Measuring the age to failure for any item can be represented by a distribution. You need to collect data on how many items failed and at what age they failed. With enough measurements, you can plot these on a distribution chart as follows. On the y-axis, the number of items is represented, on the x-axis the age to failure.
Increasing the number of measurements and reducing the interval (x-axis) leads to the distribution of values or the so-called probability density function (pdf). Typically, this probability density function is referenced as f(x).
The chance a value falls between 
and 
is equal to the area under the curve between and 
Every distribution has a mean, a median, and a mode. These are called central tendencies. Mean is the center of the distribution. Median is where half the measured values fall on either side. Mode is the highest point in the distribution.
-
On the above figure they all coincide.
-
Mean is also referred to as the location parameter.
Every distribution also has spread, which is the variation between the values in the distribution. This spread is called variance. Standard deviation is often used as well and is the square root of the variance. Standard deviation is also called the scale parameter.
For the normal distribution one standard deviation from the mean accounts for 68.27 percent of the distribution, two standard deviations from the mean accounts for 95.45 percent and three standard deviations account for 99.73 percent.
