As in the earlier situation, note that:
Also,
that is, 
is a
deterministic function of the various parameters obtained by numerically solving the
differential equation model. The ordering of coalescence determines that crack i is
the 
crack to be born, and also which crack dies when crack i is born. The
crack only exists at times between birth and death, and we define
and
The realisation time from a homogeneous Poisson
process is gamma distributed with scale 
and shape parameter k, since it is
the sum of exponentially distributed random variables.
Let 
be the number of coalescences in interval i, where interval 1 is [20,30],
interval 2 is [30,40], interval 3 is [40,50] and interval 4 is [50,60] (where
intervals are given in thousands of cycles). Then are realisations of a Poisson
distribution with rate . That is to say the likelihood for the is:
O is an ordering of the times of birth and death for the different cracks and determines which cracks coalesce. In the context of spatial data, O would obviously depend upon some parameters representing the spatial nature of the specimen, such as local microcrack density, but this data is not available here.