Statistics for Maintenance Modelling: Basic Probability Concepts

# The Cumulative Density Function¤

Return

The cumulative density function gives the probability that a random variable X will be less than some specified value x (e.g. the probability that an item fails before time t). Mathematically it is written:

where f(t) is the probability density function at t. For the standard (mean zero and variance 1) Normal Distribution this formula can be written:

Often Tables (see for example the tables on the StatsoftInc website) are given in statistical text books giving the values of the following function:

This quantity is represented by the shaded area in the distribution shown here.