**3. Results and Discussion**

In the 1st ALT, the housing of the HKS failed at 3000 cycles. Figure 9 shows the failed product from the marketplace and the 1st ALT. Upon carefully observing the failure locations from the marketplace and the first ALT, it was found that the failures were around the housing and its support in the HKS structure as a consequence of high impact stress.

Figure 10 provides a graphical presentation of the 1st ALT results and the failure data from the field shown on the Weibull plot. As the two patterns had similar slopes on the plot, each loading state of the 1st ALT and the field over the product lifetime were alike under the operational conditions of customers. Thus, it should be expected that the test samples will fail like those in the field. For the shape parameter, β, the final shape parameter from the chart was affirmed to be 2.0, compared with the estimated value—2.0. Based on both test results in the Weibull plot, the parametric ALT was effective because it identified the design flaws that were accountable for the field failures. In other words, as substantiated by two items—the visual representation in the pictures and similar slopes in the Weibull plot—these systematic methods were well-founded in identifying the problematic designs that accounted for the failures from the field. These failures decided the product (refrigerator's) lifetime.

**Figure 9.** Failed HKS from the marketplace and in the first ALT: (**a**) Failed product after first ALT; (**b**) product with crack in field.

**Figure 10.** Market data and outcomes of 1st ALT on Weibull plot.

Due to the design defect of no support in the high-stress areas, the repeated impact loading in conjunction with this structural defect may have produced fracturing of the HKS housing. This design defect can be altered by adding the support ribs, C1 (Figure 11). Stress analysis, which can be combined with fatigue analysis and parametric ALT, was carried out by using a finite element analysis (FEA). When the HKS was fixed against the wall (or surface) as the boundary conditions, the straightforward impact loads, as seen in Figure 7, were applied. Using materials and processing conditions similar to those of the finished HKS, the constitutive properties of the materials such as HIPS (HKS housing) were determined. The maximum stresses for the old and new designs were estimated separately. Based on these results, the appropriateness of the current designs for the HKS housing was evaluated. After modifying the new designs to improve the design against fatigue, the estimated stress concentrations in the HKS housing decreased from 21.2 to 15.0 MPa using the FEM analysis. It was expected that this new design should be effective in reducing fatigue failure of the HKS housing when subjected to repeated load under the consumer usage conditions.

**Figure 11.** Failed HKS housing in the first ALT: (**a**) Its root cause; (**b**) design modifications.

With the confirmed shape parameter β of 2.0, the real mission cycles computed from Equation (20) were 23,000 cycles for the six sample units. If the HKS failed at less than once for 23,000 cycles, its lifetime would be assured to be B1 life 10 years. As seen in Figure 12, in the second ALT, from the outside corner, the torsional shaft in the HKS that was made of ductile iron failed at 12,000 cycles. Such ductile cast iron accounts for a major family of metals that are extensively used for gears, automobile crankshafts, dies, and numerous machine parts because of its good machinability, fatigue strength, and high modulus of elasticity. They have a mass fraction (%) as follows: Carbon (3.0–3.7), silicon (1.2–2.3), manganese (0.25), magnesium (0.07), phosphorus (0.03) [53].

**Figure 12.** Root cause and design modification of cracked torsional shaft (cast iron) in the second ALT: (**a**) Root cause; (**b**) design modification.

When closely examining the product failure in the 2nd ALT, the torsional shaft in the HKS had insufficient strength to endure the repeated impact loading of the opening/closing of the door. When subjected to repeated impact loads, the stress amplification of mechanical components such as the torsional shaft in the HKS not only occurred at minute defects or cracks on a microscopic level of material but could also happen in stress concentrations such as in sharp corners, fillets, holes, and notches on the macroscopic range that are normally explained as stress raisers. For example, the stress concentration at the sharpedged corners depended on fillet radius [54]. To improve the design, the torsional shaft was altered by giving it more rounding from R0.5 mm to R2.0 mm, C2 (Figure 12).

For the HKS upgrade, the design basis of new samples was determined to be more than the lifetime target—B1 life 10 years. To confirm the design of the HKS, a 3rd ALT was performed. As the affirmed value, β, on the Weibull plot was 2.0, for the lifetime target—B1 life 10 years—the actual mission cycles in Equation (20) were 23,000 for the six-sample size. In the third ALT, there were no design issues in the HKS until the experiment reached 23,000 cycles. It was therefore concluded that the altered design parameters obtained from the 1st and 2nd ALTs were successful.

Table 3 provides a summary of the ALT results. With the alternative designs, the HKS was assured to have a lifetime target—B1 life 10 years. That is, we knew that the product would have 99% reliability (or 1% unreliability) for 10 years with a yearly failure rate of 0.1%.


**Table 3.** Results of ALTs.
