In R&D environments in industry, experiments are carried out to gain knowledge. But what actually is knowledge, and what does it look like?
Often the objective of experiments is to find better or optimum settings; but we believe the knowledge gained from an experiment should go beyond just identifying best settings.
First of all, experiments should be set up according to the principles of Design of Experiments. But unfortunately in our consultancy practice we see a lot of experiments that violate these principles and, as a result, fail in the sense that no conclusions at all can be drawn from them.
Take the following simple example in which a food manufacturer wants to develop a new product, a cake mix. There are four ‘ingredient parameters’ and two ‘home bake parameters’ that are expected to have an effect on the taste score (the higher the score, the better) as by a taste panel:
Our first question might be, ‘what are the best settings of the six factors within their ranges?’ But while it may be nice to know these ‘best’ settings, in reality the factors vary only minimally.
Because we don’t want the taste score to drop drastically should we deviate just a little from the ‘best’ settings, our next question is about sensitivities: ‘what happens to the taste score when the factors are changed a little?’
For this reason, the output of a DoE should not only give the best settings but also the sensitivities over the whole range of settings. The CQM Excel add-in displays such sensitivities in a graph. So for the cake-mix example, the sensitivities might look like this:
The blue line on the left of the graph shows what happens to the taste score as we change factor A ( amount of Fat) from low (4 grams, coded as -1) to high (7 grams, coded as 1) while all other factors remain at their mid-range values. It shows an average increase in taste score from 4.9 to 5.1.
Similarly, the other blue lines show the respective effects for the factors B, C, …, F.
The right of the graph shows three interactions: AB, AE and CF. An interaction shows the combined effect of two factors (e.g. the interaction AB shows the sensitivity for Fat when the amount of Fibre is 1 gram (green line) and when the amount of Fibre is 2 grams (red line). The difference between these sensitivities (given by the red and green lines) defines an interaction between Fat and Fibre.
The sensitivities in the graph can also be written in a mathematical equation:
taste score = 5 + 0.1*A – 0.4*B + 0*C + 0.3*D + 0*E + 0.6*F + 0.3*A*B – 0.4*A*E + 1.2*C*F + error
where A, B, …, F are settings for the six factors on the coded scale from -1 to 1 and the error summarizes the ‘random’ variations due to all other factors that were not kept constant during the experiment.
Such a mathematical model is also called a transfer function. It approximates the behaviour of the baking process and therefore helps us understand how the process works, and can be used for further calculations including:
- prediction of the taste score over the whole design space
- calculation of the best settings for the factors A, B, …, F
- prediction of the mean and spread in taste, when the factors A, B, …, F show spread at the customer (see more at /cake-mix-case)
- trade-offs in case of conflicting responses (see more at /cake-mix-case),
- finding a robust design. That is, the recipe that is the least sensitive to variations in baking time and oven temperature in home-use situations (see more at /cake-mix-case)
- trade-offs and tolerance analysis (see more at /robust-design-and-tolerance-analysis)
We believe transfer functions are an extremely useful way to summarize and communicate knowledge. They not only give a full understanding of the process, but are also easy to document and transfer.