# Purpose of Design of Experiments

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The purpose of the design of experiments is to find a combination of input variables that will result in an output variable with the desired value.

The goal of any experiment is to obtain information about the relationship between one or more independent variables and a dependent variable. This relationship is often described by a mathematical model that relates the independent variables' values to the dependent variable's value. For example, if you want to know whether increasing the amount of fertilizer increases crop yield, then your independent variable might be the amount of fertilizer, and your dependent variable could be crop yield. In addition, crop yield could be affected by many other independent variables, such as temperature, rainfall, seed variety, humidity, soil type, etc.

The number of possible combinations of inputs can be very large, so it's important to use some sort of optimization method to find the best combination. This is done using a statistical model for the relationship between the input and output variables.

### 1. To identify and narrow down the factors affecting the output.

Design of Experiment is used when you want to know what factors significantly affect the output. You may also want to know if there are any interactions between two or more factors.

Knowing the factors that do NOT affect the output is equally important. If an input does not affect the output significantly, that knowledge can help consider the cheaper or easier options.

### 2. To model the process response

Once you have narrowed down the key inputs, you would want to create a mathematical model of the process. This model can help you understand how the input variables affect the response.

### 3. To determine the optimum conditions for the process.

Once you have identified the factors that affect the output, you need to determine the optimum level of inputs that will lead to the desired output. The goal could be to maximize, minimize or achieve a target level of the response variable.

## Conclusion

Experimental Design helps us understand the relationships between different factors and their effects on the output. It allows us to make predictions about the behaviour of our system under different conditions.

## Exponential Distribution

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