*6.2. Reliability Results*

Figures 18–21 depicts the reliability curves for steel specimens with load-induced stress values 79 MPa, 87 MPa, 96 MPa and 104 MPa, respectively. In each of these figures, the reliability of the cast parts is presented with a 0% and 5% variability in the load-induced stress. It can be observed that a 5% variability in load has not significantly affected the component's reliability. This could be due to the fact that the software derives an equivalent loading for non-constant amplitude loadings. However, the component reliability for the same targeted life decreases with increasing load induced stress. Moreover, the effect of Weibull shape parameter β is also analyzed and presented. Previously, it is reported that the coefficient of variation in hardness and strength of the specimens is very less [1], which suggests a higher value of β to be more realistic. Therefore, reliability is computed at various values of β, i.e., 3–5 and 10. The higher the value of β, the components will be more reliable for the same targeted lives as shown in Figures 18–21.

A summary of reliability computations for steel is presented in Figure 22. The plot indicates the reliability of components for the runout conditions used in fatigue life prediction, i.e., 10<sup>6</sup> cycles against the load induced stress. A region of safe loading is defined based on how many components survive at a particular load. It is noted that, independent of β, more than 86% components survive for the infinite life at a load-induced stress of 85 MPa. However, this is a conservative estimate of safe loading on component to allow for possible variations in component strength, which is represented by β in reliability calculations. From experience, it is readily accepted that apparently same components fail at different points of time during service life. Therefore, in a strength-limited design, it is appropriate to consider such variations in reliability computations. Nevertheless, if such variations are assured to be at a minimum, the use of a higher value of β is more realistic, which in this case resulted in a reliability of more than 95% at a load induced stress of 95 MPa in Figure 22. Hence, with the optimized mold design and a higher β = 10, it is reasonable to infer a safe load-induced stress up to 95 Mpa.

**Figure 18.** Reliability results with a load-induced stress of 79 MPa.

**Figure 19.** Reliability results with a load-induced stress of 87 MPa.

**Figure 20.** Reliability results with a load-induced stress of 96 MPa.

**Figure 21.** Reliability results with a load-induced stress of 104 MPa.

**Figure 22.** Summary of reliability results for cast steel.

Figure 23 shows the reliability results for time-dependent load induced stress based on Equation (6). Here, a plot of reliability of component versus the ratio of scale parameters,i.e., θS θσ in Weibull distribution is made to evaluate the results. It is evident from Figure 23 that the reliability of a component increases with increasing design factor. If the material's strength S is four times the mean load-induced stress σ, the parts result in ~90% reliability which reduces to 54.5% when S = σ. It should be noted that the results in Figure 23 are valid for βS = 2βσ which suggests that the strength is Weibull distributed and load-induced stress is Rayleigh distributed.

**Figure 23.** Reliability results for time-dependent load-induced stress.
