Drenick, in fact, proved that the ROCOF of a complex repairable system, comprising a large number of individual modules, tends to a constant value.
In modelling a varying ROCOF, therefore, any statistical technique which is based on the assumption that the data are independent and identically distributed, and thus reorders observations by magnitude, is not valid.
It is essential then, when analysing data sampled from the service life of a repairable system, to determine whether the ROCOF is approximately constant and, hence, the underlying process is stationary or, alternatively, whether the times between its successive events demonstrate any particular trend.
For this reason, any testing for trend using the above statistic should always use a cumulative failures versus cumulative time plot (in the case of many systems running simultaneously), which from this point onwards will be referred to as the ROCOF plot.
As explained in the previous section, in order to assess the validity of the IID assumption a ROCOF curve has to be drawn and the Laplace test for trend estimated.