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To identify the effect of (Taguchi design‐) screened CPPs (independent variables) such as castor oil concentration (1–2 ml, A), chitosan concentration (6–18 mg, B), and poloxamer concentration (75–100 mg, C) on the three CQAs (dependent or response variables) like MPS (R₁), PDI (R₂), and ZP (R₃), a three‐factor face‐centered central composite design (CCD) was used. A total of 20 experiments, including 6 replications of central points (the leverage value of 0.1182 and α value of 1) together with 8 factorial points and 6 axial points (shown in Table 2.6), were run using Design‐Expert^® software. While the leverage value indicates the potential for a design point (axial, central, or factorial) for influencing the model fit, the α value determines the geometry of the design region and for face‐centered CCD, it is equal to 1 defining a square design geometry. Table 2.7 summarizes the screened CPPs and their levels. The values of CQAs were fed into the software and second‐order mathematical model was used to study the factor–response (CPPs–CQAs) relationship. An appropriate polynomial model was chosen based on the significant terms (p < 0.005, ANOVA), the least significant lack of fit, coefficient of variance, the multiple correlation coefficient, and adjusted multiple correlation coefficient provided by Design‐Expert^® software. The center point was repeated six times to determine the repeatability of the method.

Figure 2.5. Half‐normal and Pareto charts for screening of influential formulation and process variables as per Taguchi design using selected critical quality attributes (CQAs): (a) mean particle size, (b) polydispersity index, and (c) zeta potential.

TABLE 2.6. Independent and Dependent (Response) Variables: Face‐Centered Central Composite Design (CCD) Scheme

Run	Type	Critical Process Parameters (CPPs, also Called as Independent Variables)	Critical Quality Attributes (CQAs, also Called as Dependent Variables)
Castor Oil (ml)	Chitosan (mg)	Poloxamer (mg)	MPS (nm)	PDI	ZP (mV)
1	Axial	2	12	87.5	676.4	0.655	27.6
2	Center	1.5	12	87.5	609.8	0.655	27.2
3	Factorial	1	18	75	247.6	0.376	24.6
4	Axial	1.5	12	75	396.4	0.275	35.5
5	Axial	1.5	18	87.5	449.4	0.661	29.1
6	Center	1.5	12	87.5	609.8	0.655	27.2
7	Factorial	2	6	100	417.1	0.62	17.1
8	Factorial	2	18	100	438.1	0.469	23.2
9	Factorial	2	6	75	390.5	0.438	28.5
10	Center	1.5	12	87.5	609.8	0.655	27.2
11	Axial	1.5	12	100	441.5	0.488	18.8
12	Axial	1	12	87.5	374.2	0.435	33.6
13	Axial	1.5	6	87.5	333.9	0.408	30.6
14	Center	1.5	12	87.5	609.8	0.655	27.2
15	Factorial	1	6	75	240.1	0.287	17.9
16	Factorial	1	6	100	447.6	0.676	15.6
17	Center	1.5	12	87.5	609.8	0.655	27.2
18	Factorial	1	18	100	453.4	0.62	25.1
19	Factorial	2	18	75	492.8	0.537	20.9
20	Center	1.5	12	87.5	609.8	0.655	27.2

MPS, mean particle size; PDI, polydispersity index; ZP, zeta potential.

Each row indicates an experiment while the columns present the composition and the critical quality attributes (CQAs) of the non‐phospholipid‐based topical ophthalmic emulsions.

The search for design space and optimized emulsion formula was carried out by numerical and graphical techniques using the software. The interaction effect of the CPPs on the CQAs was visualized using the response surfaces and 3D contour plots of the fitted polynomial regression equation. Furthermore, the quantitative comparison between the theoretical prediction and obtained experimental values was used by plotting the predicted versus observed value curve to validate/verify the chosen face‐centered CCD model. The predicted error is the difference between the experimental value and the predicted value divided by predicted value.

TABLE 2.7. Low and High Levels of Critical Material Attributes (CMAs) and Critical Process Parameters (CPPs, also Called as Independent Variables) Along with the Goals of Critical Quality Attributes (CQAs, also Called as Dependent Variables) Used for Making Face‐Centered Central Composite Design (CCD) Throughout the Initial Pilot Screening Study to Prepare Topical Ophthalmic Emulsions

Screened CMAs and CPPs	Quantity	Levels
Low	High
X 1: Castor oil (ml)	1, 1.5, 2	1	2
X 2: Chitosan (mg)	6, 12, 18	6	18
X 3: Poloxamer (mg)	75, 87.5, 100	75	100
CsA (% w/w)	0.05 or 0.1
Glycerin (g)	2.25
Double distilled water (ml)	Upto 100
Selected CQAs		Goal
R 1 : Mean particle size		Minimize
R 2 : Polydispersity index		Minimize
R 3 : Zeta potential		Maximize

Note: Italics numbers and texts indicate constant quantity of independent variables while the quantity of other independent variables were altered.