**2. Material and methods**

The experimentation strategy is an approach to conduct and planning. The best-guess approach, combined, mixture and one-factor-at-a-time approach and factorial experimentation are the main approach used. One-factor-at-a-time for each factor consists of baseline level selected as reference, then varying successively factor in its range remaining and fixing the other factors in the goal to analyze the representative or abstruse factors joint effect on the response.

In this strategy, experiments are conducted by simultaneously varying six factors over two levels (namely low level and high level). The two levels are so chosen that they cover the practical range of the parameters under consideration **Table 1**. This case study presents an example of using the response surface for the modeling of the swelling pressure *Ps* (**kPa**) and the analysis of results with


#### **Table 1.**

*Factors for response surface study.*

ANOVA. For the presented implementation of DOE technique, Design-Expert10 software was employed to obtain the appropriate functional equations. The right tools at knowledge of research take in account mathematics and statistics to solve the problem considering each potential of the approximation.

The response surface methodology RSM in DOE techniques is widely used for machining processes. Experiments based on RSM technique relate to the determination of response surface based on the general equation [25]:

$$\mathbf{y} = \mathbf{A\_0} + \mathbf{A\_1}\mathbf{x\_1} + \dots + \mathbf{A\_l}\mathbf{x\_l} + \mathbf{A\_{12}}\mathbf{x\_1}\mathbf{x\_2} + \mathbf{A\_{13}}\mathbf{x\_1}\mathbf{x\_3} + \mathbf{A\_{11}}\mathbf{x\_1}^2 + \mathbf{A\_{1j}}\mathbf{x\_l}^2 \tag{1}$$

Where A0 , Ai , A*ij* are respectively interaction, linear, quadratic and intercept coefficients. xi input independent variables. Continuous factors affect the quantitative response which is analyzed by response surface methodology (RSM), this later best fitting representative critical factors, commonly chosen in the screening phase of the experimental program. The final obtained results using RSM are polynomial models display the true response surface in the best approximation over a region of factors.
