A mechanical or structural component is considered to be safe
and reliable when the strength or resistance of component exceeds the value of
load acting on it. Thus, the computation of the reliability of the component
requires the knowledge of the random nature of the strength(
) and the load(
). If the probability density functions of
and are known to be 
and 
as shown in Figure 1, then the reliability
of the component can be evaluated by constructing integral equations. If and are independent, then the
interference area shown in Figure 1, between the probability density functions
of and , gives a measure of the probability of
failure. The reliability of a component 
is given by
where 
is the joint density function of and . In certain cases, such as the cases in
which and follow normal, lognormal, exponential
distributions, the integral equation can be reduced to a simple form. However,
in a more general case, the reliability of the component can be found only by
evaluating the integrals numerically. Two methods of evaluating the reliability
of mechanical components are discussed in this chapter.
Figure 1 Graphical representation for reliability analysis