The Psychology of Quality and More
Design of Experiments (DOE): How to understand it
How to understand it
In many problem situations, it is a common mistake to assume immediately that the most obvious factor is the sole cause, and to devise a solution based on this assumption. It is also common to be surprised when the solution is not as effective as hoped. For example, a horticulturist may find that a fertilizer causes leaf burn in warm weather and immediately assumes that temperature is the only cause. However, the only way to know this is to recognize all possible contributory factors and to perform a series of experiments where these factors are varied in a controlled way. Thus the horticulturist might recognize humidity and illumination as additional factors that can affect the biochemical reactions within leaves.
When performing an experiment, there are two things that can be changed: factors and their levels. A factor is a measurable item such as humidity or temperature, which, when changed, might affect the result of the experiment. The levels of the factor are the set of values, such as 20 or 30° C, that the factors may have. In any experiment, there are a number of trials in which the levels of a fixed number of factors are varied, as illustrated in Fig. 1.
Fig. 1. Trials and factors
The complete set of possible combinations of levels and factors in an experiment is called the full factorial, and is often too large to perform a trial using each combination. A significant part of 'Design Of Experiments' is in determining what subset of the full factorial (or fractional factorial) should be selected for trial. A common approach is to vary just one factor, keeping all other factors at constant levels, but this can result in an incomplete picture as the effect of interactions between factors is ignored, as illustrated in Fig 2.
Fig. 2. Factorial combinations
A set of trials that forms a consistent and complete experiment follows several rules. A balanced experiment ensures 'fairness' by requiring that the different levels of each factor occur equally often. In an orthogonal experiment, the effect of different factors can be separated out so separate causes can be identified (a test for this is illustrated below). The effects of all factors should also be measurable or estimable to a reasonable degree.
Fig. 3. Orthogonal and balance
In practice, many experiments can be simplified by using only two levels of each factor. This may occur naturally or it may be used when a single change in level will show whether the factor is significant or not.
Once the experiment is completed, the problem is to determine the real effects of each individual factor. There are statistical approaches to this, but a simple and effective way is to plot the average values of each factor and level, both individually and in combination, as illustrated. The most significant individual factor will thus have the steepest line, although this will also depend on the levels used. Significant combinations of factors will have lines with large angles between them (a good sign of significance is where the lines cross one another).
Fig. 4. Results of experiment
And the big