Types of Design of Experiments

Trials are run at all possible combinations of factor settings. The sample size is the product of the numbers of levels of the factors. For example, a factorial experiment with a two-level factor, a three-level factor and a four-level factor has 2 x 3 x 4 = 24 runs.

Full factorial designs are often too expensive to run, since the sample size grows exponentially with the number of factors.

They are typically used when the number of factors and levels are small, and when we want all possible interaction information. Hence the most commonly used factorial designs are 2^k full factorials.

Screening designs are among the most popular designs for industrial experimentation. They’re typically used in initial stages of experimentation to narrow down the long list of potentially important factors and interactions to only a few important effects.

Screening designs usually require fewer experimental runs than other designs. The experiments are small and efficient, involving many factors.

Some classical screening designs include fractional factorial designs, Plackett-Burman, Cotter and mixed-level designs.

Goal: Used for exploratory purposes (for example, to identify a handful of important effects).

Response surface experiments are typically used in the latter stages of experimentations when the important factors have been identified. It usually involves a small number (generally two to eight) of continuous factors that have been identified as active.

It is used to model the curvature in the relationship between the factors and the response. It allows us to find settings of our factors to minimize or maximize a response or to hit a specific target.

In order to estimate the curvature, the design requires at least three levels for the factors. As a result, response surface designs can get extremely large unless the number of factors is limited.

Goal: To optimize processes by developing a predictive model of the relationship between the factors and the response.

Mixture designs are used when factors are interdependent, and when each component in a mixture is dependent upon the settings of other component settings. For example, in the case of stainless steel made up of Fe, Cu, Cr and Ni, the relative proportions of these components contribute to the properties of resulting steel.

A factor's value is its proportion of the mixture, which falls between zero and one. Mixture experiments have three or more factors with the sum of the factor proportions equal to one (100%). Hence, its experimental space is typically triangular and forms a simplex.

Some types of mixture designs include simplex centroid, simplex lattice, ABCD design and extreme vertices. Learn more.

Goal: Optimize recipe for a mixture of several ingredients.

Split plot designs are typically used when an experiment involves hard-to-change variables, i.e., temperature of an industrial oven or the location of a cornfield. Traditional randomized experiments require factors to be tested for each run, which is impractical in this case.

Split plot designs is a blocked experiment, having the blocks serve as experimental units for a subset of factors. In split plot experiments, a treatment is applied to more than one experimental unit because a factor(s) is associated with batch processing, or it is hard or costly to change. 

As a result, split plot experiments are more practical to be carried out in the industrial world.

Some types of split plot designs include split-split plot design (nested relationship) and strip plot design (cross relationship).

Goal: Enable experiments to be carried out even with presence of hard-to-change variables.

Taguchi array designs are used to identify signal factors (or control factors), which minimizes the effect of noise factors that are typically difficult or expensive to control.

It is carried out based on Taguchi’s inner and outer array approach. Inner array: control factors to find optimum settings. Outer array: noise factors looking at how response behaves in wide range noise conditions.

The alternative method used is combined arrays, which are generally more cost-effective and informative than Taguchi arrays.

Goal: To ensure consistency in output, by finding control factor settings that generate acceptable responses despite natural environmental and process variability.

Definitive screening designs are mostly used in the earliest stages of experimentation. Unlike traditional screening designs, which usually require follow-up experimentation to resolve ambiguity if there’s any two-factor interaction, definitive screening design can reliably accomplish the task of screening even if there are a couple of second-order effects.

This is a highly efficient design that avoids model ambiguity and enables us to identify important factors quickly and efficiently. It estimates main effects and quadratic effects, and when only a few of the factors are important, you can also estimate some of the interaction effects.

Goal: To study many factors at once and identify the most important factors. Sometimes also used for optimization.

Custom designs are used in almost any experimental situations, including factor screening and optimizations. They’re designs of experiments that are customized to solve our problem.

Custom designs do a better job of achieving our experimental goal in just one experiment. For example, if we want to study four factors, and our experimental goal is optimization. Three of the factors are continuous, and the fourth is a two-level categorical variable. Due to budget constraints, we’re limited to conduct only 14 trials. None of the existing traditional designs fits the bill, but we can use custom designs to solve our problem. See more examples.

Custom design is the more efficient method in experimentations, offering far more flexibility to researchers. Most practitioners use custom designs in their work to save time and cost.

Using JMP software, we can easily construct a design that fits our use case and scenario best. 

Goal: Construct optimal designs that fit our needs.