A food company decides to improve the taste of one of the jams it produces. To do so, different prototypes of the jam are prepared by varying the content in grams of three ingredients of the formula. Each prototype is then given to different consumers who grade the taste using a questionnaire. The overall score of each prototype is an average of the answers to the questionnaire's questions.
The 3 factors involved in the experiment, together with their low and high levels, are shown in the following table.
The objective is to decide which prototypes will be used and analyze the results once the experiment has been done. There is a restriction that must be taken into account in the design of the experiment: it is not possible to experiment with all factors at the high level or all factors at the low level.
At this stage of the study, we want to perform an experiment that makes it possible to obtain a model with purely quadratic terms. One can use the Box-Behnken design which has the advantage of never experimenting with all factors at either high or low levels.
Stat > DOE > Response Surface > Create Response Surface Design
We carry out the experiments in random order as proposed by Minitab. The following table shows the answers for each of the experimental conditions: