DoE, as simple as preparing a “suspiro de limeña”​

Part I Do you have an idea and do not know how to go from theory to practice? How many trials will be the minimum required to reach reliable conclusions? Perhaps this is one of the most frequent questions when starting a new project to evaluate the improvement of a process or create new products. Before embarking on a new adventure, you should have a thorough knowledge of the subject of study, define the problem you want to solve, determinate the objectives, establish the parameters you want to evaluate and the response you are going to measure, as well as, the units of measurement that you will use to quantify them. Among the tools we have available, we find the design of experiments (DOE). DOE is a methodology that relies on statistical tools to reach objective and truthful conclusions. Although it is a very powerful tool, it can only be supported by an expert in the study field whom can provide a correct interpretation of the results. Previous concepts, In DOE, our parameters or variables are called factors, and each value taken by that parameter (factor) is known as level. Classic factorial designs are two-level designs, it means, if you have the temperature as a factor, you could choose two temperature values, 40 ° C and 80 ° C, in these cases usually maximum and minimum values are used. But there is also the possibility of working with factors with more than two levels. We will go a little further and we would work with factors of more than two levels, but not all with the same number of levels, but with different amounts of levels. When one works with factors at different levels, we call them multilevel design. To understand a little more the application of DOE, we will present the preparation of Suspiro de limeña (limeña's sight, a dessert from Perú capital city, Lima). Suspiro de limeña is a dessert created in Lima, whose name was inherited from the poet José Gálvez. History says that José's wife prepared a dessert so soft that the ecstatic poet said it was as soft as the sigh of a Lima lady. The following example was performed using Stat-Ease® Design-Expert® software (https://www.statease.com/). For our example, we will focus on preparing the delicious suspiro de limeña (the manjar de yema or manjar from yolk). Suspiro de Limeña can be prepared with milk, sugar, egg yolks, and fruit extract. For our example, milk, sugar, fruit extract and cooking time will be our factors. In table 1 we can observe each factor and its respective levels.

Table 1. Factors and levels of the design of experiments.

The preparation of suspiro de limeña is divided into the following stages: 1. The milk is mixed with 30 g of sugar and boiled (Mix A). 2. Other 30 g of sugar is mixed with the yolk and beaten (Mix B). 3. Beat together A and B until you get the napa point (when dividing the mass with a spatula, the mass does not come together). The mixing is carried out under slow heating, at a temperature not exceeding 80 ° C. 4. Finally, let it cool and add the extract of your favorite fruit. This recipe will let you enjoy the suspiro de limeña delicacy with your favorite fruit.

Figure 1. Fruits ready to be used in our suspiro de limeña delicacy. Once our factors and levels have been defined, as well as the method of preparation of the suspiro de limeña delicacy, we have to identify our response. In this case, we will choose the color as response, we will use a scale from 1 to 10, where the lower value will indicate a color with a lighter hue. We already have our factors, levels, and response stablished, so we will generate our multilevel design of experiments (DOE). Let's experiment!

Table 2. Multilevel design of experiments generated for the factors and levels established. Wait for the next publication on DOE, now it's time to evaluate the results. Let's analyze the results! ©Daniel Obregón, 2019