# 14.3: Design of Experiments via Random Design

## 3.1 Introduction

Random design is an approach to designing experiments. As the name implies, random experimental design involves randomly assigning experimental conditions. However, numbers should not be picked without any thought. This type of experimental design is surprisingly powerful and often results in a high probability to create a near optimal design.

1. Choose a number of experiments to run (NOTE: This may be tricky to pick a number because it is dependent upon the amount of signal recovery you want.)
2. Assign to each variable a state based on a uniform sample. For instance, if there are 5 states, each state has a probability of 20%.

Random designs typically work well for large systems with many variables, 50 or more. There should be few interactions between variables and very few variables that contribute significantly. Random design does not work very well with relatively smaller systems. Generally speaking, Taguchi and random designs often perform better than factorial designs depending on size and assumptions. When choosing the design for an experiment, it is important to determine an efficient design that helps optimize the process and determines factors that influence variability.

There is more than one type of random design, randomized block design and completely randomized design. Randomized block design involves blocking, which is arranging experimental units into groups so they have a common similarity. The blocking factor is usually not a primary source of variability. An example of a blocking factor may include eye color of a patient, so if this variability source is controlled, greater precision is achieved. Completely randomized design is where the groups are chosen at random.

In various technological fields, it is important to design experiments where a limited number of experiments is required. Random design is practical for many design applications. Extensive mathematical theory has been used to explore random experimental design. Examples of random design include areas of data compression and medical imaging. The research conducted to support the practical application of random design can be found at <http://groups.csail.mit.edu/drl/journal_club/papers/CS2-Candes-Romberg-05.pdf>.

Other research has been conducted recently on random design, and more information can be found at: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1614066

## 3.2 Completely Randomized Design (CRD)

### 3.2.1 Description of Design

Completely randomized design (CRD) is the simplest type of design to use. The most important requirement for use of this design is homogeneity of experimental units.

### 3.2.2 Procedure for Randomization

1. Assign treatments to experimental units completely at random.
2. Verify that every experimental unit has the same probability of receiving any treatment.
3. Perform randomization by using a random number table, computer, program, etc.

### 3.2.3 Example of CRD

If you have 4 treatments (I, II, III, IV) and 5 replicates, how many experimental units do you have?

{I} {IV} {III} {II} {II} {III} {III} {II} {I} {III} {I} {IV} {III} {IV} {I} {IV} {II} {I} {II} {IV} =20 randomized experimental units

## 3.3 Randomized Block Design (RBD)

### 3.3.1 Description of Design

Randomized block design (RBD) takes advantage of grouping similar experimental units into blocks or replicates. One requirement of RBd is that the blocks of experimental units be as uniform as possible. The reason for grouping experimental units is so that the observed differences between treatments will be largely due to “true” differences between treatments and not random occurrences or chance.

### 3.3.2 Procedure for Randomization

1. Randomize each replicate separately.
2. Verify that each treatment has the same probability of being assigned to a given experimental unit within a replicate.
3. Have each treatment appear at least once per replicate.