## Design of Experiment

 Design of experiment (DOE)is one of the four major data collection methods for statistical analysis. Below are listed the four different ways that data can be collected. Collected data is called a sample.

• Collecting historical data.

• Collecting new data from the natural process.

• Collecting new data by disturbing the natural process.

• Collecting data from specially designed experiments.

Design of experiment is based on conducting the experiment in controlled conditions so that the relation between specific factors and the outcome of the experiment can be understood and alternative explanations of the outcome can be eliminated. DOE is a fundamental tool of experimental research, measurement system analysis and statistical analysis.

## Types of Design of Experiment:

The science of statistical experimental design relies on following types of DOE:

1. Single Factor Experimental Testing: The outcome of the experiment depends on one factor only, which is varied in controlled manner.

2. Multivariate Testing: The outcome of the experiment depends on two or more factors. The DOE for multivariate testing can be further differentiated into three subtypes:

1. Discrete Choice Modeling: Modeling of experiments where one or more choices are left to make other choices.

2. Optimal Design Modeling: Experiments are conducted in waves to determine the best results in shortest possible time under the varying relationships and constraints.

3. Taguchi Methods: The experiment is conducted by controlling the environment as well as the control variables.

3. Factorial DOE: Factorial design covers those experiments which depend upon two or more 'discrete level' control variables, and the experiment can take any combination of these variable levels. Factorial designed experiments can be conducted in two ways:

1. Full Factorial Design: This experiment is conducted in all possible combinations of the discrete variables on which outcome depends.

2. Fractional Factorial Design: When the number of combinations for full factorial DOE is too large, the experiment is conducted at only some possible combinations (at least half are omitted).

## Examples of the Design of Experiment:

1. The effectiveness of a certain drug for treatment of a disease is to be ascertained. Two similar experiments are conducted in parallel. Each experiment consists of a control group (which receives no treatment) and an experiment group (which receives the treatment). Members of each group are statistically selected according to the principles of experimental research. The outcomes of both the groups are compared, and the hypothesis is accepted or rejected only if results from both experiments agree.

2. An engineer wants to ascertain the performance of an electric motor at different speeds. He conducts the experiment on two machines (designated as A and B) and runs them at 2000 and 3000 rpm. A full factorial DOE will have the following levels: (speed of machine A, speed of machine B): (2000,2000), (2000,3000), (3000,2000), (3000,3000). Based on the results, the engineer can determine how a similar machine would perform under similar conditions.

## Summary

 Design of Experiment is a basic mechanism of measurement system analysis, statistical analysis and experimental research. It refers to the conduction of specially designed experiments under conditions where factors that can influence the outcome of the experiments can be controlled. Based on the results of such experiments, hypotheses can be accepted or rejected. Experimental design is generally conducted on samples but the results are expected to hold true for the entire populations.

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