Statistics for Maintenance Modelling: Continuous Lifetime Distributions 2

# The Cumulative and Reliability Functions for the Normal Distribution¤

Unfortunately the cumulative density function does not have an analytical form, and so has to be approximated or solved numerically. Many statistics books have tables of this integral for the case = 0, = 1, i.e. the standard normal distribution, and (t) is defined as the resulting integral, i.e. (t) = . Hence in the general case F(t) = .

As R(t) = 1 - F(t), the reliability function has the same problem. The shape of the reliability function is:

As with the extreme value distribution, the normal distribution allows negative lifetimes. However again the probability of negative values is minimal if is taken to be large enough compared with .