**5. Factorial Design for Drug Delivery**

Design of Experiments (DoE) is defined as a planning strategy that will be carried out to obtain the information from the collected data effectively. It is a structural method used to determine the relationship between different factors (independent variable, input, process parameter, formulation component, etc.,) and their responses (dependent variable, response variable, output, product quality feature, etc.,). Also, this model is a mathematical model that correlates all the relevant factors and the results obtained against these factors. The results can be interpreted, predicted and the design space can be determined by optimization with this mathematical model. Systematic DoE approaches have advantages such as less experimental study, easier problem identification and prevention, any active agent adjuvant interaction and product performance to guarantee an effective formulation, and process optimization for good results in the scale up process.

An ideal drug form design should be depended on the understanding of the physicochemical and mechanical transformations of the materials that will eventually turn into the desired product. However, due to the diversity and complexity of the drug components, it is usually not fully understood. Factorial design with a systematic approach the product and production process can be understood in depth. In this way, a development approach can be provided which takes into account the variability of the inputs and other risks that may arise against product quality.

It is very important to obtain the basic knowledge of the study in order to produce as much information as possible with the right modeling. The statistical analysis is the first stage of experimental work before optimizing the formulation. Simple models are used in statistical screening. For example, linear models with only the main factor effects, or linear models, including binary interactions. In this way, the factors that have the most effect on the outputs are determined with the least number of tests possible. Factors with little or no significant effect can be displayed. In addition, by decreasing the number of factors, optimization design with a smaller number of attempts can be used.

The choice of DoE should be based on the number and type of factors to be investigated. For example, if the goal is only to reduce the number of factors and find a few factors that have the highest effect on the outputs, and if there are too many factors to be investigated, then the statistical elimination by constructing linear models can be selected. The results consist in lowering the number of attempts and evaluate only the main factor effects. The most preferred statistical screening methods in drug formulations are two-level partial full factorial design and Plackett-Burman design [12].

After statistical screening, response surface modeling (RSM) designs are started. The number of factors should be reduced by the statistical elimination design before the RSM design, so that the number of trials is not high and the statistical significance is important/relevant or other synonym and strong prediction models can be established. RSM is an approach where statistical and mathematical techniques are used together for the development and optimization of pharmaceutical processes. Includes modeling techniques used to determine the relationship between dependent variables and the independent variables that affect them.

RSM designs for drug formulations allow us to understand the relationship between factors and response variables, as well as factor interactions (synergistic effect of two or more factors), quadratic effects, and cubic terms. In this way, the optimum value ranges of the factors are provided. Process problems can be solved. Robust processes that are less sensitive to process variability can be developed.

Each additional experiments and sample analysis performed to product development in the pharmaceutical industry means that spending a lot of money, time and labor loss. The selection, implementation and interpretation of the appropriate factorial design that serves to reach the result accurately and rapidly is very important. Selecting the appropriate experimental design ensures that development studies are completed with a small number of trials. In order to optimize the process and formulation, mathematical models are described that best relationship between these critical factors and quality characteristics [13].
