Design Creation

Accessing the DOE module to create a design is done by using the menu: Insert – Create design…. The user will be directed to the Start tab of the Design Experiment Wizard.

The Create design… dialog contains a dynamic sequence of tabs, where the next tab content often depends on the input in the current tab.

General buttons

Cancel

At any time it is possible to exit the Create Design dialog and go back to The Unscrambler® main interface. To do so hit the Cancel button.

Finish

At the bottom of the tabs is the Finish button that is first disabled .
When sufficient information has been entered on the pages, the Finish button is enabled .
By hitting this button the user finishes the wizard and the design matrices are created in The Unscrambler® navigator.

Status bar

The status bar represents the different tabs’ status. If a tab is valid its status becomes green. If a tab presents mistakes or incomplete information, its status is yellow. If a tab is not valid its status is red.
Once the status bar is all green the design can be generated by clicking on the enabled Finish button.

Help

The Help button will direct you to the help documentation.

Start

The first tab is divided in four sections:

• Name
• Goal
• Description
• History

Start tab

Name

One needs to enter a name in the Name cell. The name will be used to generate the data set matrices related to the DOE in
The Unscrambler® tree. The first tab will not be valid if this cell is not specified.

Goal

There are three options for the purpose of this DOE analysis; select the one that is the most appropriate.
It is important to select it properly as this is one of the criteria that the Design Experiment Wizard uses to select the most suitable design.

Screening

In a screening experiment the goal is to know if the design variables have a main effect on the response variable(s).
When selecting this goal, the Design Experiment Wizard will propose either a Plackett-Burman design or Fractional Factorial (with low resolution 3) design, if the designed variables are not under constraints.

Note: Mixture and D-optimal designs are also possible if the variables have some constraints.

Screening with interaction

In a screening with interaction experiment the goal is to assess both the main effects and the interactions of the design variables on the response variable(s).
When selecting this goal, the Design Experiment Wizard will propose either a Fractional Factorial (with high resolution ≥ 5) or a Full Factorial design, if the designed variables are not under constraints.

Note: Mixture and D-optimal designs are also possible if the variables have some constraints.

Optimization

When choosing optimization as the goal, the design investigates as well the quadratic effects of the designed variables: main effects, interactions and square terms on the response variable(s).
By choosing this option, the Design Experiment Wizard will suggest either a Central Composite or Box-Behnken design, if the designed variables are not under constraints.

Description

Edit the blank section to store information on the design such as a description of the purpose of the experimentation, and details about the experiments.

History

This part contains information on the history of the design such as the creator, the date of creation and possible revisions. It is auto-generated by the Design Experiment Wizard.

Define variables

In this tab, define the design space as well as other variables such as the response variables and the non-controllable variables.

It is divided into two sections:

• Variable table: It shows the defined variables.

• Variable editor: It allows to add a new variable or to delete or edit an already defined variable.

Define variables tab

Variable table

This table contains information on all the variable to take into account in the experimentation. The variables are ordered:

1. Designed variables
2. Non-controllable variables
3. Response variables

The variables can be reordered within their category by using Ctrl+arrow up or down.
To edit a variable, select the corresponding row, and modify the information in the variable editor. Click OK to validate any change.
To delete a variable, select the corresponding row and click the Delete button.

Variable editor

Click the Add button to create or add a new variable.

Specify the characteristics of the new variable as follow:

Identity (ID)

The identity of the variable will be auto-generated.

Name

Enter a descriptive name in the Name field.

Analysis Type

Select by using the radio button, the appropriate type for the variable among the following:

Design variables: Variables submitted to experimentation.

Non-controllable variables: Variables not submitted to experimentation but may have an effect on the design. They can be measured and it will be possible to include them in a regression model.

Response variables: Variables that are possibly affected by the changes in the design variables.

Constraints

Select by using the radio button, the appropriate constraint for the variable among the following:

None: By default, if the variable is not submitted to any constraint.

Linear: If at least two variables are submitted to a common constraint, for example , they should be defined as having a linear constraint.

Mixture: If at least 2 variables are part of a mixture, they should be defined as having a mixture constraint.

Analysis Type of levels

The levels are either continuous when they can take all value between two levels or category when only the level values are possible. Choose the one that suits the variable to be defined.

Level range / Levels

For continuous variables: place the bounds of the design space with the lowest and the highest possible in the Level range field. By default the levels are -1 and 1.

For category variables: the Levels section makes it possible to edit the real values for the level. The default values are “Level1” and “Level2”. * For continuous variables that are submitted to a mixture constraint: the default value are 0 and 100 which express the composition as percentages. This can be edited.

Those values will appear in the table in the column Level values. From this definition the column # of levels will be generated by the Design Experiment Wizard.

Choose the design

Different types of experimental design

Different designs can be created depending on the:

• Number of variables
• Constraints on the variables
• Goal of the experiment.

The Unscrambler® selects the most appropriate design following some rules.

Beginner and expert mode

In Beginner mode, the display makes it possible to select the design by analyzing the goal and the types of variables. In Expert mode, select the design by choosing the name of the design to use.

It is possible to change the view by using the Beginner/Expert cursor

.

Choose the design tab in Beginner mode

Information

The information box provides information on the selected design.

Design selection criteria used by the design wizard

The Design Experiment Wizard will always suggest a design taking into account 3 criteria:

• Goal
• Number of variables
• Constraints on the variables

The rules are as follows

1. If no constraint:

   If goal is Screening and # of variables ≥ 7, then Plackett-Burman.

   If goal is Screening and # of variables > 2 and < 7, then fractional factorial design with resolution III.

   If goal is Screening with interaction and # of variables > 4, then fractional factorial design with resolution V.

   If goal is Screening with interaction and # of variables ≤ 4, then full fractional design.

   If goal is Optimization and # of variable ≤ 6, then Central composite design.

   If goal is Optimization and # of variable > 6, this is not possible because it requires too many experiment. Divide the optimization in steps.

2. If Mixture constraint:

   It is not possible to define less than 2 variables submitted to mixture constraint. If the experiment contains only mixture variables, then the choice will be among the mixture designs depending on the defined goal: Screening gives an axial design, Screening with interaction gives a Simplex-Lattice design and Optimization gives a Simplex-centroid.

   If at least two variables are part of a mixture, but not all, then the appropriate design is a D-optimal.

3. If linear constraints:

   It is not possible to have less than 2 variables submitted to linear constraint. The appropriate design is a D-optimal.

Changing to another design

It is possible to select another design than the one selected by the Design Experiment Wizard. A warning will appear if this modification is not in accordance with the settings for the goal and the variables.
The suggested design is in bold and it is always possible to go back to it.

Design details

This tab is customized depending on the selected design.

Full Factorial, Fractional Factorial and Plackett-Burman designs

In this tab, it is possible to see the confounding pattern if any, and the number of experiment to run.

Design details: Full Factorial, Fractional Factorial and Plackett-Burman

One of the designs is preselected in accordance with the settings. It is possible to change it.
The designs have been ordered into two categories corresponding to the goal of the experimentation:

• Screening
• Screening with interaction

If the preselected design does not suit the experimental conditions, select another one using the radio buttons.

For a fractional factorial design there may be several possible resolutions corresponding to several possible confounding patterns. To change the resolution and the confounding pattern, there are two options:

• Click on the confounding pattern and select the most appropriate one
• Change the resolution with the radio buttons.

The confounding pattern can be visualize using the identity of the variables in the form : A + BC, or using the name of the variable. To enable this tick the box Show names.

Below the confounding pattern, some information is displayed such as the number of experiments to run and the number of center samples preselected.

Central Composite and Box Behnken designs

Design details: Central Composite and Box Behnken designs

Options for Central Composite and Box Behnken designs

• Circumscribed
• Inscribed
• Faced
• Box Behnken

For more information on these options look in the next section.

Select the right design

To select the option that best fits the experimental goal, use the following table for guidance.

Design	Number of levels	Uses point outside high and low levels	Accuracy of estimates
Circumscribed	5	Yes	Good over entire design space
Inscribed	5	No	Good over central subset of the design space
Faced	3	No	Fair over entire design space, poor for pure quadratic coefficients
Box Behnken	3	No	Good over entire design space, more uncertainty on the edge of the design area

Change the design

To change from the preselected design to another design, use the radio buttons.

D-optimal design

This design correspond to design with variables submitted to constraints such as:

• Multilinear constraints on some variables
• Mix of mixture and process variables.

This tab is used to:

1. Set the constraints
2. Edit the model
3. Check the condition number

Design details: D-optimal design

Set the constraints

Multilinear Constraints button

By clicking the button Multilinear constraints a window opens where one selects the settings of the multilinear constraints.

Editing multilinear constraints

To add a new constraint, click on the Click to add new constraint button.

Start by editing the coefficients, then the operator, accessible from the drop-down list

.

Finally edit the target. It is possible to change the decimal points for the formula in the specified field.
Add more constraints by hitting again the Click to add new constraint button.
Click on OK when all the constraints have been added.
To delete a constraint select it in the Current constraints table and click on the Delete button.
To edit a constraint select it in the Current constraints table and modify it in the Edit constraint coefficients table.

Note: If the design contains mixture and process variables, a constraint is added automatically on the mixture variables: their sum is equal to 100 %. This constraint is editable so it is possible to change the total amount to another value if a filler is used.

Edit the model

Initial design type

• Full factorial is the option to be chosen when working with non-mixture variables or when mixture and non-mixture variables are mixed.

• Lattice mixture is to be used when there are only mixture variables in the design. Those variables are submitted to constraints.

Initial design type: Mixture and multilinear constraints

Number of variable investigation levels: This is the number of level each variable can take: the range is divided in equal portions to place the levels.

Model

The minimal model is a linear model. It is possible to include two more type of parameters (effects):

• Include interactions
• Include squares

Check the model to include the necessary terms:

1. Screening: the model to study is a linear model. No need to add interaction and square terms
2. Screening with interaction: the model should include the interaction terms so tick the Mixture interactions option
3. Optimization: the model should include the interaction terms as well as the square terms so tick both the Mixture interactions option and the Mixture squares option.

# of design points

A number is automatically set there this is the minimal number of experimental points; it can be changed using the arrows.

The minimal number of experiment is set as follow:

• Screening designs and screening with interaction: number of parameters + 4
• Optimization designs: number of parameters + 6

Generate button

When hitting this button the D-optimal algorithm runs and a design is generated.

Check the condition number (CN)

The condition number is used to check the quality of a D-optimal design.

Mixture designs

Only mixture variables

Design details: Mixture design

Axial

An axial design consists of extreme vertices, overall center, axial points, end points.
It can only be used for linear modeling, and therefore it is not available for optimization purposes.

End points bring more degrees of freedom to analysis, thus more accuracy. It is possible to include or remove the end points. To do so, select or deselect the Include End Points option.

Include end points

Lattice

A Simplex-lattice design is a mixture variant of the full-factorial design. It is available for both screening and optimization purposes, according to the lattice degree of the design.

The degree of a Simplex-Lattice design corresponds to the maximal number of experimental points of one of the Mixture variables. It is possible to edit this degree by changing the default value.

Centroid

A Simplex-centroid design consists of extreme vertices, center points of all “subsimplexes”, and the overall center. A “subsimplex” is a simplex defined by a subset of the design variables. Simplex-centroid designs are available for optimization purposes, but not for a screening of variables.

Adjust mixture constraints

In some cases, the defined level values may not define a regular simplex. A message may appear asking to adjust the mixture constraints.
A regular simplex is a simplex that has the same dimension for all its segments. This is what is typically used in DOE and gives smaller designs. If the designed variables do not define a regular simplex, hit the Adjust mixture constraints button and choose one of the following actions.

Adjust mixture constraints

1. Make levels consistent: The levels will be changed to be defining a simplex.

1. Reset to user specified levels: to revert the any modifications and go back to the originally defined levels.

1. Adjust with normalized levels: All variables will have a 0 to 100% variation.

1. Ignore inconsistencies: The levels will not be modified. However as this is not suitable fro proper mixture design a D-optimal design will be selected instead.

Mixture and multilinear constraints or Mixture and Process variables

If the design has more constraints:

• Either additional variables that are not part of the mixture,
• Or additional multilinear constraints,

it should be resolved with a D-optimal design.

Additional experiments

This tab allows one to manage the replication of the design as well as the center and reference samples.

It includes four sections:

• Design variables
• Replicated samples
• Center samples
• Reference samples

Additional experiment tab

Design variables

The design variables table can be used to visualize the level values, in particular to select the center value of the category variables.

Replicated samples

The number of replicated samples indicates the number of times the main experiments are run. Replication is used to measure the experimental error. Usually this is done on the center sample but it can be replaced by other measurements. However increasing the number of replicates on the design experiment gives more precise estimates of the effects due to better coverage of the experimental error. Use at least two replicates if the experimental results are likely to vary from time to time.

Note: Replicates or replicated samples are not the same as repeated measurements. Replicates mean that a new experiment is run using the same settings for the design variables as in a previous one, while repeated measurements means measuring the response values for the same experiment several times.

Center samples

Center samples are used for curvature checking and usually for error variance estimation. In the latter case, use at least two (preferably three or more) center samples. By default the Design Experiment Wizard suggest a number of center samples. It can be modified by using the up and down arrows next to Number of center samples.

The center samples are samples located in the center of the design. The location is defined by the levels of the design variables. It corresponds to the average (mean) of the different variables in the design. A real center sample is only possible if all the variables are continuous. However if the variables are not all continuous one can define the levels using category variables. To do so, double-click on the sample to be modified; a new dialog box will appear.

Modify center sample

In this example, variable D is the one that is category. Its value can be changed using the drop-down list. It is also possible to delete this specific center sample by clicking on the Delete button. When the level values for the category variables have been specified, click on OK.

Reference samples

In the field reference samples, it is possible to define samples which are incorporated for comparison. A typical reference sample is a target sample, a competitor’s sample or a sample produced after changes to a given recipe. The values of the design variables are not entered and are set as missing; it can be modified later in The Unscrambler®.

Randomization

This tab allows to manage the randomization of the experiments.

Randomization tab

Randomization produces groups for study that are comparable in unknown as well as known factors likely to influence the outcome. It is used to avoid bias.

However it is sometimes useful to perform some experiments in sequence. For example, if a parameter is difficult to change like the temperature, it may be more practical to make all experiments with the same temperature at the same time. In the tab Randomization, it is possible to specify blocks of similar samples to be kept together during randomization.

Designed variables to randomize

This table display the status of randomization of the designed variables. It is possible to edit the randomization status of the variables by clicking on the Detailed randomization button.

By clicking on this button a new window opens. The selected variables will be randomized. The center samples can also be randomized or not. Click OK.

Define randomization

Randomized experiments

This table shows the sequence of experiments to run.

Re-randomize

If for any reason it is necessary to change the order of the samples, hit the Re-randomize button, and a new sequence of experiments will be generated.

Summary

This tab gives a summary of the set-up design, now that it has been completely specified.

Summary tab

In addition, it is possible to calculate the power of the design by

1. Entering some parameters:

   Alpha

   desired significance level for the test, set at 5%.

   Delta

   difference to detect on the response

   Std. dev. (also called Sigma)

   estimated standard deviation on the response

   The ratio Signal over Noise (S/N) is given as an indication.

2. Hit the Recalculate power button. The power for each response variable will be displays in the table.

The smallest value will be reported in the summary table and it will be the power of the design.

This gives specific information on the design to judge its performance compared to the number of experiments to run.

It is always possible to go back to the different tabs to review and alter the previous settings.

Design table

This tab shows the list of experiments to perform.

Design table tab

There are several visualization options:

Randomized or Standard sequence

Randomized sequence is the sequence defined in the Randomization section. Standard sequence is the sequence used to generate the design.

Display order

Actual values or design levels

Actual values are the level values specified plus the one generated by the Design Experiment Wizard.

Design levels are the levels defined as +1 for high level, -1 for low level, and 0 for center as well as other specific values depending on the chosen design.

Display values

Select the options to be used thanks to the available radio buttons.

After hitting the Finish button, the design matrices will be generated in The Unscrambler®.

 

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