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Colorimetry was used to measure the color shade. The L* value is the white/black color space. The a* value is the red/green
space, and the b* value is the blue/yellow space. Target L*, a*, and b* values are listed in Table III. The total color difference (ΔE*) is calculated from the differences between L*, a*, and b* values and the target by taking
the square root of the sum of differences squared. Specifications for L*, a*, and b* values were defined based on ΔE* < 2.0.
Figure 1: Pareto chart of the standardized effects of the experimental variables on the L* value, which describes the white/black
color space, Alpha = 0.10. (ALL FIGURES ARE COURTESY OF THE AUTHORS)
All 450 samples were analyzed by regression to detect the factors that had a significant L* value. The data analysis revealed
that all six factors (i.e., level of titanium dioxide, red dye, and MCT in the coating system, and percentage of weight gain,
coating exhaust temperature, and spray rate) had significant effect on the L* value. The regression model had a R2 (adjusted) of 92.10% and a lack-of-fit p-value of 0.000. The relative effect of the variables is shown in Figure 1. The data analysis revealed that TiO2 and red dye had the most significant effect; both exhaust temperature and spray rate also had a significant effect on L*.
Figure 2: Pareto chart of the standardized effects of the experimental variables on the a* value, which describes the red/green
color space, Alpha = 0.10.
A similar regression analysis was performed to identify the factors that may have significant effect on the a* value. The
data analysis revealed that the same six factors had significant effect on the a* value. The regression model had a R2 (adjusted) of 91.57% and a lack-of-fit p-value of 0.000. The relative effect of the variables is shown in Figure 2. The data analysis revealed that the levels of TiO2 and red dye had the most significant effect; both exhaust temperature and spray rate also had significant effect on the a*
value.
Figure 3: Pareto chart of the standardized effects of the experimental variables on the b* value, which describes the blue/yellow
color space, Alpha = 0.10.
Lastly, a similar regression analysis was performed to identify the factors that may have a significant effect on the b* value.
The data analysis revealed only four factors (i.e., TiO2 and red dye levels, percentage of weight gain, and coating exhaust temperature) had significant effect on the b* value. The
regression model had a R2 (adjusted) of 86.6% and the lack-of-fit p-value of 0.000. The relative effect of the variables is shown in Figure 3. The data analysis revealed that TiO2 and red dye levels had the most significant effect; both exhaust temperature and spray rate also had a significant effect
on b* value.
Figure 4: Contour plot of calorimetry measurements (L*, a*, and b* values) in relation to red dye and titanium dioxide concentrations
in the formulation. Variables held constant were weight gain (3%), medium chain triglyceride concentration (7.0%), exhaust
temperature (40 °C), and spray rate (10 g/min).
An optimization of the factors targeted for the L*, a*, and b* value was calculated using multiregressional analysis. Optimal
material and process factors are highlighted in red in Figure 4, which shows that the colorant level had a larger effect on color shade compared with the process effects (e.g., exhaust temperature
and spray rate). For the optimized solution at 3% weight gain, the predicted L*, a*, and b* values were 75.86, 32.21, and
9.07, respectively. The predicted ΔE* was 0.0, which is a perfect match. A process specification of the TiO2 and red dye was also calculated based on the lower and upper percentage limits of both ingredients. The white area of the
plot in Figure 4 is the allowable level of the color ingredient that would meet ΔE* < 2.0. A different color specification can be determined
by using the same design space.
