Fractional occupation time is a quantity 
which is the
proportion of time for which the continuous stress, S(t) is
above some level, u. This is one property of experienced stress.
is the number of times S(t) crosses the stress level, u.
A crossing is the transition from a stress level less than u to
one in excess of u or vice-versa.
The properties of the local maxima of S(t) can be important. The
number of times a maximum stress is reached within a period 
, 
, together with the size of the maxima, is a useful
statistic. In particular, the distribution of the height of the
peaks, 
, is of interest.
The relationship of one peak to the next is of interest and an idea of the range of loading is fundamental to any fatigue modelling. In some circumstances, it may be possible to model the loading in the form of a wave, in which case the quantities of interest are amplitude and wavelength.
Where a process has many high frequency oscillations, but there is an overall structure to the magnitude of such oscillations, it may be possible to create an envelope, that is, a function which bounds S(t). In [14], [42], they discuss details of how to do this for a random signal. The loading can then be considered as represented by the properties of the envelope.
In the case of a complicated loading history, it is sometimes possible to approximate this by a sequence of constant amplitude loadings. Cycle counting is one way of doing this [15].
It is possible to use these statistics, that is, 
and the envelope functions, to summarise the
loading experienced by a system, and then use data from similar
loading situations to make reliability predictions. Indeed, it is
because of this that such methods are important.
While the type of loading plays a vital part in the fatigue process, this research concentrates on the study of material properties examined under laboratory conditions. In this case, the data come from sinusoidal loading with a well defined maximum, minimum and a constant controlled stress range. Time may thus be represented in terms of number of cycles, which is well defined, and is denoted N. It is clear that using N as time brings with it the implicit assumption that the frequency of stressing is unimportant, and in any case can be taken account of. In practice this is a reasonable assumption. Increasing the frequency of the stressing under laboratory conditions allows simulation of loading which would be experienced in real conditions over many years.