MANUAL No - Forest and Wood Products Australia

Manual No. 8: Termite Attack 41
Equation Section (Next)
4.1 Introduction
4 THE PROBABILISTIC MODEL
For engineering purposes, it is useful for a termite attack to be considered to be a probabilistic
event. This report describes the development of a model to predict the risk of attack on a
house in Australia. Such a model is useful for assessing (in a quantified manner) the value of
various protection strategy proposals.
4.2 The Basic Probability Model
4.2.1 The probability Distributions
The probability density function of the time for a house to be attacked by termites is assumed
to be of the type shown in Figure 4.1. The form of this function was chosen to fit the data
found in the Termite Tally. The equation for the density function is assumed to be
p a bt
(4.1)
where a and b are the distribution parameters, and t is the time since time zero, the time at
which the house was constructed. The value of a may be either positive or negative, as shown
in Figure 4.1. The notation of ta and tmax will be used to denote the lower and upper end of the
probability density function.
For the case a 0,
and for the case a < 0,
for both cases the integration max
p dt =1 leads to
t
ta
ta = 0 (4.2a)
ta = – (a/b) (4.2b)
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