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## Quick reference

### Theory of Design of Experiments

The theory behind Design of Experiments is that a mathematical model can be created by statistically analysing the values of the output factors (response) based upon controlled set of input factors. This statistical model generates high confidence in the ability to design the system and optimize the performance.

### When to use

The DOE analysis should be used when there is a need to understand how multiple factors can impact the performance of product, process, or system.

### Instructions

An understanding of the basic theory behind DOE can be helpful when design the study and analysing the data. DOE develops a mathematical model of the effect of each of the control factors on the output or response factors. This model can be used to optimize performance, design process settings and tolerances, and identify critical factors for problem solving.

The DOE method uses all the data, unlike Trial and Error or OFAAT which may include tests that do not contribute to the design or the solution of the problem. The analysis is a statistical analysis that can provide confidence levels for the model that is created. The analysis can also be used to determine appropriate tolerance levels for the control or input factors to ensure the output or response is always acceptable.

The DOE model is different from a physical model. A physical model will often include chemical and biological effects and interactions. It is usually much more complex than the DOE mathematical model. Because the DOE mathematical model is based upon an analysis of the factors within a certain region (low level to high level) it is only valid when factors are within that region. Since the DOE model is a mathematical model, it can normally be solved mathematically to determine an optimum set of input factors for best performance.

The DOE method is used in design analysis whenever there is a new product or technology that is not well characterized. This may be due to new factors that are being controlled, or new capabilities that are required. This analysis defines the design space of the product, process or system.

The DOE is also an excellent analysis for understanding how to control a product, process, or system to eliminate or minimize a quality defect or problem. The DOE model can be manipulated to minimize cost, cycle time, or quality defects.

### Hints & tips

- A DOE is only as good as the factors included in the analysis. Later lessons will focus on factor selection, which is key to a good analysis.
- The statistics used in creating a DOE model are straightforward. Later lessons will show how to use statistical applications to do the analysis and how to conduct the analysis using a spreadsheet like Excel.

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