Effex app documentation – Software documentation

Docs: Home

Mon, 01 Jan 0001 00:00:00 +0000

The screen below is the home page of our software. Using the buttons on this page, you can

start your search for a design,
go to your personal library of saved designs or catalog searches, and
access the documentation.

Docs: My DoE items

Mon, 01 Jan 0001 00:00:00 +0000

With our software, you can save the designs you purchased for future consultation. You can also save specifications of designs that you find interesting but yet did not purchase.

Docs: Catalog search

Mon, 01 Jan 0001 00:00:00 +0000

Obvious differences aside, our catalog search page works as if you were to purchase an item at a popular webshop. With our unique set of controls you can filter the experimental designs using different criteria at the same time. This solves the intrinsic problem of designs created with a single optimality criterion (optimal design), as you will be able to assess not only the trade-off between competing design evaluation criteria, but also their relation with the cost of a design, that is, the run size.

Docs: Comparison

Mon, 01 Jan 0001 00:00:00 +0000

You have learned how to select designs from one or several catalog searches. Probably, after the first exploration of the catalog, there are still a few candidate designs that you would like to compare in detail to identify the one that fits best your experiment.

In this section you will find how to interact with the different elements: the table and the interactive graphical comparison. You will also learn about the most important features: highlighting the Pareto efficient points, automatic selection of a design, interactive colormaps, detailed comparison.

Docs: Design detail

Mon, 01 Jan 0001 00:00:00 +0000

Docs: Factor ranges

Mon, 01 Jan 0001 00:00:00 +0000

2-level categorical factors accept a string or a number as the lower and upper levels.

Some notes on the randomization:

The randomization produces a random assignment of the rows of the design matrix to each run of the experiment.
The columns are not randomized.
For designs with a blocking factor, the randomization occurs within each block and the order of the blocks are themselves randomized as well.

Docs: Design report

Mon, 01 Jan 0001 00:00:00 +0000

Click here to get a PDF with the information displayed on this page.

A user can download all characteristics of a design with the functionality available at the Design detail page:

The characterization in PDF format is available for all designs, while the characterization in Word format is only available for purchased designs.

The report is structured in 9 sections:

Summary
Morphology
Aliasing
Efficiencies
Fraction of design space plots
Powers for effect types and deifferent estimable models
Projection properties
Model effects related characteristics
Powers for model effects and different estimable models

We now explain each section in detail.

1. Summary

Number of runs: number of tests of the experimental design.
3-level factors: number of factors that are studied at three levels, which correspond to the minimum, average and maximum values of a given continuous range. These factors allow the estimation of main and quadratic effects and they are used to model quantitative factors.
2-level factors: number of factors that are studied at two levels. These factors can be used to model either quantitative or categorical factors with two levels. If a 2-level factor is quantitative, then the two-levels correspond to the minimum and maximum values of a given continuous range. If the 2-level factor is categorical, then the two levels indicates the two categories that the factor can take. All the characterizations of the designs consider the 2-level factors as categorical.
Center points: number of tests of an experimental design where all 3-level factors are set to their average value.
Maximum 4th order correlation: maximum value of the absolute correlation between two second-order terms (this is, between two-factor interaction effects and/or quadratic effects).
Number of blocks: number of groups of runs that the design is partitioned in. In our catalog, the blocking factor is orthogonal to all main effects.
Block size: number of runs per block. In our catalog, all blocks have the same size.

2. Morphology

Degrees of freedom for pure error: the responses of the replicated runs of a design can be used to estimate the pure error independently from the model. This enables a lack-of-fit test while modeling the data. The Degrees of freedom for pure error takes all replicates into account (center runs and any other replicated runs).
Number of replicates: indicates how many different runs are replicated in the design. The higher the value, the higher the coverage of the design space when calculating the pure error.
Mirror: equals true if the design has a foldover structure, this is, for every run in the design, the run result of switching the low and high values in all the factor levels is also present in the design.
Uniform precision in the main effects: indicates if all columns of the 3-level factors have the same number of entries equal to the factor average level. It indicates that the power to detect a single main and/or quadratic effects is the same for all factors.
Uniform precision in the interaction effects: indicates if all columns of the two-factor interactions in the model matrix have the same number of entries equal to zero. It indicates that the power to detect a single interaction effect is always the same.
Intrablock correlation coefficient: when a design has a random blocking factor, there are two sources of variation: $\sigma^2_{\varepsilon}$ which quantifies the residual error variance, and $\sigma^2_{\gamma}$ is the block variance. The ratio between these two variances is denoted as $\eta=\sigma^2_{\gamma}/\sigma^2_{\varepsilon}$. The intrablock correlation coefficient equals $\frac{\eta}{\eta+1}$. If there are no blocks, then both $\eta$ and the intrablock correlation coefficient equal zero and the introblock correlation is not reported. If the blocks are treated as a fixed effect, the intrablock correlation coefficient equals $1$. When the blocks are treated as a random effect, the intrablock correlation coefficient lies between $0$ and $1$.

3. Aliasing

Balanced main effects: indicates if the number of times any factor is set to its lower level equals the number of times the same factor is set to its upper level.
Average 2nd order correlation: average value of the absolute correlation between the main effects of two factors.
Maximum 2nd order correlation: maximum value of the absolute correlation between the main effects of two factors.
Average 3rd order correlation: average value of the absolute correlation between the main effect of a factor and a second-order effect.
Maximum 3rd order correlation: maximum value of the absolute correlation between the main effect of a factor and a second-order effect.
Average 4th order correlation: average value of the absolute correlation between two second-order effects.
Maximum 4th order correlation: maximum value of the absolute correlation between two second-order effects.
OMARS: equals true if the design is an Orthogonal Minimally Aliased Response Surface Design, this is, when the main effects are balanced, and the maximum 2nd and 3rd order correlation equals $0$.
Maximum eta correlation between the block effect and a main effect: maximum value of the correlation¹ between the block effect and a main effect.
Maximum eta correlation between the block effect and an interaction effect: maximum value of the correlation¹ between the block effect and an interaction effect.
Maximum eta correlation between the block effect and a quadratic effect: maximum value of the correlation¹ between the block effect and a quadratic effect.
Maximum eta correlation between the block effect and a second-order effect: maximum value of the correlation¹ between the block effect and a second-order effect.

4. Efficiencies

In this section we present the most common efficiencies for the statistical models that are estimable. The models are of the next four different types:

ME model: this includes all the main effects of the original factors
ME + IE model: this includes all the main effects and two-factor interactions
ME + SOE model: this includes all the main effects and second order effects (two-factor interactions and quadratic effects).
ME + QE model: this includes all the main effects and the quadratic effects.

The characteristics reported are the D-, A- and G-efficiency and the average prediction variance.

5. Fraction of design space plot

The fraction of design space plot indicates the distribution of the prediction variance across the design space. This plot is obtained by calculating the prediction variance of random points within the design space and ordering them. In the horizontal axis one can find the value of the prediction variance, while on the vertical axis we indicate the fraction of design space. For example, if we draw an horizontal line from the point located at the vertical coordinate $0.5$and we intersect it with the curve, we obtain a prediction variance such that the %50%$ of the design space has a prediction variance equal or lower to it.

We provide a plot for every estimable model (ME, ME+IE, ME+SOE and ME+QE models).

6. Powers for effect types and different statistic models

In this section there are three tables, one for each of three significance levels $\alpha \in {0.01, 0.05, 0.1}$. Each table contains the powers to detect model effects for five different values of the signal-to-noise-ratio (SNR). The other headers in the table are:

Model: underlying model considered in the power calculation
Effects: effect type considered, which can be main, interaction of quadratic effect.

Each entry in the table is the minimum power to detect the effect type, with the underlying model at the SNR and alpha indicated.

7. Projection properties

This section consists of two tables. The first table offers details on the estimation quality of second-order models based on subsets of the factors. For any subset, these models include an intercept, all the main effects, all the two-factor interactions, and all the quadratic effects of the numerical three-level factors in the subset. The second table offers details on the estimation quality of a model with main and interaction effects based on subsets of the factors. For any subset, these models include an intercept, all the main effects, and all the two-factor interactions.

Both tables have the same columns:

f3: number of 3-level factors considered
f2: number of 2-level factors considered
total, OK, %: total number of projection models, number of estimable models that are estimable, and the percentage
D-efficiency: average D-efficiency for all the estimable projection models
A-efficiency: average A-efficiency for all the estimable projection models
G-efficiency: average G-efficiency for all the estimable projection models
Prediction variance: average average prediction variance for all the estimable projection models

The columns labeled as f3 and f2 give information on how many 3- and 2-level factors are considered in the projection models. The columns total, OK, % indicate the estimability of those models. Finally, the rest of the columns indicate how well these models can be estimated and how precise the estimation is.

We provide here information on the relative standard error (REE), the fracional increase in confidence interval length (FICIL), and the variance inflation factors (VIF) for the individual effects in every estimable model.

9. Powers for model effects and different estimable models.

Powers to detect individual effects in every estimable models for different significance levels and signal-to-noise ratios.

Correlation ratio in Wikipedia ↩︎

Docs: Guided DoE

Mon, 01 Jan 0001 00:00:00 +0000

The Guided DoE page simplifies the experimental design generation and selection process. Here, depending on the user inputs, the software can recommend optimal designs generated using the coordinate-exchange algorithm or the best designs from the catalog.

Docs: Modeling

Mon, 01 Jan 0001 00:00:00 +0000

Docs: Optimization

Mon, 01 Jan 0001 00:00:00 +0000

To optimize for a specific response variable, a model must first be selected. To select a model, follow the instructions here.

For the response variable that is of interest, when a model has been selected, in the Dataset modeling info page, the row corresponding to this response variable will become activated in the last table titled Select models. When this happens, the user will be able to select this response by ticking the check box corresponding to this response. Here is an example.

In this table, the row corresponding to the response variable ABRASION has been activated since a model has been selected for this response variable. The image also shows that on ticking the corresponding check box, the Start optimization button has been activated.

The software allows the user to optimize multiple responses simultaneously. In the Start optimization button, the number of responses selected for optimization is displayed. In the example above, since there is only one response selected, in the button you see this mentioned as ‘(1)’. In the same example, if we selected two responses, this is what it would look like.

On clicking the Start optimization button, the prediction values are calculated for various combinations of the input factors. A new screen will pop up to allow the user to find the optimal settings for each input factor.

Note: If the user wishes to change the selected model for a specific response, this can be done by clicking on the Select models button.

Docs: Notifications

Mon, 01 Jan 0001 00:00:00 +0000

Clicking on the notifications tab, will open a small window on the right. If and when calculations are requested in the software, an update on the completion of such a requested calculation will be provided in this window. In the software, calculations can be requested when generating a design and performing modeling calculations.

When a design generation calculation is completed, clicking on the corresponding entry in the notifications tab will display the results of the design generation procedure. To select a design from the results, refer here.

When a modeling calculation is completed, clicking on the corresponding entry in the notifications tab will display the page concerning the analyzed data set where the modeling results can be found. For more information, refer here.

Docs: Glossary

Mon, 01 Jan 0001 00:00:00 +0000

A

A(Model)

This is the A-efficiency of an experimental design for a given model including the intercept. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to its ability to screen active (i.e statistically significant) effects among all the model terms. The higher the value for A-efficiency, the better is the experimental design according to this metric. For example, A(ME), refers to the A-efficiency of an experimental design for a main-effects model including the intercept. This is presented under Catalog Search.

AIC

This is the value for the Akaike Information Criterion for the corresponding linear regression model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. The lower the value, the better is the model according to this metric. This metric is presented during modeling under Model details.

AICc

This is the value for the corrected Akaike Information Criterion for the corresponding linear regression model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. The lower the value, the better is the model according to this metric. This metric is presented during modeling under Modeling results and Model details.

Avg pred var (ME)

This is the average prediction variance of an experimental design for a model with only the intercept and all main effects. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to the precision with which predictions can be made using a model with only the intercept and all main effects. This is presented under Catalog Search.

Avg ρ (E1,E2)

This is the average correlation between any single effect column of type E1 with any single effect column of type E2 for an experimental design. The effect type E1 or E2 may correspond to MEs, IEs, QEs or SOEs. The correlation between two effect columns is an indication of how independently their effects can be estimated from each other. The lower the correlation, the more independent are the estimates of the effects. This information is presented under the aliasing tab in Detailed comparison.

B

Balance (ME)

If true, all design columns of the experimental design have the same number of upper and lower levels. This information is presented under the aliasing tab in Detailed comparison.

BIC

This is the value for the Bayesian Information Criterion for the corresponding linear regression model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. The lower the value, the better is the model according to this metric. This metric is presented during modeling under Model details.

Blocking

If True, the experimental design has one column associated with a blocking (or grouping) variable. A blocking variable or a nuisance variable is a variable that you do not directly control but which can impact your results if not taken into account. For all experimental designs previously selected using catalog search (which can be found under My DoE items), the existence or non-existence of a blocking variable is indicated using True/False. The option to include an experimental design with a blocking variable is presented in Define your experiment under Catalog Search. Use this link to learn more about blocking variables.

C

Center points

Number of test combinations where the settings for all the three-level quantitaive factors are set to the middle levels of their respective individual input ranges. In some cases, this may be desired by the user to test for non-linear effects by performing experiments at the middle levels of all three-level quantitative factors more than once. As a side effect, the higher the number of center points, the more replicates you have in your design. This is presented under Catalog Search.

Condition number

This is the ratio between the maximum and minimum eigen value of the information matrix of the model matrix. Similar to VIF, this number quantifies the degree of multicollinearity between terms in your model. As a rule of thumb, if the condition number is between 10 and 30, this is considerate to indicate a moderate level of multicollinearity, where as values greater than 30 indicate a strong level of multicollinearity. This is presented under Model details.

Corner

If True, the experimental design has at least one test combination where the levels for all three-level quantitative factors are set to their respective extreme (either upper or lower) values in their individual input ranges. In some situations, this may be desired by the user when testing extreme combinations of the input variables is considered to be informative. This is presented under Catalog Search in the summary table and also under Detailed comparison.

D

D(Model)

This is the D-efficiency of an experimental design for a given model including the intercept. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to its ability to screen active (i.e statistically significant) effects among all the model terms. The higher the value for D-efficiency, the better is the experimental design according to this metric. For example, D(ME), refers to the D-efficiency of an experimental design for a main-effects model including the intercept. This is presented under Catalog Search.

DF pure error

For an experimental design, this is the number of degrees of freedom available to estimate the pure error, which is defined as the number of replicated points in the design, and is calculated as the difference between the total number of runs in and the number of runs with unique test combinations. The higher the degrees of freedom to estimate the pure error (i.e the greater number of replicated test combinations), the better is the estimate of the RMSE (which is the estimate of the run-to-run standard deviation), which in turn makes the statistical significance tests more powerful. This is presented under Catalog Search and .

F

Foldover

If this is true for a design, then this means that except for the center runs (test combinations where all three-level quantitative factors are set to their middle levels), all other test combinations have their opposite test combinations also present in the same design. The majority of OMARS designs are also foldover designs, however, there are non-foldover OMARS too available in the software. Non-foldover OMARS designs often possess capabilities to fit larger and more complex regression models than their foldover counter parts. This is presented under Design detail.

G

G (ME)

This is the G-efficiency of an experimental design for a given model including the intercept. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to the precision with which predictions can be made using the given model including the intercept. The higher the value for G-efficiency, the better is the experimental design according to this metric. For example, G(ME), refers to the G-efficiency of an experimental design for a main-effects model including the intercept. This is presented under Catalog Search.

I

Two-factor interaction or IE columns are obtained by multiplying main-effect columns corresponding to two different factors. Such effects allow the user to study whether the effect of changing the level setting of one input variable on the response variable is dependent on the specific level that is set for another input variables. Most modern processes always have some interaction effects at play. Hence, such type of effects are always interesting to study.

M

Max ρ (E1,E2)

Maximum correlation between any single effect of type E1 with any single effect of type E2. The effect type E1 or E2 may correspond to MEs, IEs, QEs or SOEs. This information is presented under Catalog Search.

Main effect. These are the first-order linear effects that are considered in the linear regression model.

Min Pow (ME,IE)

Minimum statistical power to detect any single active IE under a base model with the intercept and all MEs preincluded (assuming α=0.05, signal-to-noise ratio equal to 1). This information is presented under Catalog Search.

Min Pow (ME,ME)

Minimum statistical power to detect any single active ME under a base model with the intercept and all MEs preincluded (assuming α=0.05, signal-to-noise ratio equal to 1). This information is presented under Catalog Search.

Min Pow (ME,QE)

Minimum statistical power to detect any single active QE under a base model with the intercept and all MEs preincluded (assuming α=0.05, signal-to-noise ratio equal to 1). This information is presented under Catalog Search.

N

Number of tests in the design i.e run size of an experiment.

O

OMARS

If true, the experimental design is an OMARS design. For more information on OMARS designs click here. This information is presented under Design detail.

P

PEC(0,x) (Model)

When the user assesses designs with only two-level quantitative (or categorical) factors, the PEC(n,x) (Model) simplies to PEC(0,x) (Model).

PEC(n,x) (Model)

PEC - Projection estimation capacity. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to its ability to estimate a variety of interesting models. This is presented under Catalog Search. For example, if PEC (n,x)(ME+IE) = 4.2 for a design, then this means that the design is capable of estimating a model with the intercept, all MEs and all IEs for any single subset of ‘n’ three-level quantitative factors with any single subset of 4 two-level quantitative (or categorical) factors, and can estimate the same type of model for any single subset of ‘n’ three-level quantitative factors with 20% (0.2) percent of all possible subsets of 5 two-level quantitative (or categorical) factors. Refer here for more info.

PEC(x,0) (Model)

When the user assesses designs with only three-level quantitative factors, the PEC(x,n) (Model) simplies to PEC(x,0) (Model).

PEC(x,n) (Model)

PEC - Projection estimation capacity. This is one of the metrics used in the software to characterize the quality of an experimental design with respect to its ability to estimate a variety of interesting models. This is presented under Catalog Search. For example, if PEC (x,n)(ME+IE) = 4.2 for a design, then this means that the design is capable of estimating a model with the intercept, all MEs and all IEs for any single subset of 4 three-level quantitative factors with any single subset of ‘n’ two-level quantitative (or categorical) factors, and can estimate the same type of model for any of the 20% (0.2) percent of all possible subsets of 5 three-level quantitative factors with any single subset of ‘n’ two-level quantitative (or categorical) factors. Refer here for more info.

PoS

Probability of Success or PoS is a metric used to describe how well a certain combination of the settings of the input variables produces the desired response variables within the user specified tolerance intervals. This is presented under Optimization. For more information on Probability of Success, click here.

PRESS

This is the value for the Predicted residual error sum of squares for the corresponding linear regression model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. The lower the value, the better is the model according to this metric. This metric is presented during modeling under Model details.

Q

Quadratic effect or QE columns are obtained by multiplying a main-effect column corresponding to a specific factor by itself. It is possible to study the non-linear effects of certain factors by including their respective QE in the model.

R

Rank(ME+SOE)

Rank of a model matrix with all MEs and SOEs. This number represents the total number of effects (from the set of all MEs and SOEs) that can be jointly estimated in a single model. This number directly reflects the size of the largest complex model that can be estimated using the given experimental design. This metric is presented during modeling under Catalog Search and Model details.

RSE

Relative standard error of estimates or RSE refers to the standard error for the estimates for each model term assuming $\sigma^2$ (i.e run-to-run process error variance) is equal to one. In simple terms, this quantifies the size of the intervals around an estimated value for a coefficient in your regression model.

The lower the RSE for a specific term in your model, the smaller the size of the interval around its estimate, and therefore, the greater the likelihood of detecting such a term as active (i.e statistically significant).

Replicates

Number of unique test combinations that have more than one occurrence in the experimental design. Having more replicates in the design, primarily, has one advantage and one disadvantage.

The advantage is that larger numbers of replicates in a design allows you to more accurately divide the estimated error variance in your model into two parts: the part that accounts for the variance that is not captured by the terms included in your model (commonly referred to as the lack-of-fit error variance) and the part that accounts for the variance from the average values for each test combination replicated more than once (commonly referred to as the pure error variance). Comparing these two of variance is what is commonly referred to as a lack-of-fit test. This test gives you an indication on whether you are missing some terms in your model. This test can only be performed when there is at least one replicate (ideally more) in the design.

The disadvantage is that the having more replicates (i.e duplicated runs) in the design instead of more unique ones, results in a design which can fit a model with only a smaller number of terms.

RMSE

Root mean squared error is the estimate of the run-to-run standard deviation after fitting a given model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. This metric is presented during modeling under Model details.

R2 adj

This is the value for the $R^2$ adjusted for the corresponding linear regression model. This is one of the metrics used in the software to characterize the statistical quality of a linear regression model. The higher the value, the better is the model according to this metric. This metric is presented during modeling under Model details.

S

SOE

Any two-factor interaction column or a quadratic effect column is referred to as the second order effects (two-factor interaction effects and quadratic effects)

V

VIF

Variance inflation factor or VIF refers to the degree to which the variance associated with a given estimate (i.e coefficient) of a model term is inflated due to multicollinearity with other terms in the same model. As a rule of thumb, if the VIF value for a term is greater than 5, this indicates that the term is highly correlated with one or more other terms in the same model.

Y

y-predicted

Prediction value for the average value for a response variable based on the given regression model. This is presented under Profilers during the optimization step.

Effex app documentation – Software documentation

Docs: Home

Docs: My DoE items

Docs: Catalog search

Docs: Comparison

Docs: Design detail

Docs: Factor ranges

Docs: Design report

1. Summary

2. Morphology

3. Aliasing

4. Efficiencies

5. Fraction of design space plot

6. Powers for effect types and different statistic models

7. Projection properties

8. Model effects related characteristics

9. Powers for model effects and different estimable models.

Docs: Guided DoE

Docs: Modeling

Docs: Optimization

Docs: Notifications

Docs: Glossary

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