156 3. COMPUTATIONAL METHODS FOR THE RELIABILITY OF A COMPONENT
P
1
A B C
P
2
Figure 3.10: A key component is under axial loadings.
erefore, the range of the reliability of the component with a 95% confidence level will be:
R D 1 F D 0:9973 ˙ 0:00008: (g)
3.9 SUMMARY
e calculation of the reliability of a component is one of the key topics for reliability-based
mechanical design since it replaces the traditional factor of safety as the measure of the design
in reliability-based mechanical design.
We must establish the limit state function of a component to calculate the reliability of the
component, which is the relationship among the reliability, component geometrical dimensions,
component strength, mechanical properties, and loading. e limit state function of a compo-
nent under static loadings will be discussed in detail in Chapter 4. e limit state function of a
component under cyclic loadings will be discussed in detail in Chapter 1 of Volume 2.
When the limit state function of a component is established, the following is the summary
of reliability calculation approaches of a component.
1. When the limit state function of a component contains only two random variables, we
can use the interference method for calculating the reliability of a component, which is
discussed in Section 3.3. We can have a theoretical, analytical result only for both nor-
mal distributions, both log-normal distributions, both exponential distributions, and both
uniform distributions.
2. When the limit state function of a component is a linear function of all statistically in-
dependently normally distributed random variables, we can use the FOSM method to
calculate the reliability, which is discussed in Section 3.5.
3. When the limit state function of a component is a nonlinear function of all statistically
independently normally distributed random variables or is a linear or nonlinear function of
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