# Parameter Study for Child Booster Seats in Frontal Collisions
## 5 Parameter Sensitivity Analysis  
In this section, sensitivity analysis is performed for all the layout parameters based on the parametric study in Section 4. The injury evaluation of the occupant should consider the comprehensive effects of children's multiple injury indices [30, 31]. This is addressed through the Weighted Injury Criterion (WIC) for adults by combining all these injuries [32, 33]. Equation (1) is the traditional WIC formula, where HIC is the head injury criterion, \(a_{\mathrm{C}}\) is 3 ms chest resultant acceleration (unit: g), D is the thoracic compression deformation (unit: mm), and \(F_{\mathrm{\it FL}}\) and \(F_{\mathrm{\it FR}}\) are the maximum axial force of the left and right thigh (unit: kN). However, weighting factors in Equation (1) for the occupant's head and chest are too high. \[\mathrm{WIC}=0.6\times\left(\frac{HIC}{1000}\right)+0.35\times\left(\frac{a_{ \mathrm{C}}}{60}+\frac{\mathrm{D}}{75}\right)/2+0.05\times\left(\frac{F_{ \mathrm{\it FL}}+F_{\mathrm{\it FR}}}{20}\right) \tag{1}\]  
Due to the intrinsic difference between the injury types and severity between the children and adults, a modified WIC is proposed for the child in the booster seats and the detailed form is shown in Equation (2). First, 3 ms head resultant acceleration \(a_{H}\) is utilized instead of the Head Injury Criterion HIC due to \(a_{H}\) reflecting a more severe injury in the same sled test and provides a safer injury estimation. Secondly, thoracic compression deformation is not considered due to the fact that children usually do not suffer this type  
Figure 15: A value of 3 ms head resultant acceleration \(a_{H}\) variation (**a**), 3 ms chest resultant acceleration \(a_{C}\) variation (**b**), upper neck tension \(F_{Z}\) variation (**c**), and the head horizontal displacement \(x_{H}\) variation (**d**) caused by the cushion angle adjustment. of injury due to a higher flexibility of ribs compared with adults [34]. Thirdly, the injury caused by \(F_{FL}\) and \(F_{FR}\) is not considered due to the fact that the child booster seat is installed on the back seats and this type of injury does not happen. Instead, neck injuries are an important injury feature of child dummies in booster seats and are included according to both ECE R129 regulation and C-NCAP. During the process of evaluating the seat protection performance, the head horizontal displacement \(x_{H}\) of the dummy is used as a constraint and its value should not exceed 550 mm according to the ECE R129 regulations. In the study of Section 4, the head horizontal displacement \(x_{H}\) meets the requirements. Therefore, the sensitivity analysis focuses on three other injury indices, including the 3 ms head resultant acceleration \(a_{H}\), 3 ms chest resultant acceleration \(a_{C}\) and upper neck tension \(F_{Z}\). The weighting factors are determined by the score of each injury category in the C-NCAP [35]. According to the scoring system of C-NCAP, the head score is 2 points, and the chest and neck score are 1 point each, so the weighting coefficient of modified WIC is defined proportionally to the score point by setting the summation of three weighting coefficients as unit 1. Therefore, the weighting coefficients for 3 ms head resultant acceleration \(a_{H}\), 3 ms chest resultant acceleration \(a_{C}\) and upper neck tension \(F_{Z}\) are 0.5, 0.25, 0.25, respectively. The scale factors for injury indices are the maximal values given in ECE R129 regulation and C-NCAP. For instance, 80 g and 55 g are the maximal values of the Q6 dummy injury indices in ECE R129 regulation, and 2.84 kN is chosen from C-NCAP due to the lack of specification in ECE R129 regulation. \[\text{WIC}=0.5\times\left(\frac{a_{H}}{80}\right)+0.25\times\left(\frac{a_{C} }{55}\right)+0.25\times\left(\frac{F_{Z}}{2.84}\right) \tag{2}\]  
The sensitivity of each parameter to WIC can be characterized by the WIC magnitude variation due to the variation of the independent variables [36].