The experimental processes are difficult to model by physical laws, because a multitude of factors can intervene simultaneously and are responsible for their instabilities and their random variations. Two types of factors are to be considered; those that are easy to manipulate according to the objectives, and those that can vary randomly (uncontrollable factors). These could eventually divert the system from the desired target. It is, therefore, important to implement a system that is insensitive to fluctuations in factors that are difficult to control. The aim of this study is to optimize the synthesis of an apatitic calcium carbonate phosphate characterized with a Ca/P ratio equal to 1.61 by using the experimental design method based on the Taguchi method. In this process, five factors are considered and must be configured to achieve the previously defined objective. The temperature is a very important factor in the process, but difficult to control experimentally, so considered to be a problem factor (noise factor), forcing us to build a robust system that is insensitive to the last one. Therefore, a much simpler model to study the robustness of a synthetic solution with respect to temperature is developed. We have tried to parameterize all the factors considered in the process within a wide interval of temperature variation (60˚C - 90˚C). Temperature changes are no longer considered as a problem for apatitic calcium carbonate phosphate synthesis. In this finding, the proposed mathematical model is linear and efficient with very satisfactory statistical indicators. In addition, several simple solutions for the synthesis of carbonate phosphate are proposed with a Ca/P ratio equal to 1.61.
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