Template:NormalDistribution

The Normal Distribution

The normal distribution is commonly used for general reliability analysis, times-to-failure of simple electronic and mechanical components, equipment or systems. The [math]\displaystyle{ pdf }[/math] of the normal distribution is given by:

[math]\displaystyle{ \begin{align} f(t)= \frac{1}{\sigma \sqrt{2\pi }}{e^{-\tfrac{1}{2}(\tfrac{t-\mu }{\sigma })^2}} \end{align} }[/math]

where,

[math]\displaystyle{ \begin{align} \mu = & \text{mean of the normal times to failure} \\ \sigma = & \text{standard deviation of the times to failure} \end{align} }[/math]

The normal distribution and its characteristics are presented in more detail in Chapter 9.