Overview of Screening Designs
Screening experiments tend to be small and are aimed at identifying the factors that affect a response. Because identification is the goal (rather than sophisticated modeling), continuous factors in a screening design are typically set at only two levels. However, a screening situation might also involve discrete numeric or categorical factors, in which case classical screening designs might not fit your situation. The Screening Design platform can handle all three types of factors: two-level continuous factors, categorical factors, and discrete numeric factors.
There are two types of designs:
• Classical designs: For situations where standard screening designs exist, you can choose from a list that includes fractional factorial designs, Plackett-Burman, Cotter, and mixed-level designs.
• Main effects screening designs: Whether a standard design is available, you can ask JMP to construct a main effects screening design. These designs are orthogonal or near orthogonal and focus on estimating main effects in the presence of negligible interactions. See “Main Effects Screening Designs”.
Underlying Principles
The emphasis on studying main effects early on in the experimentation process is supported by the empirical principle of effect hierarchy. This principle maintains that lower order effects are more likely to be important than higher order effects. For this reason, screening designs focus on identifying active main effects. In cases where higher order interactions are of interest, screening designs assume that two-factor interactions are more important than three-factor interactions, and so on. See “Effect Hierarchy” in the “Starting Out with DOE” chapter and Wu and Hamada, 2009.
The efficiency of screening designs also depends on the principle of effect sparsity. Effect sparsity asserts that most of the variation in the response is explained by a relatively small number of effects. See “Effect Sparsity” in the “Starting Out with DOE” chapter.
To appreciate the importance of effect sparsity, consider an example where you have seven two-level factors. Contrast a full factorial design to a screening design:
• A full factorial design consists of all combinations of the levels of the factors. The number of runs is the product of the numbers of levels for each factor. In this example, a full factorial design has 27 = 128 runs.
• In contrast, a screening design requires only a fraction of the runs in the full factorial design. The main effects of the seven factors can be studied in an eight-run screening design.
Analysis of Screening Design Results
Screening designs are often used to test a large number of factors or interactions. When there are degrees of freedom for error, allowing construction of an error estimate, the experimental results can be analyzed using the usual regression techniques (Analyze > Fit Model).
However, sometimes there are no degrees of freedom for error. In this case, assuming effect sparsity, the Screening platform (Analyze > Specialized Modeling > Specialized DOE Models > Fit Two Level Screening) provides a way to analyze the results of a two-level design. The Screening platform accepts multiple responses and multiple factors. It automatically shows significant effects with plots and statistics. For details, see “The Fit Two Level Screening Platform” chapter. For an examples in the current chapter, see “Modify Generating Rules in a Fractional Factorial Design” and “Plackett-Burman Design”.
Examples of Screening Designs
This section contains the following examples:
Compare a Fractional Factorial Design and a Main Effects Screening Design
In this example, suppose an engineer wants to investigate a process that uses an electron beam welding machine to join two parts. The engineer fits the two parts into a welding fixture that holds them snugly together. A voltage applied to a beam generator creates a stream of electrons that heats the two parts, causing them to fuse. The ideal depth of the fused region is 0.17 inches. The engineer wants to study the welding process to determine the best settings for the beam generator to produce the desired depth in the fused region.
For this study, the engineer wants to explore the following seven factors:
• Operator is the technician operating the welding machine. Two technicians typically operate the machine.
• Speed (in rpm) is the speed at which the part rotates under the beam.
• Current (in amps) is a current that affects the intensity of the beam.
• Mode is the welding method used.
• Wall Size (in mm) is the thickness of the part wall.
• Geometry indicates whether the joint is a single-bevel joint or a double-bevel joint.
• Material is the type of material being welded.
Notice that three of these factors are continuous: Speed, Current, and Wall Size. Four are categorical: Operator, Mode, Geometry, and Material. Each of these categorical factors has two levels.
After each processing run, the engineer cuts the part in half. This reveals an area where the two parts have fused. The length of this fused area, measured in inches, is the depth of penetration of the weld. The depth of penetration is the response for the study.
The goals of the study are the following:
• Find which factors affect the depth of the weld.
• Quantify those effects.
• Find specific factor settings that predict a weld depth of 0.17 inches with a tolerance of ±0.05 inches.
Your experimental budget allows you at most 12 runs. Construct and compare two designs for your experimental situation. The first is a classical fractional factorial design using eight runs. The second is a main effects screening design using 12 runs.
Constructing a Standard Screening Design
In this section, construct a standard screening design for this experimental situation.
Specify the Response
1. Select DOE > Classical > Screening Design.
2. In the Responses panel, double-click Y under Response Name and type Depth.
Note that the default Goal is Maximize. Your goal is to find factor settings that enable you to obtain a target depth of 0.17 inches with limits of 0.12 and 0.22.
3. Click on the default Goal of Maximize and change it to Match Target.
4. Click under Lower Limit and type 0.12.
5. Click under Upper Limit and type 0.22.
6. Leave the area under Importance blank.
Because there is only one response, that response is given Importance 1 by default.
The completed Responses outline appears in Figure 9.2. Now, specify the factors.
Specify Factors
You can enter the factors manually or automatically:
• To enter the factors manually, see “Specify Factors Manually”.
• To enter the factors automatically, use the Weld Factors.jmp data table:
1. Select Help > Sample Data Library and open Design Experiment/Weld Factors.jmp.
2. Select Load Factors from the Screening Design red triangle menu. Proceed to “Choose a Design”.
Specify Factors Manually
1. Type 3 in the Add N Factors box and click Continuous.
2. Double-click X1 and type Speed.
3. Use the Tab key to move through the rest of the values and factors. Make the following changes:
a. Change the Speed values to 3 and 5.
b. Change X2 to Current, with values of 150 and 165.
c. Change X3 to Wall Size, with values of 20 and 30.
4. Type 4 in the Add N Factors box and select Categorical > 2 Level.
5. Double-click X4 and type Operator.
6. Use the Tab key to move through the rest of the values and factors. Make the following changes:
a. Change the Operator values to John and Mary.
b. Change X5 to Mode, with values of Conductance and Keyhole.
c. Change X6 to Geometry, with values of Double and Single.
d. Change X7 to Material, with values of Aluminum and Magnesium.
Your Responses and Factors outlines should appear as shown in Figure 9.2.
Figure 9.2 Responses and Factors Outlines for Weld Experiment
Choose a Design
1. Click Continue.
Because the combination of factors and levels that you have specified can be accommodated by a standard fractional factorial design, the Choose Screening Type panel appears. You can either select a standard design from a list or construct a main effects design.
Note: Setting the Random Seed in the next step reproduces the results shown in this example. When you are constructing a design on your own, this step is not necessary.
2. (Optional) From the Screening Design red triangle menu, select Set Random Seed, type 12345, and click OK.
3. Accept the default selection to Choose from a list of fractional factorial designs and click Continue.
4. Select the first Fractional Factorial design. See Figure 9.3.
Figure 9.3 Design List for Two Continuous Factors and One Categorical Factor
This specifies an eight-run Resolution 3 fractional factorial design. For information about resolution, see “Resolution as a Measure of Confounding”.
5. Click Continue.
In the Output Options outline, note that Run Order is set to Randomize. This means that the design runs will appear in random order. This is the order you should use to conduct your experimental runs.
Figure 9.4 Completed Screening Design Window
6. Open the Aliasing of Effects outline under Display and Modify Design.
Figure 9.5 Aliasing for an Eight-Run Fractional Factorial Design
Recall that you selected a Resolution 3 design (see Figure 9.3). In a Resolution 3 design, some main effects are confounded with two-way interactions. The Aliasing of Effects outline indicates that, for this Resolution 3 design, every main effect is completely confounded with three two-way interactions. If you suspect that two-way interactions are active, this is a poor design. For a description of confounding, see “Two-Level Regular Fractional Factorial”.
7. Click Make Table.
Figure 9.6 The Design Data Table
Notice the following:
‒ The table uses the names for the responses, factors, and levels that you specified.
‒ The Pattern column shows the assignment of high and low settings for the design runs.
‒ This fractional factorial design is a Resolution 3 design. It enables you to study the main effects of seven factors in eight runs.
Constructing a Main Effects Screening Design
Main effects screening designs are orthogonal or near orthogonal designs. In this section, construct a main effects screening design for your seven factors.
1. Open your Screening Design window. If you have closed it, then run the DOE Dialog script in the Design Data table.
2. Click Back.
3. Click Continue.
Note: Setting the Random Seed and the Number of Starts in the next two steps reproduces the exact results shown in this example. When constructing a design on your own, these steps are not necessary.
4. (Optional) From the Screening Design red triangle menu, select Set Random Seed, type 12345, and click OK.
5. (Optional) From the Screening Design red triangle menu, select Number of Starts, type 50, and click OK.
6. In the Choose Screening Type panel, select the Construct a main effects screening design option.
7. Click Continue.
Under Number of Runs, the selected option is Default with the number of runs set to 12. Keep this setting.
8. Click Make Design.
Figure 9.7 Main Effects Screening Design
9. Open the Design Evaluation outline and then open the Color Map on Correlations outline.
Figure 9.8 Color Map on Correlations for 12-Run Main Effects Screening Design
The Color Map on Correlations shows that the main effects are uncorrelated with each other. This is indicated by the solid blue off-diagonal cells in the upper left corner of the color map. Each main effect is partially aliased with some two-way interactions, indicated by the gray cells. You can see, by hovering your cursor above one of the gray cells, that the absolute correlations are 0.333.
In this case, the 12-run main effects screening design is a Plackett-Burman design, which you could have obtained in the Design List. However, in many design situations, the partial aliasing that occurs in a main effects design is preferable to the complete confounding that occurs in a fractional factorial design that you adapt to your experimental situation.
The next section shows an example of a situation where no standard design exists. In this case, JMP constructs a main effects screening design.
Main Effects Screening Design where No Standard Design Exists
Main effects screening designs are orthogonal or near orthogonal designs for the main effects. You can use them in place of standard designs and in situations where standard designs do not exist. Main effects screening designs are excellent for estimating main effects when interactions are negligible.
In the following experimental situation, no standard design exists. You need a design to study 13 factors: 2 are categorical, one with 4 levels and one with 6 levels, and 11 are continuous.
1. Select DOE > Classical > Screening Design.
In the Responses panel, there is a single default response called Y. Keep this as the default response.
2. In the Factors panel, click Categorical and select 4 Level.
This adds the variable X1 with levels L1 through L4.
3. Click Categorical and select 6 Level.
This adds the variable X2, with levels L1 through L6.
4. Enter 11 next to Add N Factors.
5. Click Continuous.
This adds 11 factors, X3 to X13, each at two levels, -1 and 1.
6. Click Continue.
The Design Generation panel appears.
There is no option to select a design from the Design List since there are no available standard designs in this situation.
Keep the default number of runs, which is 24.
Figure 9.9 Screening Design Window for 13-Factor Design with Design Generation Panel
7. Click Make Design.
A Design and a Design Evaluation outline appear.
8. Open the Design outline to see the randomized design.
Note: The algorithm that generates the design uses a random starting design. To reproduce this design, save the script with the random seed by selecting Save Script to Script Window from the red triangle menu next to the report title.
Next, examine the Color Map on Correlations to see that this specific design is orthogonal.
9. Open the Design Evaluation > Color Map on Correlations outline.
The color map (Figure 9.10) shows red entries (using JMP default colors) on the main diagonal, indicating correlations of one. This is because each diagonal cell corresponds to the correlation of a term with itself, which is one. Off-diagonal correlations are all deep blue, indicating that correlations between distinct terms are zero. Hold your mouse pointer over any cell to see the relevant terms and their absolute correlation.
Figure 9.10 Color Map on Correlations
10. Click Make Table to construct the design table.
The table contains the runs for your experiment in random order. Conduct the experiment in this randomized order and insert the results in column Y. Run the Model script in the data table to analyze your results.
Screening Design Window
The Screening Design window is updated as you work through the design steps. For more information, see “The DOE Workflow: Describe, Specify, Design”. The outlines that appear are separated by buttons that update the window. These follow the flow in the figures below.
Figure 9.11 Screening Design Flow when a Standard Design Exists
Figure 9.12 Screening Design Flow when No Standard Design Exists
Responses
Use the Responses outline to specify one or more responses.
Tip: When you have completed the Responses outline, consider selecting Save Responses from the red triangle menu. This option saves the response names, goals, limits, and importance values in a data table that you can later reload in DOE platforms.
Figure 9.13 Responses Outline
Add Response
Enters a single response with a goal type of Maximize, Match Target, Minimize, or None. If you select Match Target, enter limits for your target value. If you select Maximize or Minimize, entering limits is not required but can be useful if you intend to use desirability functions.
Remove
Removes the selected responses.
Number of Responses
Enters additional responses so that the number that you enter is the total number of responses. If you have entered a response other than the default Y, the Goal for each of the additional responses is the Goal associated with the last response entered. Otherwise, the Goal defaults to Match Target. Click the Goal type in the table to change it.
The Responses outline contains the following columns:
Response Name
The name of the response. When added, a response is given a default name of Y, Y2, and so on. To change this name, double-click it and enter the desired name.
Goal, Lower Limit, Upper Limit
The Goal tells JMP whether you want to maximize your response, minimize your response, match a target, or that you have no response goal. JMP assigns a Response Limits column property, based on these specifications, to each response column in the design table. It uses this information to define a desirability function for each response. The Profiler and Contour Profiler use these desirability functions to find optimal factor settings. For further details, see the Profiler chapter in the Profilers book and “Response Limits” in the “Column Properties” appendix.
‒ A Goal of Maximize indicates that the best value is the largest possible. If there are natural lower or upper bounds, you can specify these as the Lower Limit or Upper Limit.
‒ A Goal of Minimize indicates that the best value is the smallest possible. If there are natural lower or upper bounds, you can specify these as the Lower Limit or Upper Limit.
‒ A Goal of Match Target indicates that the best value is a specific target value. The default target value is assumed to be midway between the Lower Limit and Upper Limit.
‒ A Goal of None indicates that there is no goal in terms of optimization. No desirability function is constructed.
Note: If your target response is not midway between the Lower Limit and the Upper Limit, you can change the target after you generate your design table. In the data table, open the Column Info window for the response column (Cols > Column Info) and enter the desired target value.
Importance
When you have several responses, the Importance values that you specify are used to compute an overall desirability function. These values are treated as weights for the responses. If there is only one response, then specifying the Importance is unnecessary because it is set to 1 by default.
Editing the Responses Outline
In the Responses outline, note the following:
• Double-click a response to edit the response name.
• Click the goal to change it.
• Click on a limit or importance weight to change it.
• For multiple responses, you might want to enter values for the importance weights.
Response Limits Column Property
The Goal, Lower Limit, Upper Limit, and Importance that you specify when you enter a response are used in finding optimal factor settings. For each response, the information is saved in the generated design data table as a Response Limits column property. JMP uses this information to define the desirability function. The desirability function is used in the Prediction Profiler to find optimal factor settings. For further details about the Response Limits column property and examples of its use, see “Response Limits” in the “Column Properties” appendix.
If you do not specify a Lower Limit and Upper Limit, JMP uses the range of the observed data for the response to define the limits for the desirability function. Specifying the Lower Limit and Upper Limit gives you control over the specification of the desirability function. For more details about the construction of the desirability function, see the Profiler chapter in the Profilers book.
Factors
Add factors in the Factors outline.
Tip: When you have completed the Factors outline, consider selecting Save Factors from the red triangle menu. This option saves the factor names, roles, changes, and values in a data table that you can later reload in DOE platforms.
Figure 9.14 Factors Outline
Continuous
Adds a Continuous factor. The data type in the resulting data table is Numeric. A continuous factor is a factor that you can conceptually set to any value between the lower and upper limits you supply, given the limitations of your process and measurement system.
Discrete Numeric
Adds a Discrete Numeric factor. A discrete numeric factor can assume only a discrete number of numeric values. These values have an implied order. The data type in the resulting data table is Numeric.
A screening design includes all levels of a discrete numeric factor and attempts to balance the levels. Fit Model treats a discrete numeric factor as a continuous predictor.
The default values for a discrete numeric factor with k levels, where k > 2, are the integers 
. The default values for a discrete numeric factor with k = 2 levels are -1 and 1. Replace the default values with the settings that you plan to use in your experiment.
. The default values for a discrete numeric factor with k = 2 levels are -1 and 1. Replace the default values with the settings that you plan to use in your experiment.Categorical
Adds a Categorical factor. Click to select or specify the number of levels. The data type in the resulting data table is Character. The value ordering of the levels is the order of the values, as entered from left to right. This ordering is saved in the Value Ordering column property after the design data table is created.
The default values for a categorical factor are L1, L2, ..., Lk, where k is the number of levels that you specify. Replace the default values with level names that are relevant for your experiment.
Remove
Removes the selected factors.
Add N Factors
Adds multiple factors. Enter the number of factors to add, click Add Factor, and then select the factor type. Repeat Add N Factors to add multiple factors of different types.
Factors Outline
The Factors outline contains the following columns:
Name
The name of the factor. When added, a factor is given a default name of X1, X2, and so on. To change this name, double-click it and enter the desired name.
Role
The Design Role of the factor. The Design Role column property for the factor is saved to the data table. This property ensures that the factor type is modeled appropriately. The Role of the factor determines other factor properties that are saved to the data table. For details, see “Factor Column Properties”.
Values
The experimental settings for the factors.
Editing the Factors Outline
In the Factors outline, note the following:
• To edit a factor name, double-click the factor name.
• To edit a value, click the value in the Values column.
Factor Column Properties
For each factor, various column properties are saved to the design table after you create the design by selecting Make Table in the Screening Design window. These properties are also saved automatically to the data table that is created when you select the Save Factors option. You can find details about these column properties and related examples in Appendix A, “Column Properties”.
Coding
If the Role is Continuous or Discrete Numeric, the Coding column property for the factor is saved. This property transforms the factor values so that the low and high values correspond to –1 and +1, respectively. For details, see “Coding” in the “Column Properties” appendix.
Value Ordering
If the Role is Categorical or if a Block variable is constructed, the Value Ordering column property for the factor is saved. This property determines the order in which levels of the factor appear. For details, see “Value Ordering” in the “Column Properties” appendix.
Design Role
Each factor is given the Design Role column property. The Role that you specify in defining the factor determines the value of its Design Role column property. When you select a design with a block, that Block factor is assigned the Blocking value. The Design Role property reflects how the factor is intended to be used in modeling the experimental data. Design Role values are used in the Augment Design platform. For details, see “Design Role” in the “Column Properties” appendix.
Factor Changes
Each factor is assigned the Factor Changes column property with the value of Easy. The Factor Changes property reflects how the factor is used in modeling the experimental data. Factor Changes values are used in the Augment Design and Evaluate Design platforms. For details, see “Factor Changes” in the “Column Properties” appendix.
RunsPerBlock
For a blocking factor, indicates the maximum allowable number of runs in each block. When a Blocking factor is specified in the Factors outline, the RunsPerBlock column property is saved for that factor. For details, see “RunsPerBlock” in the “Column Properties” appendix.
Choose Screening Type
After you enter your responses and factors and click Continue, one of the following results occurs:
• If a standard design can accommodate your factors and levels, two options appear in the Choose Screening Type panel. See “Choose Screening Type Options”.
• If no listed standard design exists for your factors and levels, then the Choose Screening Type panel does not appear. The Design Generation outline for constructing a main effects screening design opens. See “Design Generation”.
Choose Screening Type Options
Choose from a list of fractional factorial designs
Enables you to select from a list of designs. This option is the default. For details, see “Choose from a List of Fractional Factorial Designs”.
Construct a main effects screening design
Opens the Design Generation outline where you can specify the number of runs in the main effects screening design. For details about main effects screening designs, see “Main Effects Screening Designs”.
Choose from a List of Fractional Factorial Designs
The list of screening designs that you can choose from includes designs that group the experimental runs into blocks of equal sizes where the size is a power of two. Select the type of screening design that you want to use and click Continue.
Figure 9.15 Choosing a Type of Fractional Factorial Design
The Design List contains the following columns:
Number of Runs
Total number of runs in the design.
Block Size
Number of runs in a block. The number of blocks is the Number of Runs divided by Block Size.
Design Type
Description of the type of design. See “Design Type”.
Resolution
Gives the resolution of the design and a brief description of the type of aliasing. See“Resolution as a Measure of Confounding”.
Design Type
The Design List provides the following types of designs:
Two-Level Full Factorial
A full factorial design has runs for all combinations of the levels of the factors. The sample size is the product of the levels of the factors. For two-level designs, this is 2k where k is the number of factors.
Full factorial designs are orthogonal for all effects. It follows that estimates of the effects are uncorrelated. Also, if you remove an effect from the analysis, the values of the other estimates do not change. Their p-values change slightly, because the estimate of the error variance and the degrees of freedom are different.
Full factorial designs allow the estimation of interactions of all orders up to the number of factors. However, most empirical modeling involves only first- or second-order approximations to the true functional relationship between the factors and the responses. From this perspective, full factorial designs are an inefficient use of experimental runs.
Two-Level Regular Fractional Factorial
A regular fractional factorial design also has a sample size that is a power of two. For two-level designs, if k is the number of factors, the number of runs in a regular fractional factorial design is 2k – p where p < k. A 2k – p fractional factorial design is a 2-p fraction of the k-factor full factorial design. Like full factorial designs, regular fractional factorial designs are orthogonal.
A full factorial design for k factors provides estimates of all interaction effects up to degree k. But because experimental runs are typically expensive, smaller designs are preferred. In a smaller design, some of the higher-order effects are confounded with other effects, meaning that the effects cannot be distinguished from each other. Although a linear combination of the confounded effects is estimable, it is not possible to attribute the variation to a specific effect or effects.
In fact, fractional factorials are designed by deciding in advance which interaction effects are confounded with other interaction effects. Experimenters are usually not concerned with interactions involving more than two factors. Three-way and higher-order interaction effects are often assumed to be negligible.
Plackett-Burman Designs
Plackett-Burman designs are an alternative to regular fractional factorials for screening. The number of runs in a Plackett-Burman design is a multiple of four rather than a power of two. There are no two-level fractional factorial designs with run sizes between 16 and 32. However, there are 20-run, 24-run, and 28-run Plackett-Burman designs.
In a Plackett-Burman design, main effects are orthogonal and two-factor interactions are only partially confounded with main effects. By contrast, in a regular Resolution 3 fractional factorial design, some two-factor interactions are indistinguishable from main effects. Plackett-Burman designs are useful when you are interested in detecting large main effects among many factors and where interactions are considered negligible.
Mixed-Level Designs
For most designs that involve categorical or discrete numeric factors at three or more levels, standard designs do not exist. In such cases, the screening platform generates main effects screening designs. These designs are orthogonal or near orthogonal for main effects.
For cases where standard mixed-level designs exist, the possible designs are given in the Design List. The Design List provides fractional factorial designs for pure three-level factorials with up to 13 factors. For mixed two-level and three-level designs, the Design list includes the complete factorials and the orthogonal-array designs listed in Table 9.1.
If your number of factors does not exceed the number for a design listed in the table, you can adapt that design by using an appropriate subset of its columns. Some of these designs are not balanced, even though they are all orthogonal.
|
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Number of Factors
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|
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Design
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Two–Level
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Three–Level
|
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L18 John and L18 Taguchi
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1
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7
|
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L18 Chakravarty
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3
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6
|
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L18 Hunter
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8
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4
|
|
L36 Taguchi
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11
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12
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Cotter Designs
Note: By default, Cotter designs are not included in the Design List. To include Cotter designs, deselect Suppress Cotter Designs in the Screening Design red triangle menu. To always show Cotter designs, select File > Preferences > Platforms > DOE and deselect Suppress Cotter Designs.
Cotter designs are useful when you must test many factors, some of which might interact, in a very small number of runs. Cotter designs rely on the principle of effect sparsity. They assume that the sum of effects shows an effect if one of the components of the sum has an active effect. The drawback is that several active effects with mixed signs might sum to near zero, thereby failing to signal an effect. Because of this false-negative risk, many statisticians discourage their use.
For k factors, a Cotter design has 2k + 2 runs. The design structure is similar to the “vary one factor at a time” approach.
The Cotter design is constructed as follows:
• A run is defined with all factors set to their high level.
• For each of the next k runs, one factor in turn is set at its low level and the others high.
• The next run sets all factors at their low level.
• For each of the next k runs, one factor in turn is set at its high level and the others low.
• The runs are randomized.
When you construct a Cotter design, the design data table includes a set of columns to use as regressors. The column names are of the form <factor name> Odd and <factor name> Even. They are constructed by summing the odd-order and even-order interaction terms, respectively, that contain the given factor.
For example, suppose that there are three factors, A, B, and C. Table 9.2 shows how the values in the regressor columns are calculated.
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Effects Summed for Odd and Even Regressor Columns
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AOdd = A + ABC
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AEven = AB + AC
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BOdd = B + ABC
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BEven = AB + BC
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COdd = C + ABC
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CEven = BC + AC
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The Odd and Even columns define an orthogonal transformation. For this reason, tests for the parameters of the odd and even columns are equivalent to testing the combinations on the original effects.
Resolution as a Measure of Confounding
The resolution of a design is a measure of the degree of confounding in the design. The trade-off in screening designs is between the number of runs and the resolution of the design.
Experiments are classified by resolution number into these groups:
• Resolution 3 means that some main effects are confounded with one or more two-factor interactions. In order for the main effects to be meaningful, these interactions must be assumed to be negligible.
• Resolution 4 means that main effects are not confounded with other main effects or two-factor interactions. However, some two-factor interactions are confounded with other two-factor interactions.
• Resolution 5 means that there is no confounding between main effects, between main effects and two-factor interactions, and between pairs of two-factor interactions. Some two-factor interactions are confounded with three-factor interactions.
• Resolution 5+ means that the design has resolution greater than 5 but is not a full factorial design.
• Resolution 6 means that there is no confounding between effects of any order. The design is a full factorial design.
A minimum aberration design is one that minimizes the number of confoundings for a given resolution. A minimum aberration design of a given resolution minimizes the number of words in the defining relation that are of minimum length. For a description of words, see “Change Generating Rules”. For a discussion of minimum aberration designs, see Fries and Hunter (1984).
Display and Modify Design
In the Design List, if you select a fractional factorial design with all continuous or two-level categorical factors, and possibly a blocking factor, the Display and Modify Design outline opens after you click Continue. Modify your design using the reports in this outline. See“Modify Generating Rules in a Fractional Factorial Design” for an example of changing the generating rules to construct a design.
Note: The Change Generating Rules and Aliasing of Effects outlines do not appear for Plackett-Burman designs or Cotter designs, because interactions are not identically equal to main effects.
Change Generating Rules
Specify the defining relation for the design. The defining relation determines which fraction of the full fractional factorial design that JMP provides. See “Change Generating Rules”.
Aliasing of Effects
Shows the confounding pattern for the fractional factorial design. Click the red arrow at the bottom of the panel to see interactions to a specified order. The interactions and their aliases are presented in a data table.
Coded Design
Shows the pattern of high and low values for the factors in each run.
Note: For Cotter designs, the Change Generating Rules and Aliasing of Effects outlines do not apply and are not shown.
Change Generating Rules
The generating rules define the relation used to construct a specific fractional factorial design. Your experimental situation might require that you define a fraction of the design that provides a coding or aliasing structure that is different from the standard fraction. You can do this by changing the generating rules in the Display and Modify Design outline. For details about defining relations and generating rules, see Montgomery (2009).
The defining relation for a design is determined by the words in the generating rules. A word is represented by a product of factors, but it is interpreted as the elementwise product of the entries in the design matrix for those columns. A defining relation consists of words whose product is a column of ones, called the identity.
Figure 9.16 Generating Rules for the Standard 25-3 Design
In each column of the Change Generating Rules panel, the factor listed at the top and the factors in the column whose boxes are selected form a word in the defining relation. For example, the first column indicates that Temperature = Feed Rate*Catalyst*Stir Rate is a word in the defining relation.
• If the +/- box is selected, the sign associated with the generating rule is positive and the corresponding word equals the identity.
• If the +/- box is not selected, the sign associated with the generating rule is negative and the corresponding word equals minus the identity.
The principal fraction of a full factorial design is the fractional factorial design obtained by setting all the defining relations equal to the identity. By default, the factorial design that JMP provides is the principal fraction. Notice that the +/- box is selected by default for all generating rules, so that each word in the defining relation equals the identity.
Generating rules determine the coding and aliasing of effects for the design. In some cases, you might want to use a fraction that results in a coding or an aliasing structure that differs from that of the standard fraction.
• To change the generating rules, select the appropriate boxes.
• To see the effect of your selections on the Aliasing of Effects results and on the Coded Design, click Apply.
For an example, see “Change the Generating Rules to Obtain a Different Fraction”.
Obtain the Defining Relations in the 25-3 Design
Figure 9.16 shows two columns of check boxes:
• The first column represents the word Temperature = Feed Rate*Catalyst*Stir Rate.
• The second column represents the word Concentration = Catalyst*Stir Rate.
Define I to represent a column consisting of the values +1. Because all factor levels are -1 or +1, the word in the first column is equivalent to Temperature*Feed Rate*Catalyst*Stir Rate = I. The word in the second column is equivalent to Concentration*Catalyst*Stir Rate = I. Together, these give the defining relations for the 25-3 design:
I = Temperature*Feed Rate*Catalyst*Stir Rate = Concentration*Catalyst*Stir Rate
Obtain the Aliasing of Effects Relations in the 25-3 Design
The aliasing structure in the Aliasing of Effects outline is determined by the defining relations and the fact that factor levels are +1 and -1. Recall that the first generating rule is Temperature = Feed Rate*Catalyst*Stir Rate and the second is Concentration = Catalyst*Stir Rate.
To obtain the first relation in the Aliasing of Effects outline, notice that applying these two generating rules gives the expression:
Temperature = Feed Rate*Catalyst*Stir Rate = Feed Rate*Concentration
The second equality follows from replacing Catalyst*Stir Rate by Concentration using the second generating rule.
Now, post-multiply the first and third expressions by Concentration to obtain the following expression:
Temperature*Concentration = Feed Rate*Concentration*Concentration
Because the column for Concentration in the design matrix contains values of -1 and +1, the term Concentration*Concentration represents a column of +1 values. The expression becomes the first alias relation shown in the Aliasing of Effects outline:
Temperature*Concentration = Feed Rate*I = Feed Rate
The other alias relations can be obtained using similar calculations.
Main Effects Screening Designs
If an experiment involves categorical or discrete numeric factors, or if the number of runs is constrained, it might not be possible to construct an orthogonal design for screening main effects. However, a main effects screening design can be constructed. See Lekivetz et al. (2015).
A main effects screening design is a design with good balance properties as described by a Chi-square criterion. See “Chi-Square Efficiency”. Such designs have desirable statistical properties for main effect models.
The algorithm used to generate the design attempts to construct an orthogonal array of strength two. Strength-two orthogonal arrays permit orthogonal estimation of main effects when interactions are negligible. These arrays are ideal for screening designs. Regular fractional factorial designs of Resolution 3 and Plackett-Burman designs are examples of strength-two orthogonal arrays.
Consider all possible pairs of levels for factors in the design. The algorithm attempts to balance the number of pairs of levels as far as possible. Given that a fixed number of columns has been generated, a new balanced column is randomly constructed. A measure is defined that reflects the degree of balance achieved for pairs that involve the new column. The algorithm attempts to minimize this measure by interchanging levels within the new column.
Chi-Square Efficiency
Suppose that a design has n runs and p factors corresponding to the columns of the design matrix.
• Denote the levels of factors k and l by 
and 
, respectively.
and , respectively.• Denote the number of times that the combination of levels (a,b) appears in columns k and l by 
.
.A measure of the lack of orthogonality evidenced by columns k and l is given by the following expression:
A measure of the average non-orthogonality of the design is given by this expression:
The maximum possible value of χ2, denoted 
, is obtained. The chi-square efficiency of a design is defined as follows:
, is obtained. The chi-square efficiency of a design is defined as follows:
Chi-square efficiency indicates how close χ2 is to zero, relative to a design in which pairs of levels show extreme lack of balance.
Design Generation
When you construct a main effects screening design, the Design Generation outline enables you to specify the number of runs. To generate the design, click Make Design.
Minimum
A lower bound on the number of runs necessary to avoid failures in design generation. When you select Minimum, the resulting design is saturated. There are no degrees of freedom for error.
Note: If you select the Minimum number of runs, there is no error term for testing. You cannot test parameter estimates. This choice is appropriate only when the cost of additional runs is prohibitive.
Default
Suggests the number of runs. This value is based on heuristics for creating a balanced design with at least four runs more than the Minimum number of runs.
User Specified
Specify the number of runs that you want. Enter that value into the Number of Runs text box. This option enables you to balance the cost of additional runs against the potential gain in information.
Design
The Design outline shows the runs for the main effects screening design. To change the run order for your design table, you can select Run Order options in the Output Options panel before generating the table.
Design Evaluation
The Design Evaluation outline provides a number of ways to evaluate the properties of the generated design. Open the Design Evaluation outline to see the following options:
Power Analysis
Enables you to explore your ability to detect effects of given sizes.
Prediction Variance Profile
Shows the prediction variance over the range of factor settings.
Fraction of Design Space Plot
Shows how much of the model prediction variance lies below (or above) a given value.
Prediction Variance Surface
Shows a surface plot of the prediction variance for any two continuous factors.
Estimation Efficiency
For each parameter, gives the fractional increase in the length of a confidence interval compared to that of an ideal (orthogonal) design, which might not exist. Also gives the relative standard error of the parameters.
Alias Matrix
Gives coefficients that indicate the degree by which the model parameters are biased by effects that are potentially active, but not in the model.
Color Map on Correlations
Shows the absolute correlation between effects on a plot using an intensity scale.
Design Diagnostics
Indicates the optimality criterion used to construct the design. Also gives efficiency measures for your design.
For more details about the Design Evaluation panel, see “Design Evaluation” in the “Evaluate Designs” chapter.
Note: The Design Evaluation outline is not shown for Cotter designs.
Output Options
Specify details for the output data table in the Output Options panel. When you have finished, click Make Table to construct the data table for the design. Figure 9.17 shows the Output Options panel for a standard design selected from the Design List. For a main effects screening design, only Run Order is available.
Figure 9.17 Select the Output Options
Run Order
The Run Order options determine the order of the runs in the design table. Choices include the following:
Keep the Same
Rows in the design table are in the same order as in the Coded Design or Design outlines.
Sort Left to Right
Columns in the design table are sorted from left to right.
Randomize
Rows in the design table are in random order.
Sort Right to Left
Columns in the design table are sorted from right to left.
Randomize within Blocks
Rows in the design table are in random order within the blocks. (Not available if you select Construct a main effects screening design.)
Center Points and Replicates
Number of Center Points
Specifies how many additional runs to add as center points to the design. A center point is a run where every continuous factor is set at the center of the factor’s range. This option is not available if you select Construct a main effects screening design.
Suppose that your design includes both continuous and categorical factors. If you request center points in the Output Options panel, the center points are distributed as follows:
1. The settings for the categorical factors are ordered using the value ordering specified in the Factors outline.
2. One center point is assigned to each combination of the settings of the categorical factors in order, and this is repeated, until all center points are assigned.
Number of Replicates
For designs in the Design List, specify the number of times to replicate the entire design, including center points. One replicate doubles the number of runs. This option is not available if you select Construct a main effects screening design.
Note: If you request center points or replicates and click Make Table repeatedly, these actions are applied to the most recently constructed design table.
Make Table
Click Make Table to create a data table that contains the runs for your experiment. In the table, the high and low values that you specified appear for each run.
Figure 9.18 The Design Data Table
The name of the table is the design type that generated it.
The design table includes the following scripts:
Screening
Runs the Analyze > Specialized Modeling > Specialized DOE Models > Fit Two Level Screening platform. Only provided when all factors are at two levels.
Model
Runs the Analyze > Fit Model platform.
Evaluate Design
Runs the DOE > Design Diagnostics > Evaluate Design platform.
DOE Dialog
Re-creates the Screening Design window that you used to generate the design table. The script also contains the random seed used to generate your design.
Run the Screening or Model scripts to analyze the data.
If the design was selected from the Design List, the design table contains a Pattern column. The Pattern column contains entries that summarize the run in the given row. Low settings are denoted by “–”, high settings by “+”, and center points by “0”. Pattern can be useful as a label variable in plots.
Screening Design Options
The Screening Design red triangle menu contains the following options:
Save Responses
Creates a data table containing a row for each response with a column called Response Name that identifies the responses. Four additional columns contain the Lower Limit, Upper Limit, Response Goal, and Importance. Saving responses enables you to quickly load them into a DOE window.
Load Responses
Loads responses from a data table that you have saved using the Save Responses option.
Save Factors
Creates a data table containing a column for each factor that contains its factor levels. A factor’s column contains column properties associated with the factor. Saving factors enables you to quickly load them into a DOE window.
Note: It is possible, but not recommended, to create a factors table by entering data into an empty table, but remember to assign each column an appropriate Design Role. Do this by right-clicking on the column name in the data grid and selecting Column Properties > Design Role. In the Design Role area, select the appropriate role.
Load Factors
Loads factors from a data table that you have saved using the Save Factors option.
Save Constraints
Unavailable for this platform because constraints are not supported.
Load Constraints
Unavailable for this platform because constraints are not supported.
Set Random Seed
Sets the random seed that JMP uses to control certain actions that have a random component. These actions include:
‒ simulating responses using the Simulate Responses option
‒ randomizing Run Order for design construction
‒ selecting a starting design for designs based on random starts.
To reproduce a design or simulated responses, enter the random seed used to generate them.
Note: To reproduce a screening design, you must enter the random seed before you select an option under Choose Screening Type. If you select a screening type, click Continue, and then enter a random seed, the resulting design might not match the design you previously obtained using that random seed.
Notice that the random seed associated with a design is included in the DOE Dialog script that is saved to the design data table.
Simulate Responses
Adds response values and a column containing a simulation formula to the design table. Select this option before you click Make Table.
When you click Make Table, the following occur:
‒ A set of simulated response values is added to each response column.
‒ For each response, a new a column that contains a simulation model formula is added to the design table. The formula and values are based on the model that is specified in the design window.
‒ A Model window appears where you can set the values of coefficients for model effects and specify one of three distributions: Normal, Binomial, or Poisson.
‒ A script called DOE Simulate is saved to the design table. This script re-opens the Model window, enabling you to re-simulate values or to make changes to the simulated response distribution.
Make selections in the Model window to control the distribution of simulated response values. When you click Apply, a formula for the simulated response values is saved in a new column called <Y> Simulated, where Y is the name of the response. Clicking Apply again updates the formula and values in <Y> Simulated.
For additional details, see “Simulate Responses” in the “Custom Designs” chapter.
Note: 
You can use Simulate Responses to conduct simulation analyses using the JMP Pro Simulate feature. For information about Simulate and some DOE examples, see the Simulate chapter in the Basic Analysis book.
You can use Simulate Responses to conduct simulation analyses using the JMP Pro Simulate feature. For information about Simulate and some DOE examples, see the Simulate chapter in the Basic Analysis book.Suppress Cotter Designs
Excludes Cotter designs from the Design List. This option is selected by default. Deselect it to show Cotter designs in the Design List.
Note: You can set a preference to always show Cotter designs. Select File > Preferences > Platforms > DOE and deselect Suppress Cotter Designs.
Number of Starts
(Main Effects Screening Designs only.) Specify the maximum number of times that the algorithm regenerates entire designs from scratch, attempting to optimize the final design.
Design Search Time
(Main Effects Screening Designs only.) Specify the maximum number of seconds spent searching for a design. The default search time is 15 seconds.
If the iterations of the algorithm require more than a few seconds, a Computing Design progress window appears. The progress bar displays Chi2 Efficiency. See “Chi-Square Efficiency”. If you click Cancel in the progress window, the calculation stops and gives the best design found at that point.
Note: You can set a preference for Design Search Time. Select File > Preferences > Platforms > DOE. Select Design Search Time and enter the maximum number of seconds. If an orthogonal array is found, the search terminates. In certain situations where more time is required, JMP automatically extends the search time.
Number of Column Starts
(Main Effects Screening Designs only.) Specify the maximum number of times that the algorithm attempts to optimize a given column before moving on to constructing the next column. The default number of column starts is 50. For details, see “Main Effects Screening Designs”.
Advanced Options > Set Delta for Power
Specify the difference in the mean response that you want to detect for model effects. See “Set Delta for Power” in the “Custom Designs” chapter.
Save Script to Script Window
Creates the script for the design that you specified in the Screening Design window and places it in an open script window.
Additional Examples of Screening Designs
This section contains the following examples:
Modify Generating Rules in a Fractional Factorial Design
The following example, adapted from Meyer, et al. (1996), shows how to use the Screening Design platform when you have many factors. In this example, a chemical engineer investigates the effects of five factors on the percent reaction of a chemical process. The factors are:
• Feed Rate - the amount of raw material added to the reaction chamber in liters per minute
• Catalyst (as a percent)
• Stir Rate - the RPMs of a propeller in the chamber
• Temperature (in degrees Celsius)
• Concentration of reactant
Production constraints limit the size of the experiment to no more than twelve runs. You decide to consider the 8-run fractional factorial design and the 12-run Plackett-Burman design. Also, you suspect the following statements to be true:
• The Temperature*Concentration interaction is active, so you want a design that does not alias this interaction with a main effect.
• The Catalyst*Temperature* interaction is not likely to be active.
• The Stir Rate*Concentration interaction is not likely to be active.
Use this information in constructing your design.
Create the Standard Fractional Factorial Design
To create the standard fractional factorial design, do the following:
Specify the Response
1. Select DOE > Classical > Screening Design.
2. Double-click Y under Response Name and type Percent Reacted.
Note that the default Goal is Maximize. The Goal is to maximize the response, but the minimum acceptable reaction percentage is 90 (Lower Limit) and the upper limit is 100 (Upper Limit).
3. Click under Lower Limit and type 90.
4. Click under Upper Limit and type 100.
5. Leave the area under Importance blank.
Because there is only one response, that response is given Importance 1 by default.
See Figure 9.19 for the completed Responses outline. Now, specify the factors.
Specify the Factors
You can enter the factors manually or automatically:
• To enter the factors automatically, use the Reactor Factors.jmp data table:
1. Select Help > Sample Data Library and open Design Experiment/Reactor Factors.jmp.
2. From the Screening Design red triangle menu, select Load Factors. Proceed to “Choose a Design”.
• To enter the factors manually, follow the steps below.
Specify Factors Manually
1. Add five continuous factors by entering 5 in the Add N Factors box and clicking Continuous.
2. Change the default factor names (X1-X5) to Feed Rate, Catalyst, Stir Rate, Temperature, and Concentration.
3. Enter the low and high values, as follows:
‒ Feed Rate: 10, 15
‒ Catalyst: 1, 2
‒ Stir Rate: 100, 120
‒ Temperature: 140, 180
‒ Concentration: 3, 6
Figure 9.19 Responses and Factors Outlines
Choose a Design
1. Click Continue.
2. From the Choose Screening Type panel, accept the default selection to Choose from a list of fractional factorial designs and click Continue.
Designs for the factors and levels that you specified are listed in the Design List (Figure 9.20).
Figure 9.20 Fractional Factorial Designs for Five Continuous Factors
3. The design that you want is the first in the list and happens to be selected by default (Figure 9.20). Accept that selection and click Continue.
Because you are limited to eight runs and have no blocking factor, your best design option is the 8-run fractional factorial design with no blocks. This design is a 25-2 fractional factorial design. It is one quarter of the full factorial design for five factors.
Change the Generating Rules to Obtain a Different Fraction
In this example, you want to know whether the Temperature*Concentration interaction is confounded with a main effect. Use the Display and Modify Design outline to view the aliasing structure for the design that you selected and to change it, if appropriate.
1. Open the Aliasing of Effects outline.
Figure 9.21 Aliasing of Effects Outline
The Temperature*Concentration interaction, which you suspect is active, is confounded with Feed Rate, a main effect. You want to change the generating rules to construct a design where Feed Rate is aliased with effects that you suspect are inactive, and where the Temperature*Concentration interaction is not aliased with a main effect.
2. Open the Change Generating Rules outline.
The default-generating rules give you the standard (or principal) one-quarter fraction of the full factorial design. Recall that you suspect that the Catalyst*Temperature and Stir Rate*Concentration interactions are not likely to be active. Redefine the generating rules so that these two interactions are confounded with Feed Rate. The redefined generating rules give you a different one-quarter fraction of the full factorial design.
3. Do the following:
‒ Deselect Stir Rate in the Temperature column.
‒ Deselect Catalyst in the Concentration column.
‒ Select Feed Rate in the Concentration column.
Figure 9.22 New Generating Rules
4. Click Apply.
Figure 9.23 Aliasing of Effects Outline for Modified Generating Rules
In the design that you have defined, Feed Rate is confounded with Catalyst*Temperature and Stir Rate*Concentration. Also, the Temperature*Concentration interaction is now confounded with the two-way interaction Catalyst*Stir Rate.
5. In the Output Options outline, accept the default Run Order setting of Randomize and click Make Table.
Figure 9.24 Eight-Run Fractional Factorial Design Table
The design table shows the design that you constructed. Notice that the table contains a column for the response that you defined in the Screening window, Percent Reacted, where you can record your experimental results.
The Screening, Model, and DOE Dialog scripts are also included. For details about these scripts, see “Make Table”.
Analyze the Results
Next you conduct the experiment, record your data, and proceed to analyze the results.
1. Select Help > Sample Data Library and open Design Experiment/Reactor 8 Runs.jmp.
You can estimate seven effects with your eight runs. Of these, you expect only a few to be active. Because you want to estimate seven effects, there are no degrees of freedom for error. For these reasons, you use the Screening platform to analyze the results.
2. Run the Screening script in the data table.
The Screening script launches the Screening platform (Analyze > Specialized Modeling > Specialized DOE Models > Fit Two Level Screening) for your response and factors.
Figure 9.25 shows the report.
Figure 9.25 Report for Screening Example
Note: Since the p-values are obtained using a simulation-based technique, your p-values might not precisely match those shown here.
The report shows both Individual and Simultaneous p-values based on Lenth t-ratios. None of the effects are significant, even with respect to the Individual p-values. The Half Normal Plot suggests that the effects reflect only random noise.
For more details about the Screening report, see “The Screening Report” in the “The Fit Two Level Screening Platform” chapter.
Plackett-Burman Design
The Fractional Factorial example shows an 8-run fractional factorial design for five continuous factors. But suppose you can afford 4 additional runs. In this example, construct a 12-run Plackett-Burman design. To facilitate completing the Screening window, use the Load Responses and Load Factors commands.
Create the Plackett-Burman Design
1. Select DOE > Classical > Screening Design.
2. Select Help > Sample Data Library and open Design Experiment/Reactor Response.jmp.
3. Select Load Responses from the Screening Design red triangle menu.
4. Select Help > Sample Data Library and open Design Experiment/Reactor Factors.jmp.
5. Select Load Factors from the Screening Design red triangle menu.
The Load Responses and Load Factors commands fill in the Responses and Factors outlines with the response and factor names, goal and limits for the response, and values for the factors. See Figure 9.19 for the completed Responses and Factors outlines.
6. Click Continue.
Note: Setting the random seed in the next step reproduces the run order shown in this example. In constructing a design on your own, this step is not necessary.
7. (Optional) From the Screening Design red triangle menu, select Set Random Seed, type 34567, and click OK.
8. From the Choose Screening Type panel, accept the default selection to Choose from a list of fractional factorial designs and click Continue.
9. Select the Plackett-Burman design, as shown in Figure 9.26.
Plackett-Burman designs with run sizes that are not a power of two tend to have complex aliasing structures. In particular, main effects can be partially aliased with several two-way interactions. See “Evaluate the Design”. Notice that the 12-run Plackett-Burman design is designated as having Resolution 3.
Figure 9.26 Design List Showing Plackett-Burman Screening Design
10. Click Continue.
11. Click Make Table.
Figure 9.27 Design Table for Placket-Burman Design
A column called Percent Reacted is included in the design table. You should conduct your experimental runs in the order shown in the table, recording your results in the Percent Reacted column.
Evaluate the Design
1. Return to your Screening Design window. If you have closed this window, run the DOE Dialog script in your design table.
2. Open the Design Evaluation > Color Map on Correlations outline.
Figure 9.28 Color Map for Absolute Correlations
The diagonal cells have correlations of one, as expected. Cells with the deep blue color correspond to effects that have correlations equal to 0. The light blue and gray shaded cells correspond to effects that have correlations greater than zero. Place your cursor over a few of these cells with your cursor to see the effects involved and their absolute correlations. For example, notice that Feed Rate is correlated with several two-way and three-way interactions.
3. Open the Alias Matrix outline.
Figure 9.29 Alias Matrix - Partial View Showing Up to Two-Way Interactions
Because the design is orthogonal for the main effects, the Alias Matrix gives the numerical values of the correlations between effects. See “Alias Matrix” in the “Evaluate Designs” chapter. For example, notice that Feed Rate is partially aliased with six two-way interactions and with four three-way interactions. These are the interactions corresponding to the entries of 0.333 and -0.33 in the row for Feed Rate.
Analyze the Results
The data table Plackett-Burman.jmp contains the results of the designed experiment. Recall that you suspect that the Temperature*Concentration interaction is active. You proceed under the assumption that this is the only potentially active interaction.
1. Select Help > Sample Data Library and open Design Experiment/Plackett-Burman.jmp.
2. Run the Model script by clicking the icon to its left.
3. Select Temperature in the Select Columns list and Concentration in the Construct Model Effects list.
4. Click Cross.
5. Click Run.
Figure 9.30 Parameter Estimates for Full Model
The Actual by Predicted Plot indicates no lack of model fit. The Parameter Estimates report shows that Catalyst is significant at the 0.05 level and that the Concentration*Temperature interaction is almost significant at the 0.10 level.
Reduce the Model
You want to identify those effects that have the most impact on the response. To see these active effects more clearly, remove insignificant effects using the Effect Summary outline.
Figure 9.31 Effect Summary Outline for Full Model
Although Concentration is the least significant effect, it is involved in a higher-order interaction (Concentration*Temperature), as indicated by the caret to the right of its PValue. Based on the principle of effect heredity, Concentration should not be removed from the model while the Concentration*Temperature interaction remains in the model. See “Effect Heredity” in the “Starting Out with DOE” chapter. The next least significant effect is Stir Rate.
1. In the Effect Summary outline, select Stir Rate and click Remove.
Feed Rate is the next least significant effect that can be removed.
2. In the Effect Summary outline, select Feed Rate and click Remove.
Figure 9.32 Effect Summary Outline for Reduced Model
The PValue column indicates that the Catalyst main effect and the Concentration*Temperature interaction are both significant at the 0.05 level. The model should not be reduced any further. If all other interactions are inactive or negligible, then you can conclude that Catalyst and the Concentration*Temperature interaction are active effects.
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