## 3 Results and Discussion
As shown in Figure 11a,b and Figure 13, failure of the dispenser system in the field and ALTs occurred in its front corner and hinge, which have a high-stress raiser. That is, the dispenser structure has no rounding at the corner and not enough thickness to withstand the repetitive impact loading that is caused by end usage. Fatigue fracture can be determined by two components: (1) the structural stress and (2) the pattern of shape (or materials) employed. Figure 12: Outcomes of fail reproduction and market failure on the Weibull plot. To endure repeated impact loads, the problematic water dispenser system utilized in the market was altered by (1) thickening the hinge rib rounding (Fillet1), C1, from 0.0 mm to 1.5 mm; (2) enlarging the front corner rounding (Fillet2), C2, from 0.0 mm to 1.5 mm; (3) thickening the hinge rib (Rib1), C3, from 1.0 mm to 1.8 mm; and (4) thickening the front side rounding (Fillet3), C4, from 0.0 mm to 8.0 mm (Table 3). Stress analysis, which may be integrated with fatigue analysis and parametric ALT, was performed by utilizing finite element analysis (FEA). As the dispenser system was attached to the upper wall, there were uncomplicated impact loads, as shown in Figure 8. Using materials and processing conditions similar to those of the dispenser, the constitutive properties of the polypropylene (dispenser lever) were determined. For the two designs, the greatest stresses were assessed. According to this investigation, the stress of the altered designs in the dispenser structure was evaluated. By modifying the current structures to im  
Figure 13: Structure of problematic lever in the field and ALTs. \begin{table}
\begin{tabular}{c c} \hline \hline C1: Fillet1 R0 \(\rightarrow\) R1.5 (first ALT) & C2: Fillet2 R0 \(\rightarrow\) R1.5 (first ALT) \\ \(\rightarrow\) R2.0 (second ALT) & C4: Fillet3 R0 \(\rightarrow\) R8.0 (first ALT) \\ C3: Rib1 T1 \(\rightarrow\) T1.8 (first ALT) & \(\rightarrow\) R11.0 (second ALT) \\ C5: Rib2 T3 \(\rightarrow\) T4 (third ALT) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary for the redesigned dispenser lever. prove the fatigue design, the approximated stress concentrations at the front corner and the shaft hinge of the dispenser lever lessened from 8.37 MPa and 5.66 MPa (Figure 14) [41,42]. In the second ALT (approximately 32,000 cycles), the fracture and cracking of the dispensing lever occurred at the front corner of the lever where there was not sufficient corner rounding (see Table 4). To identify the root cause of the unsuccessful dispenser system, the failed product was checked. There were structural design defects, namely hinge rib rounding and front side rounding. As a modification, we altered it by (1) enlarging the hinge rib rounding (Fillet 1), C1, from 1.5 mm to 2.0 mm and (2) enlarging the front side rounding (Fillet 3), C4, from 8.0 mm to 11.0 mm. While the water dispenser assembly design was improved in the second ALT, it only achieved 32,000 mission cycles. Thus, the desired life was still not achieved. The dispenser system had insufficient fatigue strength for the repeated impact stress. Therefore, a third ALT was performed. It was confirmed that the estimated value of \(\beta\) in the Weibull diagram was 3.5. In the third ALT, there were no structural flaws in the dispenser system until the ALT was performed for 68,000 cycles. At 68,000 cycles, the fracture and cracking of the dispensing lever occurred at the front of the lever, which still had insufficient strength (see Table 4). The front lever (Rib2), C5, was thickened from 3.0 mm to 4.0 mm. Over the route of ALTs with structural modifications, the water dispenser was established to have a B1 life of 10 years with a cumulative failure rate of 1%, based on Equations (41) and (42), when the actual cycles, \(h_{a}=68,000\ cycles\), by plugging in the lifetime target, \(x=0.01\), the sample size, \(n=8\), the accelerated factor, \(AF=4.0\), the shape parameter, \(\beta=3.5\), the and failure number, \(r=0.0\). Table 4 represents an abridged result of the ALTs.