Q 461. While DOE is better known for Optimization, it can also be used for screening. What is a Screening Design in DOE? Provide examples to support your answer.

 

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Screening Designs: Screens factors that are not statistically significant 

 

Intention: Used for exploratory analysis.

Focus: Estimates main effects in presence of negligible interactions.

 

Most suitable for Industrial experimentation during early states of design.

When there are many significant factors, screening design can be used to condense the list to fewer once.

 

Time and again, it becomes tedious to study all the factors in detail. Screening design can be used effectively and compared to traditional design methods, screening design just require fewer experimentation runs.

To say in short, experiments are “Small and efficient”.

 

Often used screening designs include:

Fractional Factorial Design (2-Level),

Full Factorial Design (2-Level),

Definitive Screening Design, &

Mixed-level design

 

Below are few Specific design:

Plackett-Burman design,

Taguchi methods,

Cotter Design

 

However, there are many different screening designs, some of the considerations for best design fit are listed below:

Questions that we can, before finalising the design method:

What's is the Overall Goal

What are the specific response types

How are these responses measures

What are the factors that need to be considered

What should be the range for the factors

Do we have block factors

Are we working on a Split plot problem

Do we have problematic combinations of the factor settings

 

Answers to the above questions, can effectively let us know in picking the perfect design model for the screening. 

 

Lets take a case of a Chemical Product ABC as an example and use Plackett-Burman (2 Level Fractional Factorial design). Based on preliminary analysis, it was identified 11 potential factors might impact the yield of the chemical product, which is listed in the below table.

 

Simply if we want to run 2 level full factorial design, Total number of runs would be 2 Power 11 = 2048 Runs.

 

Some of the interactions between the potential factors might have trivial importance, Plackett-Burman design can be effectively used here. Lets run the design by just setting the Base number of runs as 12.

 

Below is the summary of the design settings:

 

Factor Combination and its Yield for 12 runs is shown in the below table:

 

Inference from Effect probability plot can be used to identify the significant few (Important Factors in the experiment), which is shown in red squares in the plot graph.

 

This brings down the potential factors from 11 to 5. 

 

Properties of the design generated can also be effectively evaluated by various other different output metrics, viz.,

Power Analysis,

Prediction Variance Profile,

Effect Probability Plot,

Fraction of Design Space Plot,

Prediction Variance Surface,

Estimation Efficiency,

Alias Matrix,

Color Map on Correlations, &

Design Diagnostics

 

Screening design might not be limited to industrial experimentation, however the applications of it can also be used in other functions as well. For Instance, lets consider Marketing example.  

 

2^7 Experiments or 128 Runs could be too much for a tight delivery time period of Product X, however screening designs based on preliminary analysis can help the product to touch new sales success stories. 

 

Benefits of Screening Designs:

Relatively Inexpensive (Saves $'s) 

Efficient approach for process improvement

Can run the experiments with limited resources 

Effective simulation 

 

A Full Factorial Design does experiments for every possible unique combination of the Independent Variables and their impact on the dependent variable. It gives information on all the main effects and all the interactions.

Screening DOE is also called Fractional Factorial DOE. It is used when there are a large number of possible independent variables and the researcher has a limit on the number of experiments that can be run. Screening DOE reduces the total runs on the number of experiments by removing those factors that are not statistically significant. This means that these factors will have a negligible effect on the output. The Plackett Burman Design is another type of screening DOE.

Benefits of Screening DOE

Saving of Time and Money. In the case of destructive testing, screening DOEs are helpful as it reduces the number of pieces of the experimental units scrapped. Fewer runs will require lesser time and resources. For example, an experiment with 10 factors would have 2^10 or 1024 unique runs. Out of these only, 56 will give the main and two-way interactions. The balance 968 will give the 3 way and higher interactions.

Drawbacks of Screening DOE

Loss of Resolution. In a Fractional Factorial design, some of the main effects are confounded or aliased with each other, this means they cannot be assessed separately. For example, in a Resolution III design, main effects are not aliased with other main effects but with other 2 factor interactions. In Resolution III design we will be able to estimate the combination of A+BC, B+AC, and C+AB.

Resolution IV Versus Resolution III. In Resolution IV the main effect is aliased with 3-way interactions whereas in Resolution III the main effect is aliased with 2-way interactions. Since higher-order interactions are usually not significant a Resolution IV Design is preferable to a Resolution III Design.

Comparison of Full Factorial Design Vs Screening

The data below, having four factors namely Speed, Quality, Service, and Density has been assessed in a Full Factorial (16 Runs) and a Half Factorial (8 Runs) Resolution IV design on Minitab. The response variable is Sat which measures the Satisfaction Level. The data in the model is purely fictional and not experimental.

The results of the above are displayed below

In the Analysis of Variance, Coded Coefficients, Regression Equation we can see that the Full Factorial design has 15 degrees of freedom and the Half Factorial design has 7 degrees of freedom.

We can see that the Full Factorial design gives four main effects, six 2-way interactions), four 3-way interactions, and one 4-way interaction. This adds up to the degrees of freedom (4 + 6 + 4 + 1 = 15). Whereas, we can see that the Half Factorial design gives four main effects, and three 2-way interactions (3). This adds up to the degrees of freedom (4 + 3 = 7).

On observing the Alias Structure, we can see that in the Full Factorial design the main effects and the 2,3,4-way interactions are not confounded, however, in the Half Factorial design we can see that the Main Effects are confounded with the 3-way interactions and the 2-way interactions are confounded with other 2-way interactions.

References

https://www.isixsigma.com/dictionary/screening-doe/#:~:text=A%20screening%20DOE%2C%20also%20commonly%20referred%20to%20as,you%20to%20run%20a%20large%20number%20of%20experiments.

For the answer provided below, it is assumed that the readers have understanding about the basics of DOE viz. Levels, Interactions, Main effects etc.

 

DOE overview:

Design of Experiments (DOE) is an advanced application of statistical methods to identify the independent factors that significantly impact a response that we are interested.

 

For instance, if we are concerned about the ‘time to cook’ (Response) for an instant food product, and let us say that we want to study the influence of few factors viz. (1) Quality of ingredients, (2) cooking temperature, (3) moisture content, (4) Quantity of certain ingredients (5) sequence of cooking process and (6) type of preservative.

 

If we want to study the effect of these factors on the response, then we have to vary these factors, try various combinations and observe the results. In this case, we have 6 factors. For varying these factors, the minimum variability that we can subject each factor is ‘2 levels’ and we need to define these ‘levels’ for each factor.

 

If we run a set of experiments to cover all the combinations of variations (2 levels) for each factor, we will have to run 64 experiments (2⁶). Running all combinations of factors and levels is known as ‘Full Factorial Design’. With replication, (running the entire design two times), the number of runs would be 128.

 

Need for screening experimentation:

Imagine if we need to conduct a full factorial experiment with 10 factors, each at two levels. The number of experiments will be 1024. And if we need to do a replication,  we will have to perform 2048 trials.

 

The experimental efforts, time and expenses could be extremely high and would prove as a deterrent to try such a full factorial experiment. In such situations, we can conduct an initial ‘screening’ to eliminate some factors that may not be significant and perform a full factorial with the remaining few factors. This is how the ‘screening experiments’ will be of help.

 

Fractional Factorial designs:

One of the methods used as screening experimentation is ‘Fractional Factorial design’. As per fractional factorial design, we need to run only fewer number of trials. The table below provides that the number of trials for a fractional factorial with 6 factors with “Resolution IV”, is 16.

 

 

 

By conducting trials as per Resolution IV design, we can assess the significance of the ‘Main effects’, but not interactions. Thus, out of the six factors, we will be able to screen out the significant factors.

 

Let us imagine that we found 3 factors as significant out of the 6 factors, after performing the screening experiment. Then, we can study these 3 factors by performing a full factorial and analyze all the main effects and interaction effects. Then, we will be performing only 8 experiments. Even if do a replication it would be 16 trials.

 

Hence, the total number of experiments, including the screening experiments will be 32 (i.e., 16+16), as against the 128 experiments for a full factorial, without screening (6 factors with replication).

 

Similarly, we can workout for 10 factors, the total number of experiments (screening + full factorial for reduced number of factors) can be brought down from 2048 to as low as 64, assuming that we find only 5 factors significant during the screening experiment.

 

It is to be noted that during such a reduction, we are not compromising any critical inferences.

 

Plackett Burman designs:

Another method used for performing screening experiments is ‘Plackett Burman’ design. These are designs of Resolution III, which means that you will be able to identify only ‘main effects’ and interactions are not considered while the screening experiment is conducted.

 

The table below provides options as per the ‘Plackett Burman’ design for various numbers of factors.

 

 

As an example, for 6 factors, you can identify a screening experimental design with 12 runs.

 

Conclusion:

To sum up, screening designs are methods used during DOE that help to significantly reduce the overall number of experiments to be conducted, when we have a large number of factors.

 

This is achieved by ‘screening out' the most significant factors using the screening experiments.

 

Screening experiments will not help to analyze interaction effects. Once we screen out the most significant factors, a full factorial experiment (or equivalent by choosing resolution V or above) can be conducted with the reduced number of factors and subjected to detailed analysis and conclusions.

 

 

Great answers by both Mohamed and Johanan. However, Mohamed's answer has been selected as the best answer for additional inputs on the considerations of screening designs and providing 2 examples.