The mean and the standard deviation of the distribution () can be easily determined considering and as two independent variables.
Figure 5.3.1 Schematic presentation of the distribution of stress on a typical structural member and variation in the material yield strength [2]
To avoid unforeseen failure as indicated above, the mechanical designs often undertake the concept of a safety factor to reduce the probability of failure and hence, increase the reliability. The safety factor may be estimated as the ratio of the mean capacity to the mean load or demand.
Thus, reliability can be defined as the probability that a system, component, or device will perform without failure for a specified period of time under a given operating conditions. If R(t) and F(t) are respectively is the reliability and the probability of failure with respect to time t, and are mutually exclusive, we can write
) can be easily determined considering 
and 
as two independent variables.
