Design of Experiments

Design of Experiments (DOE) is a study of the factors that the team has determined are the key process input variables (KPIV's) that are the source of the variation or have an influence on the mean of the output.

A DOE (or set of DOE's) will help develop a prediction equation for the process in terms of Y = f(X1,X2,X3,X4,....Xn).

DOE are used by marketers, continuous improvement leaders, human resource professionals, sales managers, and many others.

The DOE study is done by setting up an experiment with a specific number if runs with one of more factors (inputs) with each given two or more levels (settings).

A DOE with 3 levels and 4 factors is a 3×4 factorial design with 81 treatment combinations. It may not be practical or feasible to run a full factorial (all 81 combinations) so a fractional factorial design is done, where usually half of the combinations are omitted.

Statistical software will help manage the entire DOE.

1) Enter the factors
2) Set the levels (at least two for each factor)
3) Determine how many runs (full factorial, fractional factorial)
4) Run the experiment at each treatment level
5) Enter the response for each treatment level
6) Use statistical software to use ANOVA on the data
7) Continue to refine until prediction equation is obtained
8) IMPROVE the KPIV's
9) Last phase is CONTROL the KPIV's

Other methods of experimentation such as "trial and error" or "one factor at a time (OFAT)" are prone to waste, will provide less information and will not provide a prediction equation. These may seem easier to run and get results but the risk is a less robust solution and decisions made on a poor experiment.

These input factors behave to create an output, the team needs to make improvements in the IMPROVE phase that control the inputs. Controlling the input factors will provide the desired response.

The DOE will quantify the factor interactions and offer a prediction equation. This ANOVA will help indicate which factors and combinations are statistically significant and which are not thus giving direction to the priority of improvements.

DOE Assumptions since ANOVA is used to analyze the data:

1) The residuals are independent
2) The residuals have equal variance
3) The residuals are normally distributed
4) All inputs (factors) are independent of one another

Most prediction equations will be linear and reliable when using only two levels. This saves time, money, and other resources while obtaining a satisfactory prediction equation.

Prediction equations are useful to analyze what-if scenarios. Many times data can not be collected at all levels and factors so a prediction equation can be used to estimate the output.

The input factors are x's and the response is Y-hat.

3 * 3 Full Factorial

The team has determined that coefficient of friction of surface, ambient temperature, and tire pressure are three critical input factors (KPIV's) to study.

The goal isn't always to maximize MPG but to understand the impact on vehicle MPG based on these factors. The problem statement may be to improve the accuracy of MPG claims on this specific vehicle.

DOE jargon