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.
The first tab is divided in four sections:
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.
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.
Note: Mixture and D-optimal designs are also possible if the variables have some constraints.
Note: Mixture and D-optimal designs are also possible if the variables have some constraints.
Mixture and D-optimal designs are also possible if the variables have some constraints.
In Optimization no category variable can be optimized. If there is category variables to be investigated it is necessary to break down the design strategy into two stages:
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.
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.
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
This table contains information on all the variable to take into account in the experimentation. The variables are ordered:
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.
Click the Add button to create or add a new variable.
Specify the characteristics of the new variable as follow:
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.
Different designs can be created depending on the:
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
The information box provides information on the selected design.
The Design Experiment Wizard will always suggest a design taking into account 3 criteria:
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.
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.
If linear constraints:
It is not possible to have less than 2 variables submitted to linear constraint. The appropriate design is a D-optimal.
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.
This tab is customized depending on the selected design.
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:
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:
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.
Design details: Central Composite and Box Behnken designs
For more information on these options look in the next section.
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|
To change from the preselected design to another design, use the radio buttons.
This design correspond to design with variables submitted to constraints such as:
This tab is used to:
Design details: D-optimal design
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.
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.
The minimal model is a linear model. It is possible to include two more type of parameters (effects):
Check the model to include the necessary terms:
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:
When hitting this button the D-optimal algorithm runs and a design is generated.
The condition number is used to check the quality of a D-optimal design.
Design details: Mixture design
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
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.
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.
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
If the design has more constraints:
it should be resolved with a D-optimal design.
This tab allows one to manage the replication of the design as well as the center and reference samples.
It includes four sections:
Additional experiment tab
The design variables table can be used to visualize the level values, in particular to select the center value of the category variables.
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 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.
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®.
This tab allows to manage the randomization of the experiments.
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.
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.
This table shows the sequence of experiments to run.
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.
This tab gives a summary of the set-up design, now that it has been completely specified.
In addition, it is possible to calculate the power of the design by
Entering some parameters:
The ratio Signal over Noise (S/N) is given as an indication.
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.
This tab shows the list of experiments to perform.
Design table tab
There are several visualization options:
Randomized sequence is the sequence defined in the Randomization section. Standard sequence is the sequence used to generate the design.
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.
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®.