels.
8	Flowchart: Click on this button to view the flowchart for the Design of Experiments.
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 the worksheet template. 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 worksheet 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.

The following figure shows you the resolution of the Fractional factorial designs. For example, if you have three factors, 2^3 = eight runs corresponds to a Full factorial design. If you perform these eight runs, you can estimate your model's main and interaction effects. This model is green since there is no aliasing in the model. For a 1/2 fractional factorial, you would be running four runs. This model has a resolution III design, which means the main effects are mixed up with the 2nd order effects. Since the primary and 2nd order effects may be significant in a model, this design is shown in red. You should ideally pick a Fractional factorial design that is shown in green color so that it helps you correctly estimate the main and at least the 2nd order interaction effects.

Options

There are two ways to specify these settings. The first is to specify the settings in the dialog box, and the second is to import the settings from a data file. The sample screenshot of the first way to define the options is below.

1	Create Design: Select this radio button to create a design using the settings given below.
2	Center Points: Specify the number of center points you want to add to your model. If you specify "None," then no center points are added, and only a linear model is developed. For Response surface designs, select the number of center points to "Auto" for the system to automatically determine the required number. However, you can change this number based on your needs. Center points can help you check for model linearity and increase the power of your designed experiments.
3	Replicates: It is a good idea to replicate the design so that you can estimate the experimental error. Replication helps you improve the power of your experimental design and calculate the P values for each term so that you can determine model significance. Increasing the number of replicates comes with the cost of having to perform a greater number of tests, which can add to the time and cost required for performing the designed experiment.
4	Randomize Runs: Specify if you want to randomize your runs. The purpose of randomization is to handle unknown noise factors. It is recommended that you always randomize your runs.
5	Design Generators: For Fractional factorial designs, you can specify a design generator. If you leave this field blank, the software will automatically pick a design generator. However, if you want a specific type of confounding, you can specify your design generator. An example is D = ABC. Here, column D is assigned to the product of A, B, and C factors.
6	Axial Points: The axial points option can only be specified for the Response Surface Methodology designs. The two options available here are Central Composite Design (CCD) and Face Centered Design (FCD). If you choose the CCD design, the system will automatically calculate your alpha value. However, you can change this value based on your specific needs. If you select the FCD design, the alpha value defaults to 1.0.
7	Blocks: Known noise factors should be blocked, and the entire design should be randomized to handle unknown noise factors. If you have specific noise factors that could impact your experimental design, you could block these factors from impacting your experimental results. Note that currently, you can only block the replicates.
8	Random Seed: If you are randomizing your design and each time you want to generate the same random numbers, you can specify a random seed value here. The random seed value should be a numeric integer. If you leave the seed value blank, a random value will be used each time.
9	Block Generator: You can assign a fractional column as a block. If you leave this blank, the software will pick a generator; otherwise, you can specify your block generator. Currently, only one block generator can be specified. Additional blocks are based on replication.

The sample screenshot of the second way to create the design is shown below. Use this option if you want to import your design from another location.

1	Import Design: Select this radio button to create a design by importing the columns from a table. At a minimum you need to specify the factor columns to import but you can specify other supporting columns as described below.
2	Search: You can enter any search terms here to filter your list of available data if you have many rows of data in your Excel file.
3	Available Data: The list of available tables is shown in this list box. It lists all the available tables in your current workbook, the names of the columns within each table, the type of data (Numeric or Text), and the number of rows of data.
4	Factor Columns: Specify the column names that contain the factors to import. For example, if you have three factors in your design as specified in your Design tab, you will need to specify the three factors in this list box. You can drag and drop the column names that contain this information from the list of available data. Note that this is an optional setting, and if you do not specify any columns in this list box, the factors are not imported and updated to the worksheet.
5	Other Columns: Specify the column that contains additional information for the design. In this list box, you can specify the standard order, run order, point type, and blocks for the experimental design. Note that this list box is optional. You will need to specify in the checkboxes below which columns you want to specify. Ensure that you enter the columns in the same order as the checkboxes. For example, if you have specified the checkboxes Point Type and Blocks, then the first column that should be specified is for the Point Type and the second column should be for Blocks. If no columns are specified, the default values are assumed for each column. The following table shows the default values that will be set if not specified. Element Default Value Standard Order The runs will be sequentially numbered from 1 to the number of runs on the worksheet. Run Order It will be assumed that there is no randomization, so the run order will match the standard order. Point Type It will be assumed that all points are corner points - a value of 1 will be used for point type. Blocks It will be assumed that there is no blocking - a value of 1 will be used for all blocks.
6	Checkboxes: Specifies which columns should be imported from tables. By default, it is required that factor columns at a minimum must be imported to create your design and the rest of the columns can assume default values. If you want to specify other column, make sure to select the checkbox and enter that column information in the Other Columns listbox in the same order as the checkboxes.

It is also possible to update the design directly on the worksheet. For example, if you want to fold the design, you can make a copy of the design manually, fold it across one or more columns, and then paste that design at the bottom of your current design. You may choose to delete rows on the worksheet that are not feasible, or you can use the Indicator column to specify which rows of the design you want to include (1) or exclude (0) from your analysis. Since you can directly edit the worksheet, the settings in the dialog box may not reflect these changes, and if you click on the Create button again, the changes you made to the worksheet may be lost. Hence, always make a backup copy of your design in case you want to use the original design.

Data

A sample screenshot of the data menu is shown below.

1	Search: You can enter any search terms here to filter your list of available data if you have many rows of data in your Excel file.
2	Available Data: The list of available tables is shown in this list box. It lists all the available tables in your current workbook, the names of the columns within each table, the type of data (Numeric or Text), and the number of rows of data. You will need to look for those columns that contain the Response information for your design.
3	Response Columns: You can enter the response data directly on the worksheet or import it from a table. If you plan to enter the data directly on the worksheet, you can leave the data tab blank. If you want to import the response data from a table, you can select the columns that contain the response data by dragging and dropping them from the list of available data. Note that if you specify multiple columns of data here, their mean or standard deviation is used to create the DOE model.
4	Response Type: If you have multiple columns, specify if you want to use the mean of all the columns as the response variable or the standard deviation of all the values as the response variable. If you specify the mean, the mean values of all the columns you entered in response columns will be used to fit the model. This is the default option. However, if you want to develop a DOE model to predict variation, you can use the standard deviation option to build a model of the data's standard deviation. Option Description Mean Use the mean of the selected columns as the response value. This is the default setting. Stdev Use the standard deviation of the selected columns as the response value.

Analyze

A sample screenshot of the analyze menu is shown below.

1	Model Reduction: Specify how you want to perform the analysis. You have the following options: Option Description Auto The software will start with all the terms in the model and progressively keep dropping terms until only the significant terms remain in the model. None The software will not perform any automatic model reduction. It will retain the terms you have selected in your model. You must do this manually if you want to drop non-significant terms from the model.
2	Select Terms: Specify which terms you want to include in your analysis. You will need to select the option for the model terms. You have the following options: Option Description Auto The software will recommend keeping the most important terms in the model up to order 2. All Terms The software will include all the available terms in the analysis model. Note that terms higher than 3rd order may not be included in final model. Up to 1st Order The software will only estimate the main effects. Up to 2nd Order The software will only estimate the main and 2nd order interactions. Manual You can specify which terms to include in the model. To select the terms, double-click on the available terms to select the term for analysis or single-click on the desired term in the list of available terms and click on the right arrow to select the term. If you want to remove an already selected term, select the term you want to delete and then click the left-click arrow.
3	Available Terms: This list box lists all the terms available in your model to pick for analysis. Note that the factor names are represented in short form (A, B, C), etc., to make it easy to understand.
4a	Select All Terms: Click on this button to move all the available terms to those included for analysis, shown in the list box on the right. This is equivalent to using all terms for your analysis.
4b	Deselect Term: Click this button to remove the selected term from the Terms Included column. You can use this to drop any terms from your model you are no longer interested in.
4c	Select Term: Click this button to move the term selected in the list of available terms to the included ones on the right. You can use this to add new terms to your model for analysis.
4d	Deselect All Terms: Click on this button to remove all terms from the included terms list. You must start from scratch and add terms you are interested in later.
5	Terms Included: This list box lists all the terms used to build your model.
6a	Center Points: Click on this checkbox to include center points in your analysis. You need to include center points in your analysis initially, and if it is not statistically significant, you can drop the center point terms.
6b	Blocks: Click on this checkbox to include blocks in your analysis. You need to include blocks in your analysis initially, and if they are not statistically significant, you can drop the block terms.

Note that not all terms you include in the included terms may be included in the software analysis results. For example, some terms may be confounded with others if you are performing a Fractional factorial design. In this case, the model cannot independently estimate each term. Fourth-order and higher interactions are not included in the analysis for General factorial designs. When you click on OK, the software will analyze the DOE, compute the outputs, and plot any graphs as specified.

Plots

A sample screenshot of the plots menu is shown below.
Ensure the tab is on Plot Results if you want to update analysis charts. Do note that the analysis results are not regenerated when you use the Plot Results tab. The software will use previous analyses that you have run to generate the plots. If you make any changes to your settings, make sure to keep your tab on Analysis Results and click on the OK button to update results.

1	Main Effects Plots: Click on this tab to specify the options to create the main effects plots. Note that if there is any item selected to display for the main effects plots, a >> sign is displayed on the page name.
2	Interaction Effects Plots: Click on this tab to specify the options to create the interaction effects plots. Note that if there is any item selected to display for the interaction effects plots, a >> sign is displayed on the page name.
3	Contour Plots: Click on this tab to specify the options to create the contour or surface plots. Note that if there is any item selected to display for the contour plots, a >> sign is displayed on the page name.
4	Other Plots: Click on this tab to specify the options to create the other plots like Pareto plots and residual plots. Note that if there is any item selected to display for the other plots, a >> sign is displayed on the page name.

Main Effects Plots

A sample screenshot of the main effects plots menu is shown below.

1	Checkbox: Click on the checkbox if you would like to plot the main effects plot.
2	Select Plots: Select the plots that you are interested in. The following options are available: Option Description None No main effect plots are generated. All All possible combinations of main effect plots are generated Significant Only significant main effect plots are generated. Note that this requires that you have already analyzed the DOE. It will use results from the last updated DOE run. A, B, ... Only the factor you select here will be plotted.
3	Graph Type: Under the graph type, specify the type of plots to generate. The available options are: Option Description Single Plot all the main effects on a single plot. This makes it easier to compare multiple plots. Multiple Plot each main effects plot on a separate plot.

Interaction Effects Plots

A sample screenshot of the interaction effects plots menu is shown below.

1	Checkbox: Click on the checkbox if you would like to plot the interaction effects plot.
2	Select Plots: Specify which interaction effects you want to plot. The following options are available: Option Description None No interaction effect plots are generated. All All possible combinations of interaction effect plots are generated Significant Only significant main effect plots are generated. Note that this requires that you have already analyzed the DOE. It will use results from the last updated DOE run.
3	Graph Type: Click on the graph type and specify the type of plot to generate. The available options are: Option Description Single Plot all the main effects on a single plot. This makes it easier to compare multiple plots. Multiple Plot each main effects plot on a separate plot.
4	X-Axis Variable: Click on the dropdown box for the X-axis variable to specify which variable you want to use for the X-axis. This option is only available if you plot a single interaction effects plot. The following options are available: Option Description Auto The software will automatically pick the X-axis for you (usually the first variable). A, B, ... The factor you specify here will be used as the X-axis.

Contour Plots

A sample screenshot of the contour effects plots menu is shown below.

1	Checkbox: Click on the checkbox if you would like to plot the contour or surface plot.
2	Select Plots: Specify which interaction effects you want to plot. The following options are available: Option Description None No contour plots are generated. AB, AC, ... Select the interaction effect for which you want to generate the contour plot. Note that both variables have to be continuous for this plot.
3	X-Axis Variable: Specify the X-axis variable for the selected contour/surface plot.
4	Graph Type: Click the variable graph type to specify the type of plot to generate. The available options are: Option Description Contour Plot the data as a contour plot. Surface Plot the data as a surface plot.
5	Other Factors & Levels: Click on the X-axis factor setting to specify the factor used for the X-axis. By default, the first variable is chosen for the X-axis. Next, specify the levels to be used for the other factors. The following options are available: Option Description Low All the remaining variables will be set at their low settings. High All the remaining variables will be set at their high settings. Custom You can specify the settings to use for the remaining variables. Next, specify how you want to enter the other settings for the contour variable. This setting only applies when you pick the "Custom" option for the previous selection. The following options are available: Option Description Coded You want to enter the settings in the coded space (-1 to 1). Uncoded You want to enter the settings in the uncoded space (example: 60 to 80).

Other Plots

A sample screenshot of the contour effects plots menu is shown below.

1	Checkbox: Click on the checkbox if you would like to generate the other plots, such as the Pareto effects plot and the residual plots.
2	Pareto Plot: Specify if you would like to show or hide the Pareto plot. The available options are: Option Description Show Plot the Pareto and/or the Residual plots. Hide Do not plot the Pareto and the Residual plots.
3	Residual Plots: Specify if you would like to show or hide the residual plots. The available options are: Option Description Show Plot the Pareto and/or the Residual plots. Hide Do not plot the Pareto and the Residual plots.
4	Target: If you want to look for an optimal target value in the results, specify the optional target value in the dialog box. This value will plot a horizontal line on the primary effects plot. The intersection of the horizontal line and the main effects plot will give an idea of the input variables' values that can result in this output value. The target value is also used to fashion the contours so that the target values can easily be found in the contour and surface plots.

Worksheet

A sample worksheet of the DOE design is shown in the figure below. Once you enter the inputs and press okay, the worksheet creates the DOE design. If your dialog box tab is on "Create Design," Once you create the run, you will need to conduct each of these tests in random order and then upload the results in the response column. Suppose you want to build a robust model that minimizes the impact of variation on the design. In that case, you may consider repeating each test and then calculating the mean and standard deviation of the numbers. You can then enter the collected data's mean or standard deviation in the response column.

When all the responses have been entered in the worksheet, click on Analysis Setup and then click on Analyze Design tab to generate the results.

Verify

A sample screenshot of the verify menu is shown 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, and 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 if required. A sample screenshot of the outputs is shown in the figure below. In the notes section, the analysis first summarizes the inputs specified for the analysis under the section Input Summary. Check this to make sure all your inputs are correctly specified. Make sure that the variables' names and variable levels are as intended. The ANOVA table lists the overall ANOVA of the model and the P values. This P-value is used to determine whether we have a statistically significant model. The R^2 and R^2(adj) of the model are also listed here, which can be used to get an idea of the model's goodness of fit to the experiments. Finally, the model coefficients are shown in the coded space. Check which model terms are significant and which ones are not. The Variance Inflation Factors (VIF) are also listed for each model. If these values are less than 5, we are okay - not a cause for worry. If required, you can drop the non-significant terms and redo the analysis until a statistically significant model remains. The model equation in the uncoded space is listed below and can be used for predictions.

The graphs section will show the graphs for this analysis, as requested. The Pareto chart of significant effects will highlight those significant effects by plotting a critical limit line in red. Any effects that are greater than this red line are considered to be significant. Note that if you have an un-replicated design, it is impossible to determine the P values; the critical red line is based on Lenth's formula to determine the PSE along with a T-factor of 2.0. If you have selected the option of only showing significant graphs, then the graph is plotted only if the term is significant. Interaction and surface plots are shown if you have requested these plots in your input options.

The analysis will also print out a histogram of the residuals along with the residuals plotted for the run order and residuals plotted concerning the fit. Ensure that the residuals are normally distributed from the histogram, and check to ensure that the residuals with the run order and fit are randomly distributed. If not, there may be a problem with your modeling assumptions, and you cannot rely on the developed model.

A sample screenshot of the output will be shown below if we analyze a fractional factorial design. The analysis notes and graphs are similar to the above Full factorial design. The only difference is that not all terms are estimated since some terms are confounded with others due to aliasing. If we were analyzing a General Factorial design, a sample screenshot of the output is shown below. The analysis results are similar to those shown for the Full Factorial design, except that no model equation is shown. If we were analyzing a Response Surface sign, a sample screenshot of the output is shown below. The analysis results are similar to those of the Full factorial design, except we can now have quadratic factors in our model.

DOE Menu Bar

For DOE 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 DOE worksheet, you can display it by clicking on the refresh button (#1 shown in the screenshot). This menu bar has three buttons: getting the design info (#2), creating d-optimal designs (#3), and making predictions (#4). Each of these buttons is described in the following sections.

Design Info

It is possible to modify the design directly on the worksheet. For example, you may have initially run a Fractional factorial design, and you want to extend this design after learning a little about your response and design. You can manually modify the design by folding a design over a factor or adding additional center points to check model linearity, etc. When you make these changes to the worksheet, the original design model of the analysis will also change. Click the Design Info button to get a summary of the latest design. It will read your worksheet and try to summarize the contents of the design.

A sample screenshot of the Design Info menu is shown in the figure below.

1	Summary: Provides a summary of the design found on the worksheet. If you are using two levels or multiple levels for each factor. It also shows the number of factors and runs found on the worksheet.
2	Factors & Levels: Provides a summary of the factors used in the design and the levels for each factor. It specifies whether the levels are numeric or text and the number of levels for each factor. If you disagree with this summary, you will need to click on Analysis Setup and modify the design as required.
3	Notes: Provides a high-level summary of the design, such as whether it contains center points and blocks, and if it is a fractional factorial, the type of confounding found in the model.

Optimize Design

D-optimal Design of Experiments (DOE) is a statistical and mathematical approach used in experimental design to optimize the information obtained from a set of experiments. DOE involves systematically varying the input factors of a process or system to observe and understand the effects on the output response. The goal of D-optimal DOE is to select the experimental conditions to maximize the precision of estimating the model parameters.

In the context of DOE, "D" stands for "determinant." The D-optimality criterion is based on maximizing the information matrix's determinant, which measures the precision of the parameter estimates in a statistical model. The information matrix is the inverse of the covariance matrix of the parameter estimates, and its determinant is related to the volume of the confidence ellipsoid for the parameters.

A D-optimal design is achieved by selecting the levels of the experimental factors to maximize the determinant of the information matrix. This results in a design that provides the most efficient and precise estimates of the model parameters, given the constraints of the experimental setup.

D-optimal DOE is beneficial when resources are limited and researchers want to extract the maximum amount of information from a limited number of experiments. It is commonly used in engineering, chemistry, and biology, where experimentation is expensive or time-consuming.

A sample screenshot of the Optimize menu is shown in the figure below.

1	Objective: Specify the objective for this analysis. There are two options for this selection: Option Description Create Design Use this setting to create a design based on the constraints specified. Evaluate Design Use this setting to evaluate a specified design.
2	Initial Design: Specify how you want to create the initial design. The available options are: Option Description Sequential Use this setting to create a design using sequential analysis. Random Randomly select the initial design.
3	Improvements: Specify if you want to make improvements to the initial design. The available options are: Option Description None After the initial design is created, make no additional changes to the design. The initial design will be the final design used for this analysis. Exchange Use the exchange method to see if the initial design can be improved further. This method exchanges one row at a time to see if the D-efficiency numbers can be improved. It adds the best possible row from the list of rows that are not included in the model and then removes the worst possible row from the current list of rows to keep the number of points in the final model.
4	Random Seed: If you create a design using the Random method, you can specify a seed value for the random number generator. If the seed value is zero, then a new set of random numbers is used each time to create the design. However, suppose you want to have repeatability in your analysis. In that case, you can specify a seed number for the random number generator so that the same set of random numbers is generated each time.
5	Num Points: Specify how many points you want to retain in your final model. These are the number of runs (N) you can afford for this experimental design. This could be due to cost factors or the fact that we don't have sufficient resources to run all experiments.
6	Indicator Column: The indicator column on your worksheet specifies which columns to use for your final optimal design. If you leave this column blank, all rows are equally likely to be selected, and the best set of N rows will be selected for the final design. However, if specific rows are never included or always included, you can specify that in the indicator column. A value of 0 implies that we do not want to include this row in the final design. Possibly, this set of experimental runs is not feasible or practical for our analysis. A value of 1 in the indicator column implies that we always want to include this row in the final design. This could be used for rows where, from experience, we want to ensure that we keep this row in our analysis. If additional rows are to be selected to meet the minimum number of points in our design, they will be chosen from rows that don't have 0 or 1 marked in that row. Use the following syntax for this column. Option Description Show Display or show the indicator column on the worksheet Hide Hide the indicator column on the worksheet
7	Model Terms: Specify the terms that need to be included in the model. These terms will be used to compute the D-efficiency scores. For example, if you specify A, B, C, AB, then the terms A, B, C, and the interaction term AB will be used for analysis.
8	Use Intercept: If you select this checkbox, the constant or the intercept term will also be included in the model for computing the D-efficiency scores.
9	Model Terms: You can either manually type in the model terms or use one of the standards to define the model terms. The available options are: Option Description Linear All the linear terms will be included in the model, such as A, B, C, etc. Interaction All the linear plus interaction terms will be included in the model, such as A, B, C, AB, AC, BC, etc. Quadratic All the linear terms, interaction terms, and quadratic terms will be included in the model, such as A, B, C, AB, AC, BC, AA, BB, CC, etc. Manual You can manually specify which terms to include and exclude from the model.
10	Results: The results of the analysis are displayed in this textbox.
11	Copy Solution: Click this button to copy the developed solution back to the worksheet. This will place 0's and 1's in the indicator column. A value of 0 implies that that row is not included in the final model, and a value of 1 indicates that that column is included in the final model.
12	Clear Indicator: Click this button to clear any values entered in the Indicator column. You can manually clear it from the worksheet or use this button to clear the values.
13	Cancel Button: Click this button to close this dialog box
14	Optimize Button: Click this button to perform the analysis and report the results in the Results dialog box.

A sample screenshot of the results of the Optimize menu that has been saved to the worksheet is shown in the figure below.

1	Exclude Row: Since the indicator column in the first row shows 0, we do not include this row in our analysis.
2	Include Row: Since the indicator column in the remaining rows shows 1, we include these in our analysis.

Make Predictions

If you would like to make predictions using the developed 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. 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. 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 and ten levels for each factor in this analysis.
• Using the Auto method for analysis will use the backward model reduction approach. It will first develop a full model with all the factors and then keep dropping factors from the bottom-up that are not statistically significant until only a statistically significant model remains.
• Using the plot results tab will not recompute the analysis results but will use the results from the last performed analysis to update the graphs.
• The model residuals' histogram plot is currently unavailable for the general factorial. Still, it is displayed for the other types of designs when you compute the analysis results (not when updating the graphs).

Examples

The following examples are in the Examples folder.

• Create a 2-level factorial design for three factors with no blocks and no center points. The data for the exercise is given in the file. (DOE 1.xlsx).
• Analyze the 2-level factorial design based on the results given in the data file. Plot the significant main and interaction effects. (DOE 2.xlsx).

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