First of all, full factorial design can only be used to fit two factor interaction mode (2FI model) and can not fit quadratic model  (second order terms) due to the main effects are confounded with the interaction effects. This is the nature of full factorial design. There are many reasons why when the model can be precise to predict the data when you added a lot of non statistically significant terms (p-value>0.1). These reasons could be:

To build better model for prediction, it is advisable to fit your data using second order model (second order model is the best for optimization. By fitting your data using second order model, more terms will be included in your final predictive model. Thus, better model can be established. In order to fit your data with second order model, there is a need to use response surface design instead of using factorial design. Furthermore, second order model tells you if there are variations in your measurements or if there is something unusual in you data by estimation lack-of-fit test. Lack-of-fit test must be insignificant in order your model to predict precisely.

First of all, full factorial design can only be used to fit two factor interaction mode (2FI model) and can not fit quadratic model  (second order terms) due to the main effects are confounded with the interaction effects. This is the nature of full factorial design. There are many reasons why when the model can be precise to predict the data when you added a lot of non statistically significant terms (p-value>0.1). These reasons could be:

To build better model for prediction, it is advisable to fit your data using second order model (second order model is the best for optimization. By fitting your data using second order model, more terms will be included in your final predictive model. Thus, better model can be established. In order to fit your data with second order model, there is a need to use response surface design instead of using factorial design. Furthermore, second order model tells you if there are variations in your measurements or if there is something unusual in you data by estimation lack-of-fit test. Lack-of-fit test must be insignificant in order your model to predict precisely.

Dear all,

In the factorial design, I often use 3 coded level: -1, 0, +1 (and I am also wondering if you can apply 3 level like me, maybe it will be better). And then, the total of experiment runs can be calculated as follows = 3^n, where n is the numbers of factors. Therefore, the total for runs by using factorial (3^3 for factorial runs and 6 for estimate pure error) is more than when using CCD or BBD design (about 20 runs for 3 factor and 5 coded levels). For my opinion, the fit of the model depends on many reasons: selection of main parameters, limitation range of each parameter, accuracy of experimental responses,... 

For me, if P-value > 0,05 this term is insignificant for the suggested model and of course this term must be removed from the model. For instance,  factor C is not significant due to its P-value is more than 0.05. However, if the interaction effect between A and C with P-value is less than 0.05 then we can consider this term can be available in the model. I have seen some similar  conclusions from previous research papers.

Thanks for good questions and answer. I have got new acknowledge from such questions and answers.

Good luck,

 Dang

The main problem with factorial design ' Confounding' . Confounding means we have  lost the ability to estimate some main or interaction effects. From my point of view as  a mechanical and material engineer, the response could be very sensitive to the parameters even if the p-value of the factor is more than 0.05. Thus, it is recommended to use a Stepwise method (do not use backward technique as it removes the P-values with more than 0.05) when you want to remove insignificant model terms. Stepwise technique removes insignificant model terms have p-value more than 0.15. Again, try to use response surface design or custom response surface design to build better model. If you tell me how many number of factor then I will be bale to advise you?

Regards 

Hello both of you,

thanks a llt for your anwers. 

Omar, I have 15 parameters to study. I tried to directly do a 3 level design (surface response) with all parameters at the same time, but the software I used, called Minitab, is not able to generate a plan with 3^15 configurations. If I could do that, I would have used D-optimal plan to reduce the number of configurations while being able to find a model with all parameters studied at the same time. As I cannot, I tried first to identify the main parameters with a fractional Taguchi design but I know that the interactions are confounded. In the book I use as reference for DOE, they say that only interactions between significant terms (pure effects), can be considered. But, as you suggested, I found that sometimes when A is significant and B is not, A*B can be sigificant. So when I do a surface response plan only with the significant terms, I miss the effect of A*B because I did not take B as an input...Maybe I will have to use a more advanced software or reduced the number of input parameters...

Please try to use D-optimal design using JMP software. This is the best you can do. I have found that by using D-optimal design through JMP software, the total number of runs is 18 runs. Custom designs are much better than factorial designs. 

Omar, 

Ok I think you are right about D-optimal plans. But do you know how to choose the number of tests ? I have to looke to the D-optimality parameter maybe ? But I don't know much about it...

Thanks.

Rémi

Rémi,

By using this software, you only need to specify the number of factors and number of levels, then the software will give you the total number of tests required. Please note that D-Optimal design is mainly for screening factors. But V-optimal design is used for optimization and is recommended method for response surface methodology. Good luck with your experiments. 

Dear colleagues,

the noted problem in Rémi’s question takes place in the cases of construction of any non-linear stochastic models, including non-linear regression models. Usually, for the construction of non-linear regression models the brute force method is used. To exclude the use of a simple brute force algorithm for the construction of non-linear regression models, we use the approach based on the normalizing transformations. This approach is as follows.. First, we normalize the original data (we transform the non-Gaussian data into the approximately Gaussian data) using the normalizing transformations. Second, we build a linear regression for the normalized data. Finally, substituting the corresponding the normalizing transformations in the linear model, we obtain a non-linear regression model for the original data. Typically to normalize the data we use the Johnson translation system (JTS) because unlike others normalizing transformations (e.g., log, Box-Cox) for JTS we can determine the type of the non-linear normalizing transformation (Johnson's family) before performing the normalization of the data. This we can determine from the values of estimates of skewness and kurtosis.